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Happy New Year, everyone! As 2024 draws to a close, I’ve finished another month of reading, so let’s close out my log of books read over 2024 with a short description of December’s reading. First up, I enjoyed reading the second entry in Dan Moren’s Galactic Cold War series: The Bayern Agenda. As with the previous entry, this was a fun spy...

I’ve completed the moderation of the exam for Intermediate Logic, and with that, the final administrative responsibilities for this semester are complete. Now it’s time to take a short break over Christmas and the New Year, and then to start a semester of research leave. I’m looking forward to time set aside to think, to write, and to talk to...

Abstract: What does the semantically anti-realist revisionary programme of Michael Dummett have to do with contemporary work on proof assistants? What are mathematicians doing when they encode their proofs in these proof assistants, based on constructive type theory? What does all this have to do with the(?) norms of assertion? (And are these...

My last PhD student at the University of Melbourne has completed his project, and is now Dr John Cleary. Congratulations, John! It was so much fun to help supervise your project. I’ve learned a lot about Albert Lautman, and his account of the development of mathematics and the dialectic of ideas, problems and mathematical progress.

This week, Aaron Cotnoir’s Instruments of Unity project and I are hosting a short visit from our friend (and my PhD supervisor), Professor Graham Priest. It’s always enjoyable to spend time with him, and tomorrow, we’re going to teach a the second-last lecture class for my Intermediate Logic cohort together, on the liar paradox and non-classical...

I mentioned yesterday that this month I’ve enjoyed rereading Kim Stanley Robinson’s Mars Trilogy. This time around, after completing my re-read, I’ve enjoyed listening to Marooned on Mars, a podcast devoted to Kim Stanley Robinson’s fiction. The initial conceit of the podcast was that the hosts, Matt Hauske and Hilary Strang (two humanities...

This teaching semester has been keeping me so busy that I have not kept up with my monthly reading logs. I’ve had enough time to read, but I haven’t found the time to keep you, my reader, up with what I’ve been reading. I’ll attempt to remedy this now, by giving a very brisk run-down of my reading over the last three months. This last three...

Last century, Michael Dummett argued that the principles of intuitionistic logic are semantically neutral, and that classical logic involves a distinctive commitment to realism. The ensuing debate over realism and anti-realism and intuitionistic logic has now receded from view. The situation is reversed in mathematics: constructive reasoning has...

Abstract: Suppose we have a language involving non-denoting singular terms. (The language of everyday mathematics provides one example. Terms like \(\frac{n}{m}\) and \(\lim_{x\to\infty} f(x)\) do not denote, for appropriate choices of \(m\) and of \(f\).) It is not too difficult to define inference rules for an appropriately free logic that...

Abstract: Michael Dummett, in a presentation to the Aristotelian Society 65 years ago (in 1959) inaugurated a long-running debate over semantic realism and anti-realism, and the issue of settling an appropriate logic as a necessary prolegomenon to fruitful discussion metaphysics. Dummett argued that the principles of intuitionistic logic are...

In this talk, I aim to give an account of norms governing our uses of generic judgements (like “kangaroos have long tails”, “birds lay eggs”, or “logic talks are boring”), norms governing inference, and the relationship between generics and inference. This connection goes some way to explain why generics exhibit some very strange behaviour: Why...

Abstract: When I use a calculator to tell me that 245 × 46 = 11,270, I learn something that I didn’t know before, even though calculators don’t have any beliefs or knowledge. Even small children know how to count things, and it is through our own capacity to enumerate and count things that we learn basic arithmetic. Calculators do not count...

py2010: Intermediate Logic is a University of St Andrews undergraduate subject in which we cover important results in logic to philosophy students. It’s taught by Greg Restall, together with a committed crew of postgraduate students. The subject introduces the proof theory and model theory of propositional, modal and predicate logic–in that...

Here’s August’s book haul: This month I enjoyed three novels. The most experimental of which was Olga Ravn’s The Employees: A workplace novel of the 22nd Century, which has the form of a series of witness statements from the crew of a ship, now far away from earth. The workers, both human and artificial, have been tending a number of exotic...

Abstract: There is a natural way to interpret the propositional connectives and quantifiers in terms of the three semantic values 0, i, and 1, where 0 and 1 are understood as falsity and truth, and i is understood as some intermediate value. These three-valued valuations do not, by themselves, determine a logic, because for that, you need to...

July and August have been really busy, not with teaching (it’s the summer teaching break), but with research and research supervision, a little bit of holiday travel, and various life things taking up my time and attention. I have had time to read, but not so much time to write paragraphs about each book. Instead of skipping the...

In this paper, I examine connections between the speech acts of assertion, denial, polar questions and justification requests, and the common ground. When we pay attention to the structure of norms governing polar questions, we can clarify the distinction between strong and weak denial, together with the parallel distinction between strong and...

Substructural logics are non-classical logics weaker than classical logic, notable for the absence of structural rules present in classical logic. These logics are motivated by considerations from philosophy (relevant logics), linguistics (the Lambek calculus) and computing (linear logic). In addition, techniques from substructural logics are...

Martin Hägglund’s This Life is an important treatise on metaphysics, philosophical anthropology, and political philosophy. It is also a critique of religious orientations to the world. In this paper, I reflect on Hägglund’s account of value and our finitude, and on his criticism of Martin Luther King, Jr’s political theology. According to...

June was also an enjoyable month for reading. This month’s reading was dominated by Diarmaid MacCulloch’s 864 page doorstopper Reformation: Europe’s House Divided. Having been educated in Australia, the view of history I was taught was oriented around the colonisation of the continent by the British and its aftermath. As far as the religious...

Abstract: In this informal talk, I will revisit some longstanding issues in philosophical logic in the light of some contemporary developments. The longstanding issues? (1) Michael Dummett’s challenge in The Logical Basis of Metaphysics to the effect that to get anywhere in fundamental issues of metaphysics we would do well to attend to the...

Abstract: In this 5 minute lightning talk, I will introduce the difference between strong and weak denial, and use it to clarify the claims I made in “Multiple Conclusions” about the connection between assertion, denial and logical consequence. The talk is a presentation at the 2024 Arché Day. The handout for the talk is available here.

May was a great reading month, but I forgot to upload my notes until June was nearly done. This month I read nine books, but one was an unpublished draft of a novel that a friend is writing, so I won’t say more about that, until there is more news to share. The other fiction reads this month could not be more different from each other. Beyond...

This is an intensive class on logical and philosophical issues in proof theory, taught at nls2024 as part of the Reykjavik Summer of Cool Logic 2024. In this course, I’ll introduce natural deduction and sequent calculus for classical, constructive and substructural logics, motivating and explaining how key results (normalisation for natural...

Earlier this month I got a lovely package in the mail. A Chinese translation of my intro logic text. My colleague and friend Min Xu completed his translation of my text, and it’s now available. The beginning of Chapter 5.

Another month, and another pile of books I’ve managed to read. This month’s reading started on the Isle of Iona, where we had a short Easter break. On the last day on the island, and then on the ferry journeys back to the “mainland”, I finished The Life of St Columba, who served as the Abbot of Iona and, as legend has it, brought Christianity to...

Abstract: Since the 1990s, we have seen how to understand a very wide range of logical systems (classical logic, intuitionistic logic, dual intuitionistic logic, relevant logics, linear logic, the Lambek calculus, affine logic, orthologic and more) by way of the distinction between operational and structural rules. We can have one set of rules...

This is a translation into Chinese of my introductory textbook Logic. It is available from Huazhong University of Science & Technology Press.

Abstract: Since the 1990s, we have seen how to understand a very wide range of logical systems (classical logic, intuitionistic logic, dual intuitionistic logic, relevant logics, linear logic, the Lambek calculus, affine logic, orthologic, ST, TS and more) as consisting of a single broad family of connectives which are set in different structural...

I’ve just emerged from two intense days of proof theory. Three of my graduate students, Sophie Nagler, Viviane Fairbank and Francisca Silva, organised a two-day workshop on proof theory and its connections to philosophy and other fields. Some of the workshop participants at the end of a busy day of proof theory.

Abstract: Since the 1990s, we have seen how to understand a very wide range of logical systems (classical logic, intuitionistic logic, dual intuitionistic logic, relevant logics, linear logic, the Lambek calculus, affine logic, orthologic, ST, TS and more) as consisting of a single broad family of connectives which are set in different structural...

This paper is a series of reflections on Ross Brady’s favourite substructural logic, the logic MC of meaning containment. In the first section, I describe some of the distinctive features of MC, including depth relevance, and its principled rejection of some con- cepts that have been found useful in many substructural logics, namely intensional...

Lately, I’ve been keeping track of my book reading, and to help focus my reflection (and as an aid to my own memory), I have taken to writing a few lines for each book I complete. March was a particularly good book-reading month, and since I’ve not posted anything on this website for more than year, I thought I’d share last month’s reading notes....

In this paper, I show how to incorporate insights from the model-theoretic semantics for negation (insights due the late J. Michael Dunn, among others, in his paper “Star and Perp: Two Treatments of Negation”), into a proof-first understanding of the semantics of negation. I then discuss the how a logical pluralist may understand the underlying...

py4612: Advanced Logic applies the tools of formal logic to make logic itself the object of study. We will explore the power and limits of logical tools and techniques. The main goals of the module will be to come to grips with some standard ‘metatheoretical’ results about logic: (1) the Soundness and Completeness Theorems, which together show...

We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalization of Routley–Meyer ternary frames and a simplification of them. The key innovation of this semantics is the use of a single accessibility relation to relate collections of points to points. Different logics...

In this essay, I examine the significance of the semantic, set-theoretic and sorites paradoxes for a number of different philosophical issues concerning logic, including the choice of a logical system, the epistemology of logic, and the boundary–if there is one–between logical and non-logical concepts. Along the way, I consider the difference...

Abstract: Martin Hägglund’s This Life: Secular Faith and Spiritual Freedom (Knopf, 2019) is an important and insightful treatise on metaphysics, philosophical anthropology, and political economy. It is also a trenchant critique of a religious orientation to the world. In this paper I will reflect on Hägglund’s account of value and our finitude,...

Abstract: In this talk, I will explain how two different kinds of semantics for negation can be used to help us understand some puzzles in the psychology of reasoning. I introduce the “Australian Plan” semantics for negation, which generalises the semantics of negation as found in “worlds” semantics for intuitionistic logic, relevant logics and...

This is short review of Jc Beall’s The Contradictory Christ, OUP, 2021.

This is an interview with me, conducted by Daniel Nellor, for the volume What are They Thinking? Conversations with Australian Philosophers. The topics range from the scope of philosophy, the place of logic in philosophy, logical pluralism, and more.

Abstract: There is a very natural way to interpret the propositional connectives and quantifiers, relative to the algebra of three semantic values, {0, i, 1} where 0 and 1 are understood as the traditional values of falsity and truth, and the third value is some intermediate value. The evaluation clauses do not, by themselves, determine the...

Natural deduction with alternatives extends Gentzen–Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives. It is a mildly bilateralist, single-conclusion natural deduction proof system in which the connective rules are unmodified from the usual Prawitz introduction and elimination...

Abstract: In this talk, I illustrate some of the key ideas of the distinctively Grammatical Thomist kind of apophaticism developed by Simon Hewitt, in his book Negative Theology and Philosophical Analysis: Only the Splendour of Light. In particular, I explore the kind of semantic anti-realism at the heart of the work, contrasting and...

Abstract: In this talk, I show how to incorporate insights from the model-theoretic semantics for negation (insights due to J. Michael Dunn, in his paper “Star and Perp: Two Treatments of Negation”), into a proof-first understanding of the semantics of negation. I then discuss how a logical pluralist may understand the underlying accounts of...

A few months ago, Anna Day, Eloise Hickey, Mark Rothery, and James Cafferky from the Undergraduate Philosophy Journal of Australasia gave me an opportunity to ramble on about my early days as a mathematics and philosophy student in the 1980s and 1990s, my current research interests, and what I’m thinking about now. They asked thoughtful questions...

In my PY1012 Reasoning lecture this evening, I used a slide with a photo of Sally Haslanger and a short section from her book Resisting Reality to give an example of an argument to a universal generalisation. (I’ve been teaching reasoning using examples from throughout the philosophical canon.) After class a young student came up to me, all...

py4601: Paradoxes is an honours Philosophy module at the University of St Andrews. It’s coordinated by my colleague, Patrick Greenough, and I’m teaching a small slice at the end on the liar paradox. If you’d like to see what I am covering, you can see some slides and notes here. Here’s what we’re covering in the whole module: A paradox is a...

py1012: Reasoning introduces the essential concepts and techniques of critical reasoning, formal propositional logic, and basic predicate logic. Among the central questions are these: what distinguishes an argument from a mere rhetorical ploy? What makes an argument a good one? How can we formally prove that a conclusion follows from some...

I grew up in Australia: my university training and my initial academic positions took place in the explicitly secular institution of the Australian university. So, it’s an uncanny experience to arrive in St Andrews to become a part of a university in a town marked by martyrdom, in which the Chaplaincy plays a central and visible role. University...

I normally don’t speak from notes, but I do know that if I get up in front of a group to speak, my natural duration is the lecture, and at 45 to 50 minutes, that just won’t do for a sermon at chapel. To prevent an over-long talk, I took the time to write things down, and edit it to an appropriate length. Now that I have it, I may as well share...

According to the AMS’s handy Mathematics Collaboration Distance calculator, my Erdős number is down to three, given the following path: Vedran Čačić, Pavel Pudlák, Greg Restall, Alasdair Urquhart, Albert Visser, “Decorated linear order types and the theory of concatenation,” Logic Colloquium 2007, p. 1–13, ed. F. Delon, U. Kohlenbach, P. Maddy...

As my colleague and PY1012 Reasoning co-lecturer, Franz Berto knows, it’s never too early to introduce your students to wombats, or to the difference between a conditional and an inference. A slide from my first week’s PY1012 lecture. Yes, next semester’s classes are just about to start, and I’m in the depths of preparation.

Today MIT Press releases our book, Logical Methods into the big wide world. It was an absolute delight to work on this long-term project with my co-author and friend, Shawn Standefer. A Stack of Copies of Logical Methods

As the cover blurb says Logical Methods is an accessible introduction to philosophical logic, suitable for undergraduate courses and above. Rigorous yet accessible, Logical Methods introduces logical tools used in philosophy—including proofs, models, modal logics, meta-theory, two-dimensional logics, and quantification—for philosophy students at...

2022 has been another big year, not that you’d know it from looking around the news section of this website. Settling in to St Andrews has taken up a lot of my energy (in a good way), and I’ve been having too much fun writing things and giving talks to spend time updating this website. With the break between Christmas and New Year, I finally had...

In The Contradictory Christ, Jc Beall argues that paraconsistent logic provides a way to show how the central claims of Christology can all be true, despite their paradoxical appearances. For Beall, claims such as “Christ is peccable” and “Christ is impeccable” are both true, with no change of subject matter or ambiguity of meaning of any term...

Abstract: In this talk, I will introduce natural deduction with alternatives, explaining how this framework provides a simple, well-behaved, single conclusion natural deduction system for a range of logical systems, including classical logic, (classical) linear logic, relevant logic and affine logic, in addition to the familar intuitionistic...

Abstract: In this talk, I give a breezy introduction to Collection Frames (joint work with Shawn Standefer), with an emphasis on how they are technically equivalent to, but conceptually simpler than Routley–Meyer ternary relational frames. The talk is an online presentation at the New Directions in Relevant Logic Online Workshop. The slides for...

py4638: Philosophy of Religion aims to provide a philosophical understanding of the phenomenon of religion and its relation to other central human activities, studying such topics as religious and cultural diversity, religious experience, belief and justification, faith and reason, religious language, religion and metaphysics, or religion and...

py3100: Reading Philosophy 1–Texts in Language, Logic, Mind, Epistemology, Metaphysics and Science is designed to develop the philosophical skills students have acquired over the first two years of their philosophy study, and acquaint them with key works in core areas of philosophy. The module involves close study of philosophical texts –...

Abstract: We know a great many technical results concerning the relationship between classical logic and intuitionistic logic, whether in the propositional, first-order or higher-order languages. We also know quite a lot about the relationship between intuitionistic and classical theories. In this talk, I will explore some of what these results...

Abstract: This talk is a free-wheeling introduction to my research, starting from work in substructural logics and logical pluralism, and ending at the many uses of proofs, including giving an account of how our modal vocabulary has the meaning that it does, and the connections between proof norms and the semantics and pragmatics of dialogue. The...

Abstract: In this talk, I introduce the difference between paraconsistency (adopting a logic for which a contradiction need not entail everything) and dialetheism (the notion that there are true contradictions), and I explain some reasons why one might take there to be true contradictions. I focus on Jc Beall’s recent work on contradictory...

Late last month, my little manuscript on Proofs and Models in Philosophical Logic was published by Cambridge University Press. This, like all entries in the new Cambridge Elements series, is a tiny little manscript, with an aim to give students, and researchers in allied fields, a quick, accessible introduction to a research topic and current...

This is a short book, in the Cambridge Elements series in Philosophical Logic. This is a general introduction to recent work in proof theory and model theory of non-classical logics, with a focus on the application of non-classical logic to the semantic paradoxes and (to a lesser extent), the sorites paradox. After a short introduction motivating...

Abstract: In this talk, I examine some of the interconnections between speech acts, such as assertion and denial, inference, justification requests, and the common ground. When we pay attention to the structure of norms governing polar (yes/no) questions, we can clarify the distinction between strong and weak denials, together with the parallel...

py4638: Philosophical Logic focuses on some of the main philosophical questions that have been raised concerning the central notions of logic. We’ll be examining contemporary debates on notions such as logical consequence, the normative status of logic, its epistemology, the meaning of the logical constants, logical pluralism, and higher-order...

Abstract: In this talk, I show how to incorporate insights from the model-theoretic semantics for negation (insights due the late J. Michael Dunn, among others), into a properly proof-theoretic understanding of the semantics of negation. I then discuss the different ways a logical pluralist may understand the underlying accounts of proofs and...

Abstract: In this talk, I examine some of the interconnections between norms governing assertion, denial, questions and answers, and the common ground of a discourse. When we pay attention to the structure of norms governing polar (yes/no) questions, we can clarify the distinction between strong and weak denials, together with the parallel...

Abstract: In this talk, I reflect on the role of worlds–possible worlds and impossible worlds—both in the semantics of various kinds of languages and logics, and in broader issues in metaphysics. I will argue that, given very modest assumptions concerning the role of worlds in semantics, that any defender of possible worlds in such a role should...

Abstract: It is straightforward to treat the identity predicate in models for first order predicate logic. Truth conditions for identity formulas are given by a natural clause: a formula s = t is true (or satisfied by a variable assignment) in a model if and only if the denotations of the terms s and t (perhaps relative to the given variable...

As June 2021 turns to a close, this is my last official day at The University of Melbourne. I’ve taught my last classes, the marking for the semester is all done, I’ve wound up all my committee work, I’ve supervised my last undergraduate theses, and wrapped up all the end-of-semester administration. I’m now packing up my office (which I’ve rarely...

This is my next book-length writing project. I am writing a book which aims to do these things: Be a useable introduction to philosophical logic, accessible to someone who's done only an introductory course in logic, covering at least some model theory and proof theory of propositional logic, and maybe a little bit of predicate logic. Be a...

Alasdair Urquhart’s work on models for relevant logics is distinctive in a number of different ways. One key theme, present in both his undecidability proof for the relevant logic R, and his proof of the failure of interpolation in R, is the use of techniques from geometry. In this paper, inspired by Urquhart’s work, I explore ways to generate...

My usual talk (a close-up view of the Old Quad and Arts West at the University of Melbourne). Abstract: In this talk, I will place contemporary research in philosophical logic in a wider historical and philosophical context, showing how recent work in logic connects to the rivalry between Platonism and Nominalism, or realism and anti-realism in...

Abstract: It is straightforward to treat the identity predicate in models for first order predicate logic. Truth conditions for identity formulas are straightforward. On the other hand, finding appropriate rules for identity in a sequent system or in natural deduction leaves many questions open. Identity could be treated with introduction and...

UNIB10002: Logic, Language and Information is a University of Melbourne undergraduate breadth subject, introducing logic and its applications to students from a wide range of disciplines in the Arts, Sciences and Engineering. I coordinate this subject with my colleague Dr. Jen Davoren, with help from Prof. Lesley Stirling (Linguistics), Dr. Peter...

PHIL30043: The Power and Limits of Logic is a University of Melbourne undergraduate subject. It covers the metatheory of classical first order predicate logic, beginning at the Soundness and Completeness Theorems (proved not once but twice, first for a tableaux proof system for predicate logic, then a Hilbert proof system), through the Deduction...

Abstract: In this talk I will show how defining rules in a hypersequent setting can give a uniform proof-theoretic semantics of identity and modality, allowing – equally naturally – for (1) modal operators for which identity statements are necessary (if true), and (2) modal operators for which identity statements can be contingently true. The...

Abstract: In this talk, I will introduce natural deduction with alternatives, explaining how this framework can provide a simple well-behaved single conclusion natural deduction system for a range of logical systems, including classical logic, (classical) linear logic, relevant logic and affine logic, by varying the policy for managing...

It is tempting to take the logical connectives, such as conjunction, disjunction, negation and the material conditional to be defined by the basic inference rules in which they feature. Systems of “natural deduction” provide the basic framework for studying these inference rules. In natural deduction proof systems, well-behaved rules for the...

As I write this, the first week of the second semester of 2020 is nearing its end, and I’ve taught my first two seminars in Logical Methods, my main undergraduate teaching responsibility for this semester. Melbourne has just entered Stage 4 of its lockdown, as we attempt to deal with the ongoing community transmission of COVID-19. The streets are...

PHIL20030: Logical Methods is a University of Melbourne undergraduate subject introducing logic to philosophy students. It’s taught by Greg Restall. The subject introduces the proof theory and model theory of propositional, modal and predicate logic–in that order. I’m using an introductory text Logical Methods, written with my colleague Shawn...

I’ve been up to a few things during the pandemic. Quite a few things, it seems. Here are links to some of the traces you can find elsewhere on the internet. I wouldn’t say that I’ve become good at using Zoom, but I have been doing a heck of a lot of it. My three subjects for this semester moved online, and running seminars, workshops, classes...

In our response Field’s “Properties, Propositions and Conditionals”, we explore the methodology of Field’s program. We begin by contrasting it with a proof-theoretic approach and then commenting on some of the particular choices made in the development of Field’s theory. Then, we look at issues of property identity in connection with different...

PHIL40013: Uncertainty, Vagueness and Paradox is a University of Melbourne honours seminar subject for fourth-year students. Our aim in the Honours program is to introduce students to current work in research in Philosophy. In 2015, I will cover some topic introducing logic and its applications to issues in metaphysics, epistemology or philosophy...

Abstract: Logic has been an important part of philosophy in the western tradition since the work of Aristotle in the 4th Century BCE. Developments of the 19th and the 20th Century have seen an incredible flowering of mathematical techniques in logic, and the discipline transformed beyond recognition into something that can seem forbiddingly...

In models for paraconsistent logics, the semantic values of sentences and their negations are less tightly connected than in classical logic. In “American Plan” logics for negation, truth and falsity are, to some degree, independent. The truth of \({\mathord\sim}p\) is given by the falsity of \(p\), and the falsity of \({\mathord\sim}p\) is given...

Abstract: Over the last century or so, the discipline of logic has grown and transformed into a powerful set of tools and techniques that find their use in fields as far apart as philosophy, mathematics, computer science, electrical engineering and linguistics. Is there anything distinctive about logic and its results, or is it just another kind...

We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompat_ibility_ is modal, negation is...

It’s been a big year. At the start of 2019, Shawn Standefer and I decided to throw all our cards in the air and upend the curriculum for the Level 2 logic unit in the philosophy program here at Melbourne. We wrote 200 pages of a draft textbook (while I really should have been finishing my other book). Shawn designed and implemented a whole raft...

Abstract: In this talk I present a new frame semantics for positive substructural and relevant propositional logics. This frame semantics is both a generalisation of Routley–Meyer ternary frames and a simplification of them. The key innovation is the use of a single accessibility relation to relate collections of points to points. Different...

PHIL20030: Meaning, Possibility and Paradox is a University of Melbourne undergraduate subject. The idea that the meaning of a sentence depends on the meanings of its parts is fundamental to the way we understand logic, language and the mind. In this subject, we looked at the different ways that this idea has been applied in logic throughout the...

Abstract: In this talk, I show how a category of classical proofs can give rise to three different hyperintensional notions of sameness of content. One of these notions is very fine-grained, going so far as to distinguish \(p\) and \(p\land p\), while identifying other distinct pairs of formulas, such as \(p\land q\) and \(q\land p\); \(p\) and...

In this paper, I motivate a cut free sequent calculus for classical logic with first order quantification, allowing for singular terms free of existential import. Along the way, I motivate a criterion for rules designed to answer Prior’s question about what distinguishes rules for logical concepts, like ‘conjunction’ from apparently similar rules...

Abstract: In this talk, I motivate and define a cut free sequent calculus for first order modal predicate logics, allowing for singular terms free of existential import. I show that the cut rule is admissible in the cut-free calculus, and explore the relationship between contingent ‘world-bound’ quantifiers and possibilist ‘world-undbound’...

This summer break, I set aside some time to turn off my devices, unplug from the internet, and read some honest-to-goodness books. Some I received from friends and family as Christmas or Birthday gifts (thanks, Sharon, Zac, Neil!), and some I had accumulated on my “to-read” pile waiting for just the right time. Here are some short reviews of my...

Abstract: In this talk, I provide two different models for a theory of grounds meeting the following desiderata:\(\def\yright{\succ}\) Grammar: There are objects, which we call grounds, which can be grounds for propositions or grounds against propositions. Derivation: A derivation of a sequent \(X\yright A,Y\) gives us a systematic way to...

Abstract: Our thoughts and our conversations are filled with generalisations. From everyday trivialities such as birds fly or trams are crowded to contested claims such as women are oppressed or Muslims are peace-loving, we think and communicate using generalisations and stereotypes. This way of understanding the world is useful and pervasive,...

Last Wednesday, I went down to the studios at ABC Southbank, to be interviewed by Libbi Gorr for ABC Radio Melbourne’s Sunday program. As I made my way through the building, and settled into the little studio, I thought I heard a familiar voice, faintly in the distance. Libbi explained that this was Kevin Rudd (the former Prime Minister), who was...

If you’ve been following my travels, you’ll get some sense that this has been a busy year. I’ve done lots of writing on my book, and I’ve managed to give lots of talks, both in the US and in Argentina, as well as at home. I haven’t posted here for nearly a year–writing elsewhere has been a higher priority. However, this weekend, I’ve made a few...

Abstract: In this talk, I aim to give an account of norms governing our uses of generic judgements (like “kangaroos have long tails”, “birds lay eggs”, or “logic talks are boring”), norms governing inference, and the relationship between generics and inference. This connection goes some way to explain why generics exhibit some very strange...

Abstract: In this talk, I will present an account of defining rules, with the aim of explaining these rules they play a central role in analytic proofs. Along the way, I’ll explain how Kreisel’s squeezing argument helps us understand the connection between an informal notion of validity and the notions formalised in our accounts of proofs and...

Abstract: I introduce the key themes from my book-in-progress, Proof Theory, Rules and Meaning. This is a talk for the symposium on the manuscript held at the Argentinean Society of Philosophical Analysis (SADAF) in Buenos Aires, in July 2018. The slides for the talk are available here.

Abstract: In this short talk, I present a new account of the nature of proof, with the aim of explaining how proof could actually play the role in reasoning that it does, and answering some long-standing puzzles about the nature of proof. Along the way, I’ll explain how Kreisel’s Squeezing argument helps us understand the connection between an...

Stephen Read’s work on Bradwardine’s theory of truth is some of the most exciting work on truth and insolubilia in recent years. Read brings together modern tools of formal logic and Bradwardine’s theory of signification to show that medieval distinctions can give great insight into the behaviour of semantic concepts such as truth. In a number of...

Abstract: In this talk, I show how a category of propositions and classical proofs can give rise to three different hyperintensional notions of sameness of content. One of these notions is very fine-grained, going so far as to distinguish \(p\) and \(p\land p\), while identifying other distinct pairs of formulas, such as \(p\land q\) and \(q\land...

I love the way I’ve met so many different people through working in logic, that I’ve made good friends, good colleagues, good teachers and mentors. I’ve been part of an enterprise that’s larger than any one person. I have been shaped by that community, and have had the opportunity to made some small mark on it myself. Logic, like any other...

Abstract: This talk is a comparison of how different approaches to hyperintensionality, aboutness and subject matter treat (classically) logically equivalent statements. I compare and contrast two different notions of subject matter that might be thought to be representational or truth first – Aboutness (Princeton University Press, 2014), and...

Working in philosophical logic, I love the opportunity to learn from so many people through history, and not only to learn, but to pass on a tradition, and to have the opportunity to extend the tradition, and to refine it a little, in passing it on. It’s been a delight to learn from some great figures, the historical figures through their...

In the previous entry I explored the connection between proofs and necessity. Here, I want to spend a little time exploring the other side of the logical street, the connection between models and possibility. As I have already explained, one core insight from 20th Century work in logic is the fundamental duality between proof theory and model...

The next two thoughts are motivated by the two complementary aspects of contemporary research in logic, proof theory and model theory. As I try to emphasise to my students, there are two broad ways you can define logical concepts like validity. Following the way of proofs, an argument is valid if there is some proof leading from the premises to...

I’m not totally happy with the word for the next item on the list of twelve things I love about philosophical logic. The word on the list is attention, and it gets at something that I have learned, and which seems to me to be an important distinctive about working in philosophical logic, but I’m not altogether sure that “attention” is the best...

Some of my phrasing in the last two posts about what I love about philosophical logic have emphasised capacities, or abilities. I’ve described the pleasure of the “aha!” moment in terms of the kinds of mastery you acquire in handling the concepts you have, and I described the joys of conceptual expansion in terms of abilities gained. This is to...

There are different delights to be found in working with concepts. It is not all a matter of gaining greater mastery of the concepts you have already acquired. There is also a special delight to be found in acquiring new concepts. I love that feeling of progress when you make a conceptual advance. A common way to do this is to disambiguate, to...

Here is a more personal reflection on what I love in working in philosophical logic. I love the “aha!” moment of recognition. This is the relief of a proof completed, or a counterexample found. It is the delight of gaining clarity into something that you had only dimly understood, or the dawning realisation that an assumption you had made is in...

The multiple realisations of a concept in logic often come from different disciplines. One thing I’ve grown to love in philosophical logic is the way different ideas, disciplines and traditions are connected in the space of the wider generality of formal logic. In my own work over the years in substructural logic, logical pluralism and proof...

Closely connected to the notion of abstraction, I love the way that logical concepts are multiply realisable. An abstract structure can be instantiated in different ways, and often in ways completely unforeseen when the original abstraction was made. The twin moves of abstraction (moving from the particular to the general) and concretisation...

As I mentioned in the previous entry, philosophical logic uses the tools and techniques from formal logic, and formal logic is nothing if it is not abstract. It gets its power — as well as its weaknesses, to be sure — by abstracting away from specifics and moving to generalities. We explain the virtues of a particular argument (in part) by...

One thing I noticed when making my way from mathematics (my undergraduate degree was a B.Sc. in Mathematics at the University of Queensland) to philosophy was the different approach when doing research in the two disciplines. To put it very coarsely, in mathematics, you prove theorems. In philosophy, you argue about things. The standards for...

Over this last weekend, I spent some time tidying out one of the electronic “junk drawers” of my writing life, a folder full of thousands upon thousands of little scraps of text, ranging from minutes of meetings, recipes I’ve saved, little ideas I came across which I wanted to save, lists of places to visit when travelling, and many other kinds...

Over the last couple of days on Twitter, I was involved in a thread, kicked off by Dan Piponi, discussing closed set logic—the natural dual of intuitionistic logic in which the law of the excluded middle holds but the law of non-contradiction fails, and which has models in the closed sets of any topological space, as opposed to the open sets,...

In a few recent papers and talks, I’ve been using flow graphs to display the flow of information in proofs. These are the kinds of things that are easy to draw, but they’re not so straightforward to typeset.

Abstract: I show that the cut-free proof terms defined in my paper “Proof Terms for Classical Derivations” form a well-behaved category. I show that the category is not Cartesian—and that we’d be wrong to expect it to be. (It has no products or coproducts, nor any initial or final objects. Nonetheless, it is quite well behaved.) I show that the...

Abstract: I show that the cut-free proof terms defined in my paper “Proof Terms for Classical Derivations” form a well-behaved category. The talk is intended to be accessible enough for those who don’t know any category theory to follow along. I show that the category is not Cartesian – and that we’d be wrong to expect to be. It has no products...

Abstract: This talk is a comparison of how different approaches to hyperintensionality, aboutness and subject matter treat (classically) logically equivalent statements. I compare and contrast two different notions of subject matter that might be thought to be representational or truth first – Aboutness (Princeton University Press, 2014), and...

I give an account of proof terms for derivations in a sequent calculus for classical propositional logic. The term for a derivation \(\delta\) of a sequent \(\Sigma \succ\Delta\) encodes how the premises \(\Sigma\) and conclusions \(\Delta\) are related in \(\delta\). This encoding is many–to–one in the sense that different derivations can have...

Abstract: I attempt to give a pluralist and syntax-independent account of classical and constructive proof, grounded in univocal rules for evaluating assertions and denials for judgments featuring the logical connectives, interpretable as governing warrants for and against claims, and which results in an interpretation of classical and...

There is a vibrant (but minority) community among philosophical logicians seeking to resolve the paradoxes of classes, properties and truth by way of adopting some non-classical logic in which trivialising paradoxical arguments are not valid. There is also a long tradition in theoretical computer science–going back to Dana Scott’s fixed point...

Talking to Jc Beall during his recent visit to Australia, I got thinking about first degree entailment again. Here is a puzzle, which I learned from Terence Parsons in his “True Contradictions”. First Degree Entailment (fde) is a logic which allows for truth value gaps as well as truth value gluts. If you are agnostic between assigning...

While I was busy writing my most recent paper, “Proof Terms for Classical Derivations”, I heard that Raymond Smullyan had died at the age of 97. I posted a tweet with a photo of a page from the draft of the paper I was writing at the time, expressing loss at hearing of his death and gratitude for his life. There are many reasons to love Professor...

It’s a new year, and it’s time for a new paper, so here is “Proof Terms for Classical Derivations” I’ve been working on these ideas for about a year, from some rough talks over most of 2016, to many conversations with my colleague Shawn as I attempted to iron out the details, to many more hours in front of whiteboards, I’ve finally got something...

This is a talk on proof theory for Melbourne Logic Day. Abstract: In this talk, I will explain how proof terms for derivations in classical propositional logic are invariants for derivations under a natural class of permutations of rules. The result is two independent characterisations of one underlying notion of proof identity. The slides are...

I’ve been interested in Robert Brandom’s inferentialism since I picked up a copy of Making it Explicit back in 1996. One interesting component of Brandom’s inferentialism is his account of what it is to be a singular term. There are a number of ways to understand inferentialism, but the important point here is the centrality of material inference...

I’m giving a talk entitled “Existence, Definedness and the Semantics of Possibility and Necessity” at a Workshop on the Philosophy of Timothy Williamson at the Asian Workshop in Philosophical Logic and the Taiwan Philosophical Logic Colloquium at the National Taiwan University. Abstract: In this talk, I will address just some of Professor...

In this paper, I will address just some of Professor Williamson’s treatment of necessitism in his Modal Logic as Metaphysics. I will give an account of what space might remain for a principled and logically disciplined contingentism. I agree with Williamson that those interested in the metaphysics of modality would do well to take quantified...

Today, between marking assignments and working through a paper on proof theory for counterfactuals, I’ve been playing around with proof terms. They’re a bucketload of fun. The derivation below generates a proof term for the sequent \(\forall xyz(Rxy\land Ryz\supset Rxz),\forall xy(Rxy\supset Ryx),\forall x\exists y Rxy \succ \forall x Rxx\). The...

I’m giving a talk entitled “Proofs and what they’re good for” at the University of Melbourne Philosophy Seminar on Thursday, August 25, 2016. Abstract: I present a new account of the nature of proof, with the aim of explaining how proof could actually play the role in reasoning that it does, and answering some long-standing puzzles about the...

I was originally scheduled to give a talk entitled “What Proofs are About” at the About Aboutness Workshop at the University of Melbourne on Saturday, July 16, 2016, but my plane back to Melbourne was delayed and I didn’t get to present the paper then. So, I’m presenting it at the Melbourne Logic Seminar instead. Abstract: This talk is a...

This is an intensive class on logical and philosophical issues in proof theory, taught by Shawn Standefer and me at nasslli 2016. We cover cut elimination, some substructural logics, and hypersequents, with a bit of inferentialism and bilateralism mixed in. Here are the slides for each day of the course. Day 1: Foundations. An introduction to the...

I’m giving a talk entitled “Terms for Classical Sequents: Proof Invariants and Strong Normalisation” at the Melbourne Logic Seminar. Abstract: A proof for a sequent \(\Sigma\vdash\Delta\) shows you how to get from the premises \(\Sigma\) to the conclusion \(\Delta\). It seems very plausible that some valid sequents have different proofs. It also...

For the first time in my home owning career, the picket fence outside my home sports a how-to-vote sign. This is a change for me. I’m a member of no political party, and I’ve never encouraged my neighbours to vote in any particular way. For almost all of my life, I’ve lived in safe Labor seats, from growing up in working class Brisbane to living...

A few weeks ago, Richard Marshall interviewed me for 3am Magazine’s series of interviews with philosophers. If you’re interested in my work on logical pluralism, proof theory and things like that, this interview might be a good place to start. I hope you like it. If you’ve got any questions, please let me know.

What could you mean by the term “proof-theoretic semantics” (PTS)? At first glance, it could mean either the semantics of proof theory, or perhaps it’s more likely to mean semantics conducted using the tools of proof theory. And that’s the enterprise that the fifteen authors intend to advance in the sixteen papers in this edited collection…

Prompted by a colleague and friend (thanks Ruth!), I’ve been asking students who took my upper level logic subjects last year what they learned about how to learn logic. This is helpful for me—I get a better understanding of how students are learning. It’s hopefully helpful for them, too, to reflect more explicitly on how they learn. But most of...

Graham Priest defends the use of a nonmonotonic logic, LPm, in his analysis of reasoning in the face of true contradictions, such as those arising from the paradoxes of self-reference. In the course of defending the choice of this logic in the face of the criticism that LPm is not truth preserving, Priest argued that requirement is too much to...

This morning I received an email from Rachael Briggs, asking me some questions about the notion of compatibility as it appears in my paper “Negation in Relevant Logics.” These questions got me to thinking that there were some ideas in that paper and a much-less-read paper of mine “Modelling Truthmaking”, which might be worth reflecting on some...

I’ve been away from home in Auckland at a conference over the last couple of days, so I’m a bit behind on the news, but tonight I’ve finally found a few moments to write something in honour of my friend and mentor, Bruce French, who was—three days ago—named an Officer of the Order of Australia in the 2016 Australia Day Honour’s list. Bruce was...

Thanks to a recent visit from Jc Beall, I was reminded of a critical discussion between Jc and our colleague and friend Graham Priest in the pages of Analysis. Jc was puzzled by a claim that Graham made in his reply to Jc’s paper, concerning nonmonotonic consequence relations and failures of truth preservation. Here, I’ll explain the disagreement...

I am giving a talk, entitled “Generality and Existence 3: Substitution and Identity” in the Melbourne Logic Workshop 2015 at the Melbourne Logic Group. Abstract: In this talk, extend a sequent proof system for free logic to include an identity predicate. Or rather, two different candidate identity predicates allowing for the substitution of a...

I’m giving a talk, entitled “Generality and Existence 4: Identity and Modality” in the HPLM Seminar at the University of St Andrews. Abstract: In this talk, extend the proof system for quantified modal logic, with both subjunctive (metaphyisical) and indicative (epistemic) modalities, to include an identity predicate. Or rather, a range of...

I’m giving a talk, entitled “Generality and Existence 1: Quantification and Free Logic” at a Workshop on Inferentialism, hosted by Arché at the University of St Andrews. Abstract: In this presentation, I motivate a cut free sequent calculus for classical logic with first order quantification, allowing for singular terms free of existential...

In between wrapping up teaching for the end of Semester 2, and getting ready for a short trip to Scotland, I’m spending some time thinking about free logic and quantified modal logic and identity. This is difficult but exciting terrain to cover. There is no obvious way to tie together the logic of quantifiers, the modalities and identity in a...

I’ve been at the University of Melbourne since 2002, and the Logic Group has been meeting regularly since my arrival there. While it’s changed significantly in its membership over the last 13 years, one thing has remained constant—we’ve been an informal, friendly bunch of people, so hard at work in teaching and research that we’ve not had time to...

Logic has been an important part of philosophy since the work of Aristotle in the 4th Century BCE. Developments of the 19th and the 20th Century saw an incredible flowering of mathematical techniques in logic, and the discipline transformed beyond recognition into something that can seem forbiddingly technical and formal. The discipline of logic...

There’s something very attractive in the idea that meanings of logical concepts—such as conjunction, negation, the quantifiers—can be specified by the role they play in proofs. If I learn the rules for conjunction: \( \def\sem#1{[\![#1]\!]} \) \[ \frac{A\land B}{A} \quad \frac{A\land B}{B} \qquad \frac{A\quad B}{A\land B} \] then I’ve “pinned...

This is a talk at the 2015 Australasian Association for Philosophy Conference at Macquarie University in Sydney. I will attempt to be precise about the notion of a merely verbal disagreement, and explain how we can fix on the meaning of our logical constants can play a coordinating role in dialogue, and how (in a certain sense), it might be...

A presentation for the Australasian Association for Logic Conference at the University of Sydney. I will discuss Tim Williamson’s arguments for the non-contingency of existence (see his Modal Logic as Metaphysics, 2013) and explain how and why they might be reasonably resisted. Along the way, I’ll try to explain the impact of proof theory for...

The view from my desk. A photo posted by Greg Restall (@consequently) on Jun 3, 2015 at 7:39pm PDT

In yesterday’s Logic Seminar, Tomasz Kowalski introduced some lovely results about analytic cut and interpolation in sequent systems for bi-intuitionistic logic. After the seminar, Lloyd Humberstone, Dave Ripley, Tomasz and I got talking about various features of bi-intuitionistic logic, some of which should be more well known than they are … so...

I’m back from last week’s quick trip to Oxford for a workshop on Verbal Disputes, just in time to wrap up the last week of teaching in my two undergraduate units as the semester winds up here in Melbourne. This was an excellent two-day workshop, capably organised by Trevor Teitel, and funded by the Ertegun Graduate Scholarship Programme for the...

I’m giving a presentation, entitled “Merely Verbal Disputes and Coordinating on Logical Constants,” on proof theory, modality, existence and verbal disputes at a workshop held at the University of Oxford in May, 2015. I will attempt to be precise about the notion of a merely verbal disagreement, and explain how we can fix on the meaning of our...

I'm here for May 20 and 21 Tomorrow I head off on a flying visit to Oxford for a Workshop on Verbal Disputes and their Philosophical Significance. I’m looking forward to catching up with old friends and making new ones. The lineup for the workshop is fantastic, so it looks like it’ll be a great time. If you’re in the area, please do come along...

Proponents of a dialethic or “truth-value glut” response to the paradoxes of self-reference argue that “truth-value gap” analyses of the paradoxes fall foul of the extended liar paradox: “this sentence is not true.” If we pay attention to the role of assertion and denial and the behaviour of negation in both “gap” and “glut” analyses, we see that...

I’m giving a research seminar on May 1 at the Catholic Theological College. The details are listed here in PhilEvents. Abstract: In this talk, I will explore some of the connections between logic and philosophy of language on the one hand, and theology—or religious practice—on the other. Instead of focussing on the role of logic and semantics as...

Jen Davoren and I are running Logic: Language and Information 2 through Coursera again in 2015. You can enrol here. This course follows on from Logic: Language and Information 1

A presentation to the Philosophy Circle at the Lyceum Club of Melbourne on Sophistry and Argumentation, and on the role of reason in the examined life.

Here’s another view of my building at work, in the autumn light. Old Quad, back entrance A photo posted by Greg Restall (@consequently) on Mar 31, 2015 at 6:20am PDT

I’m giving a talk entitled “Incarnation and Detachment: Philosophy, Prayer, and Taking Positions” at the first 2015 meeting of the Christian Scholars Network. (We’ll meet at the Dan O’Connell Pub at 7pm on Tuesday March 24. Come early to share dinner before the talk and discussion.) In the talk I’ll discuss some of the parallels between the range...

On the afternoon of Sunday March 1, Sydney Road in Brunswick was transformed by its annual Street Party. Over four blocks of this busy inner north thoroughfare was closed to trams and cars, lined by stalls, punctuated with live bands, and filled with crowds. Everyone was sampling wares, eating, drinking and soaking in the atmosphere. It’s a...

Just today, I stumbled across a video of an interview with me from 2013, explaining our thinking behind teaching introductory logic on Coursera, and the connections between this and classroom teaching. Come for the ideas, stay for the crazy hand gestures.

I’m delighted to finally announce that I have a job to offer on my five year ARC funded research project in philosophical logic and its applications, “Meaning in Action: new techniques for language, logic and information.” It’s a two year postdoctoral research position, with a little bit of teaching on the side. If you’re interested in...

I have known about the Mathematical Genealogy Project for quite some time, but, prompted by Richard Zach I notice two new and wonderful things. First, David Alber has produced in Geneagrapher a neat tool to download genealogy data and save a .dot file, which can be read by Graphviz and displayed as a directed graph. Here’s a detail from my...

The Power and Limits of Logic Teaching started for first semester, with the launch of Logic: Language and Information 1 on Coursera. That’s been a lot of fun already, with over 17,000 enrolled. There’s something very exciting about being involved with a large number of students all around the world, choosing to work hard to learn logic for the...

Jen Davoren and I are running Logic Language and Information 1 through Coursera again in 2015. You can enrol here.

Rembember that you are dust, and to dust you shall return. Remember that you are dust (@consequently) on Feb 18, 2015 at 5:57am PST

What is negation? One answer you find in the literature is that negation is the operator that makes each instance of the Law of the Excluded Middle (LEM) and the Law of Non-Contradiction (LNC) turn out to be true. That is, every sentence of the form \[ p\lor \neg p \qquad \neg(p\land\neg p) \] is true, no matter what sentence we use in the place...

I’ve added a search feature to the site in the footer of each page. There seems to be enough on the site that search is genuinely useful. I’ve used DuckDuckGo, which has a comprehensive index of this place, and which can be styled to match the visual treatment of the rest of the site. Please let me know if there are any problems with the...

A blast from the past While recovering the archives for this site, I came across another blast from the past: the weblog I ran with Jc during the early days of our research on logical pluralism.

If you glance at the news archive, you’ll see that once again it stretches back to the dim past of weblog days, the year 2000. Thanks to the wayback machine, I was able to recover entries from my old blog (powered by Blogger, from well before it was acquired by Google), and fulfil a commitment I made in March 2001 to move the old archives over to...

It’s good to be back in the office. The Parkville Campus of The University of Melbourne is a delightful place to work. It’s February, and I’m back in the office. A photo posted by Greg Restall (@consequently) on Feb 1, 2015 at 4:36pm PST

Previous incarnations of this website provided a facility for comments in the usual way for a weblog in the first decade of the 2000s—a comment form on each entry. This one doesn’t. Why not?

My last post to consequently.org was in late in 2010, well over four years ago. You’d be justified in thinking that I’d abandoned the place—but you’d also be wrong. I’ve been tinkering with it behind the scenes. The software I’d been using to maintain the website has long since fallen into disrepair, so updating it meant porting everything to...

A seminar at the workshop Algebra and Substructural Logic 5 (La Trobe, December 2015). I explain how the `trace model’ for relevant arithmetic (introduced here) can be extended quite naturally to model a logic including a de Morgan negation. The result is not a model for the logic R, but for its weaker cousin, TW.

Different natural deduction proof systems for intuitionistic and classical logic—and related logical systems—differ in fundamental properties while sharing significant family resemblances. These differences become quite stark when it comes to the structural rules of contraction and weakening. In this paper, I show how Gentzen and Jaśkowski’s...

I gave a presentation to postgraduate students in the Monash University Christian Union about life as a Christian academic, and my journey from being an undergraduate in Mathematics at the University of Queensland in the late 1980s, to my current role as Professor of Philosophy at the University of Melbourne.

A seminar at the University of Melbourne Logic Group. I sketch some of the features of models of naïve theories of properties or classes defined by finding a space C that is isomorphic to the class of continuous functions [C ∪ D → Ω].

I gave a masterclass on Ludwig Wittegenstein’s Tractatus Logico-Philosophicus in the University of Melbourne’s 10 Great Books Masterclass in 2014.

Beall and Restall’s Logical Pluralism (2006) characterises pluralism about logical consequence in terms of the different ways cases can be selected in the analysis of logical consequence as preservation of truth over a class of cases. This is not the only way to understand or to motivate pluralism about logical consequence. Here, I will examine...

PHIL10003: Philosophy, the Great Thinkers is a University of Melbourne undergraduate subject, introducing philosophy to students through close readings of core texts. I taught with Dr. Chris Cordner and Dr. Ruth Boeker. In my classes, we looked at David Hume’ Dialogues Concerning Natural Religion and Natural History of Religion, with some side...

A presentation at the Metaphysical Basis of Logic Workshop at the Northern Institute of Philosophy, University of Aberdeen.

I taught an intensive class on proof theory and its applications to Philosophy at the NIP Summer School on the Foundations of Logic and Mathematics, June July 2014.

A presentation in a workshop in the Philosophy of Logic at Arché. The distinction between defined terms and undefined terms provides a metaphysically “light” way to give a semantics for free logic. Singular terms may be undefined, and if they are undefined, they are not appropriate substitution instances for inference rules for the quantifiers....

PHIL40007: Philosophy of Language and Mind is a University of Melbourne honours seminar subject for fourth-year students. Our aim in the Honours program is to introduce students to current work in research in Philosophy. In 2014, I introduced the students to the normative pragmatism and inferentialism of Robert Brandom, through a close reading of...

In 2014, I participated in the Arts Foundation subject MULT10016: Reason. I taught six classes, on Plato, Aristotle and Hume.

In this paper I urge friends of truth-value gaps and truth-value gluts – proponents of paracomplete and paraconsistent logics – to consider theories not merely as sets of sentences, but as pairs of sets of sentences, or what I call ‘bitheories,’ which keep track not only of what holds according to the theory, but also what fails to hold according...

A special issue of the Logic Journal of the IGPL, on Non-Classical Mathematics. Editorial Preface, Libor Bĕhounek, Greg Restall, and Giovanni Sambin. "Mathematical pluralism," Graham Priest "A first constructive look at the comparison of projections," Douglas S. Bridges and Luminiţa S. Vîţa "Lipschitz functions in constructive reverse...

Philosophical logic has been, and continues to be, a driving force behind much progress and development in philosophy more broadly. This collection of 12 original papers by 15 up-and-coming philosophical logicians deals with a broad range of topics, including proof-theory, probability, context-sensitivity, dialetheism and dynamic semantics. If...

The two-dimensional modal logic of Davies and Humberstone is an important aid to our understanding the relationship between actuality, necessity and a priori knowability. I show how a cut-free hypersequent calculus for 2d modal logic not only captures the logic precisely, but may be used to address issues in the epistemology and metaphysics of...

According to Stephen Read, Thomas Bradwardine’s theory of truth provides an independently motivated solution to the paradoxes of truth, such as the liar. In a series of papers, I have discussed modal models for Read’s reconstruction of Bradwardine’s theory. In this paper, provide a hypersequent calculus for this theory, and I show that the cut...

Proof theory for modal logic has blossomed over recent years. Many ex- tensions of the classical sequent calculus have been proposed in order to give natural and appealing accounts of proof in modal logics like K, T, S4, S5, provability logics, and other modal systems. The common feature of each of these different proof systems consists in the...

Consequence is a, if not the, core subject matter of logic. Aristotle’s study of the syllogism instigated the task of categorising arguments into the logically good and the logically bad; the task remains an essential element of the study of logic. In this essay, we give a quick history of the way logical consequence has been studied from...

Majer and Peliš have proposed a relevant logic for epistemic agents, providing a novel extension of the relevant logic R with a distinctive epistemic modality K, which is at the one and the same time factive (Kφ → φ is a theorem) and an existential normal modal operator (K(φ ∨ ψ) → (Kφ ∨ Kψ) is also a theorem). The intended interpretation is that...

Molinism is an attempt to do equal justice to divine foreknowledge and human freedom. For Molinists, human freedom fits in this universe for the future is open or unsettled. However, God’s middle knowledge – God’s contingent knowledge of what agents would freely do in this or that circumstance – underwrites God’s omniscience in the midst of this...

I sketch an application of a semantically anti-realist understanding of the classical sequent calculus to the topic of mathematics. The result is a semantically anti-realist defence of mathematical realism. In the paper, I develop the view and compare it to orthodox positions in the philosophy of mathematics.

This is an idiosyncratic history of philosophical logic in Australia and New Zealand, highlighting two significant points of research in Australasian philosophical logic: modal logic and relevant/paraconsistent logic.

Just testing to see if this thing is on. Yes, it seems to be working. How about that!? It’s pretty rusty, but apparently this site still works. That’s good to see.

A possible world is a point in logical space. It plays a dual role with respect to propositions. (1) A possible world determines the truth value of every proposition. For each world w and proposition p, either at w, p is true, or at w, p is not true. (2) Each set of possible worlds determines a proposition. If S, a subset of W is a set of worlds,...

I examine Belnap’s two criteria of existence and uniqueness for evaluating putative definitions of logical concepts in inference rules, by determining how they apply in four different examples: conjunction, the universal quantifier, the indefinite choice operator and the necessity in the modal logic S5. This illustrates the ways that definitions...

We study the interpretation of Grzegorczyk’s Theory of Concatenation TC in structures of decorated linear order types satisfying Grzegorczyk’s axioms. We show that TC is incomplete for this interpretation. What is more, the first order theory validated by this interpretation interprets arithmetical truth. We also show that every extension of TC...

In this paper we show how the formal counterexamples to Hume’s Law (to the effect that you cannot derive a properly moral statement from properly descriptive statements) are of a piece with formal counterexample to other, plausible “inferential barrier theses”. We use this fact to motivate a uniform treatment of barrier theses which is immune...

Majer and Peliš have proposed a relevant logic for epistemic agents, providing a novel extension of the relevant logic R with a distinctive epistemic modality K, which is at the one and the same time factive (Kφ → φ is a theorem) and an existential normal modal operator (K(φ ∨ ψ) → (Kφ ∨ Kψ) is also a theorem). The intended interpretation is that...

This paper shows that once we have propositional constants t (the conjunction of all truths) and u (the disjunction of all untruths), paradox ensues, provided you have a conditional in the language strong enough to give you modus ponens. This is an issue for views like those of Jc Beall, Ross Brady, Hartry Field and Graham Priest.

In this article, I praise Hartry Field’s fine book Saving Truth From Paradox (Oxford University Press, 2008). I also show that his account of properties is threatened by a paradox, and I explain how we can only avoid this paradox by coming to a clearer understanding the connections between accepting and rejecting (or assertion and denial) and the...

This paper explores models for arithmetics in substructural logics. In the existing literature on substructural arithmetic, frame semantics for substructural logics are absent. We will start to fill in the picture in this paper by examining frame semantics for the substructural logics C (linear logic plus distribution), R (relevant logic) and CK...

This note explains an error in Restall’s ‘Simplified Semantics for Relevant Logics (and some of their rivals)’ (Journal of Philosophical Logic 1993) concerning the modelling conditions for the axioms of assertion A → ((A → B) → B) and permutation (A → (B → C)) → (B → (A → C)). We show that the modelling conditions for assertion and permutation...

Time flies like an arrow. Fruit flies like a banana. If you’ve been following my twitter feed, you’d realise I’m still alive. You wouldn’t think that from the activity – or lack thereof – here. (Though a few papers have appeared – or changed their publication status – on my writing page.) Here’s where we are: It’s been a busy, eventful...

Philosophers love a priori knowledge: we delight in truths that can be known from the comfort of our armchairs, without the need to venture out in the world for cofirmation. This is due not to laziness, but to two different considerations. First, it seems that many philosophical issues aren’t settled by our experience of the world – the nature of...

Posting has been light, since I’ve been powering through work at the end of the semester, and getting ready for a quick trip west to Europe, for Non-Classical Mathematics 2009 and Logica 2009, preceded by a quick visit to Dresden to see Heinrich Wansing, and to break up the train trip from Frankfurt to Prague. So, posting here has paused for a...

This is Part 2 of a series of comments on Ian Rumfitt’s paper “Knowledge by Deduction” (Grazer Philosophische Studien, vol. 77 (2008) pp. 61–84). In Part 1, I focussed on Rumfitt’s direct criticism of my approach in “Multiple Conclusions,” and I tried to show that his criticism missed the mark, and that it missed the mark in an important way....

Thanks to Ole Hjortland, I’ve been alerted to Ian Rumfitt’s paper “Knowledge by Deduction” (Grazer Philosophische Studien, vol. 77 (2008) pp. 61–84.). In it, he makes a number of critical comments on multiple conclusion accounts of logical consequence, and in particular, he makes some critical remarks on my paper “Multiple Conclusions.” Now,...

I’ve been thinking about generalisations of Russell’s paradox, cleaning things up so you can’t get around the problem by changing the logic of connectives. I don’t think that mucking around with negation or implication gets to the heart of the issue. (This view is shared by some very insightful people. I haven’t come to it alone.) Getting...

Earlier today I received the sad news that Bob Meyer, my former colleague at the ANU, and friend, two-time collaborator, died last night, after a long struggle with cancer. Bob will be sorely missed by many of us. His warmth and humour, his brilliance, and his willingness to talk logic (and much more) to anyone and everyone, will all be...

In this paper I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, feature as an idealisation of more fundamental logical features arising out of the proof theory for each system. The result is not a...

Allen Hazen pointed me to this nice interview Julian Bagnini conducted with Ernie Lepore, on words. Lepore comes to the same sort of conclusion as Kaplan – that identity conditions for words are tricky. He’s right.

We explain how Eric Mazur’s technique of Peer Instruction may be used to teach philosophy, logic and critical thinking — to good effect.

The quote from yesterday’s quiz was from the inimitable David Kaplan, in the article “Words” (Proceedings of the Aristotelian Society, Supplementary Volume, LXIV 1990). As Robbie mentioned in the comments “Words” is such a cool paper. I want to give an example of how cool it is. It’s tempting to think of words, repeatable things that the are,...

Whoever thought that teaching in three subjects, chairing one committee, participating in another one with a honking big project to keep on the rails for the next few months, supervising n research students (for a seriously large value of ‘n’) and trying to keep your research ticking over would keep you busy with work? I did think that. But now...

Here is today’s quiz question. Which master of exposition said this, and where? After arguing for years, unconvincingly, that semantic value (properly understood) is not affected by substitution, I hit upon a brilliant, new, and completely successful, strategy: argue, instead, that semantic value is affected by substitution. Here’s a hint: the...

I’m back in Melbourne. Z and I have been back for over a week – and I’ve been back at work since the middle of last week, slowly setting up while Z has been settling into school. C returns tomorrow, and the place will feel like home at last. The philosophy blogosphere is all a-flutter with the release of the 2009 Leiter Report. We have known for...

We’re having a wonderful time on our holiday, cruising through the southwest of the USA. The sights have been spectacular, varied and unexpected. The highlight so far was Bryce Canyon. The Grand Canyon is grand, and sublime in its own way. Bryce Canyon was totally unexpected: I had no idea erosion could do just that. Z ran around like a madman...

Here are some random, miscellaneous items of news, concerning what’s been happening around here, around now. It’s exhausting, but lots of fun, to host visitors. Since just before Christmas, we’ve had visits from two good friends (separately) and four family members (one batch of three and one solo), as well as meals with other friends over the...

We’re going on a holiday! Tomorrow at noon, we’ll be on a Qantas 747 to LA, and at the other end, the three of us will be enjoying four weeks of break. It’s mostly time off for all of us, with a few detours for work talks for me (at Pitt, and at UConn) and for Christine (at Harvard, San Diego, Berkeley and maybe Stanford). It’s our ‘consolation...

The appendix to Kukla and Lance’s book is the preliminary development of a score-keeping semantics that begins with the broader field of vision opened up when we eschew the declarative fallacy and make use of abstract versions of the pragmatic distinctions developed in the body of the book.

It’s Christmas break here, and I’m taking a break, with visits from family and friends, and then a trip to the USA for a holiday (and for a couple of little side trips to see friends and give a few talks). More about that in a little while. To share the Christmas spirit, I’ll share a favourite carol: The tree of life my soul hath seen, Laden with...

(What follows is a bundle of ideas I’ve been trying to write up for some time. Instead of making it a fully fledged paper, I’ve decided to rough it out first as a blog post. If anything comes of it, I’ll polish it up. Let me know what you think.) Are there any possible worlds? The idea of a point in logical space – at which every proposition is...

I’m on a roll with the writing: I’ve managed to get another paper converted from slides-from-a-talk to real, live, words on a page and actual proofs. The paper I’ve worked on over the last couple of days is from my presentation from WCP4 on non-classical theories like non-classical theories of numbers, classes, or truth. I’m very happy with this...

Stephen Read’s work on Bradwardine’s theory of truth is some of the most exciting work on truth and insolubilia in recent years. In this paper, I give models for Read’s formulation of Bradwardine’s theory of truth, and I examine the behaviour of liar sentences in those models. I conclude by examining Bradwardine’s argument to the effect that if...

It’s good to get back into writing. Here’s a paper “Truth Values and Proof Theory” that I’ve been thinking about for a long time. I presented a research seminar on this material last year – it’s taken me this long to write it up, due to other commitments. Here’s the abstract: In this paper I present an account of truth values for classical logic,...

My trip to Guangzhou was super. Thanks, Guoxin, Min and Xuefeng for looking after me and showing me the sights of Guangzhou, and to Professors Ju and Zhu for the invitation. It was a wonderful experience for me, and I look forward to many more visits to China, and to the Institute of Logic and Cognition. Since then, I’ve been off to Canberra for...

The primary purpose of this site seems to be travel announcements, so rather than break the trend, I’ll post another travel announcement. On Sunday, I’m off to the Institute of Logic and Cognition at Sun Yat-Sen University, to give three lectures on my research. This is my first trip to China, so I’m more excited (and more nervous) than usual for...

I update “Truthmakers, Entailment and Necessity” with a response to Stephen Read's wonderful Mind 2000 argument to the effect that I got the disjunction thesis wrong. I think I didn't get it wrong, but figuring out why it's OK to hold that a truthmaker makes a disjunction true iff it makes a disjunct true is not as straightforward as I first...

Stephen Read has recently discussed Thomas Bradwardine’s theory of truth, and defended it as an appropriate way to treat paradoxes such as the liar. In this paper, I discuss Read’s formalisation of Bradwardine’s theory of truth, and provide a class of models for this theory. The models facilitate comparison of Bradwardine’s theory with...

Phew! What a long rest-of-the conference! I’m now back in Tallinn, after the rest of the conference: 5 talks on Day 3, and one wrapup talk on Day 4. My comments concerning Days 3 and 4 will not be as extensive as those for Days 1 and 2. I liked these as much as the earlier talks – it’s just that my stamina has flagged. Day 3 The day kicked off...

OK, it’s a short day here today – thankfully, since I’m knackered after Day #1 – with two talks. Last night we dined at an Italian Restaurant, and I learned more about Roger Swyneshed from Stephen Read, than I ever expected to learn. Talks today are: Peter Pagin, on Universalist and Actualist Consequence. Peter connected his work with Kathrin...

We’re coming semi-live from Tartu, as long as my computer’s battery lasts, anyway. For live off-the-cuff comments, try my experimental twitter stream, which is profoundly silly, but fun to fiddle with on my phone when my fingers are itchy. The lineup today. Me, giving “Pluralism and Proofs.” I think I went well. Look at Ole’s sneak-preview of...

If this is Thursday, it must be Tartu. The conference starts today, and I’m up first. The nerves have started to jangle just a bit, since the audience is about as high-powered as any in my experience at international conferences. It’s just as well as those who intimidate me the most this time around (due to their all-round awesomeness combined...

I’ve arrived in Amsterdam. Getting here was touch-and-go. My decent wait between my Melbourne → Singapore flight and my Singapore → Amsterdam leg whittled down to around 45 minutes. That involved a trek through the terminal, a tense wait at Transfer Desk C (where people in the queue in front of me were arguing with the staff about visas, and...

Bag packed, ticket & passport at the ready, computer charged, phone charged and synced, books to read located, papers to read/referee/assess all printed or downloaded. I must be going on a flight. The trip takes me from Melbourne to Singapore to Amsterdam to Tallinn to Tartu, and then I retrace my steps to get back here in ten days. That’s too...

I had thought that we (the Faculty of Arts at the University of Melbourne) were trying to keep our difficulties an internal affair, but apparently we’re not. Given that this is all public news, I suppose I could comment. The take-home-message from this memo from the Dean: (1) The budget in the Arts Faculty is not yet in the black, though it’s...

Out of the five Australians who were chosen as nominating editors of this year’s Philosophers’ Annual, four are from The University of Melbourne. The lucky 4 are Hazen, Schroeter (François), Schroeter (Laura), and Restall. (The other Australian is David Chalmers.) 4 out of 28 is a good strike rate (that’s 1 in 7, if you’re too lazy to do the...

I’ve been pretty quiet here, lately. I’ve been busy with things, getting stuff done. I hope to be posting more soon, when various up-in-the-air things are more settled. Still, here are some recent highlights which are worth sharing. WCP4 was a blast. It was very busy, but lots of fun was had: it was good to catch up with many folks I hadn’t seen...

I’m off to Tartu in late August, for what looks like a really fun conference on logical pluralism. The list of speakers is extraordinarily high-powered. Having so many smart people talk about logical pluralism is exciting, and not a little bit scary. If you’re interested in coming along, let the organisers know by July 1. If you’re interested in...

The journal Informal Logic, on argumentation theory and related issues, is now open access and online, after a 27 year history as a print (closed access) journal. The editors have sent out a request for interested parties to subscribe. Subscription is free: just fill in this form on the site. The editors are aiming get enough subscribers to...

Alas, we are in the news for not-very-good reasons. Given the recent retirements in Philosophy at Melbourne, it would be worse than surprising if any of the new redundancies hit Philosophy. However, the atmosphere around here not good – what concerns us most is the scope for new hiring when the Faculty as a whole is in the red so much. It is very...

We diagnose the two envelope “paradox”, showing how the indifference principle plays a role in prompting the conflicting assignments of the expected outcomes for switching or keeping.

I point out that non-classical “solutions” the paradoxes of self-reference are non-particularly easy to give. Curry’s paradox is very very hard to avoid, if you wish to give a semantically cohrerent picture.

In this short paper, I compare and contrast the kind of symmetricalist treatment of negation favoured in different ways by Huw Price (in “Why ‘Not’?”) and by me (in “Multiple Conclusions”) with Robert Brandom’s analysis of scorekeeping in terms of commitment, entitlement and incompatibility. Both kinds of account provide a way to distinguish the...

We argue that the participatory language, used in the New Testament to describe the the efficacy of Jesus’ death on the cross, is essential for any understanding of the atonement. Purely personal or legal metaphors are incomplete and perhaps misleading on their own. They make much more sense when combined with and undergirded by, participatory...

This has been a good day. (Here is the video — in three parts.) As PJK said, when you change the government, you change the country…

This solid volume with the ominous black cover and eerie glowing disc lettered with inscrutable strings of characters such as “DNdQ,” “LSDJd,” and “L2LDJQ±” is the fruit of over 30 years of Ross Brady’s logical labours. And it is worth the wait…

Modal logic is a well-established field, and the possible worlds semantics of modal logics has proved invaluable to our understanding of the logical features of the modal concepts such as possibility and necessity. However, the significance of possible worlds models for a genuine theory of meaning–let alone for metaphysics–is less clear. In this...

Are you an undergraduate student in philosophy, or do you know any undergraduate philosophy students? If so, you might be interested in the Melbourne Philosophy Undergraduate Workshop to be held from September 21 to 23. This will be a chance for Australian and New Zealand undergraduate students who are interested in philosophy, to get together to...

I gave a talk on Logic in Australia at Monash University’s Arts in Action festival in early June. (This was a part of a long-running project on a History of Australasian Philosophy. The talk is now appearing, in two parts, on the (wonderful) ABC Radio National program, The Philosopher’s Zone. The first part was broadcast this weekend, but the...

I’ve been back in Melbourne for a while. The trip was very enjoyable, but I’ve returned to Melbourne with a chest bug, which has meant that I’m not quite up to full speed yet. All non-essential activities (and alas, some essential ones, I fear) are progressing much more slowly than usual. Here are some highlights of the trip. Logica 2007 with so...

I’ve arrived in a sunny and summery Prague. The locals tell me they it’s cooler than the unseasonably warm that it’s been in the last few years, but it seems nicely summery for one who has come from a winter. I’m now chatting in the office with Timothy, Jarda and Vladimir, and monopolising Jarda’s computer while the others do work preparing for...

I’m waiting in Gate 9 at the international terminal Melbourne Airport, getting ready to board my first flight on my trip to Europe. It’s not a short hop – Singapore/Frankfurt/Prague, but at least I’ll be in a very nice place for what to all appearances will be a very enjoyable conference. From then, it’s Bonn, and then Denmark (København, and...

You learn something new every day. What we mistakenly called gargoyles are actually finials. (I’ve corrected the caption on the photo – in case you don’t understand what Christine meant.) Christine took that photo on a finial-photographing expedition with Zachary and a friend from his class in school, on Zachary’s birthday a few weeks ago.

As I’ve said before, logic jobs in Philosophy Departments are pretty rare. Well, as Richard mentioned earlier, there’s a logic job in Philosophy at Auckland. A little bird has told me that even though the deadline is close (May 18), they’re keen to get the word out to get as many applicants as possible. So, if you qualify (PhD or equivalent in...

The program for Logica 2007 has been released, and it looks great. It looks like it will be seriously good, and it will be my first ever conference held in a monestery.

This Tuesday, I’m going to a party: It’s a launch for Christine’s book Inside Lawyers’ Ethics, which she’s coauthored with Adrian Evans from Monash Law School. The book will be launched by Louise Sylvan, from the ACCC. This party will be held at the Monash University Law Chambers in the city. Congratulations, Christine and Adrian! It seems to be...

1007 words on symbolic logic – concentrating on the history of 20th Century logic, aimed at an audience of social scientists

In this paper I introduce a sequent system for the propositional modal logic S5. Derivations of valid sequents in the system are shown to correspond to proofs in a novel natural deduction system of circuit proofs (reminiscient of proofnets in linear logic, or multiple-conclusion calculi for classical logic). The sequent derivations and proofnets...

Second order quantification is puzzling. The second order quantifiers have natural and compelling inference rules, and they also have natural models. These do not match: the inference rules are sound for the models, but not complete, so either the proof rules are too weak or the models are too strong. Some, such as Quine, take this to be no real...

Liveblogging talks was a bit beyond me, but I’ve been keeping up with a few notes on the talks here in Banff. They’re not as extensive as my notes on Branden and Delia’s talks, but they’ll give you an idea of the fun we’ve been having here. (After lunch today, there’s a batch of five talks, including mine. I’m not sure when I’ll be able to write...

I’ve finished up the slides for my talk in Banff. If you’re interested, the slides are available here Modal Models for Bradwardine’s Truth [1.3MB pdf] It’s a talk giving a modal logic interpretation for a medieval theory of truth due to Thomas Bradwardine, as it’s reconstructed by Stephen Read. This will hopefully help out Steve’s project, by...

The next Banff talk is Delia Graff Fara, on “Relative identity and de re modality.” She’s defending the thesis that material objects are identical to the matter of which they’re constituted. For example, the statue Goliath (G) is identical to the lump of clay Lumpel (L). She wants to allow that L = G, while having L and G differing in their...

The first talk in Banff is by Branden Fitelson, who is giving a ‘“Survey” of Formal Epistemology: some propaganda, and an example’. It’s a part of the general movement towards carving out the discipline of ‘formal epistemology’. It’s a partly political talk, recounting the motivation for Formal Epistemology. He recounted Bob Meyer’s manifesto of...

I’m in sunny and wintry Banff at the Mathematical Methods in Philosophy workshop. The program is very full, and I won’t be able to report on everything going on here. (Heck, I haven’t even reported back from our time in India, despite popular demand.) So, please let me give my apologies in advance if youre talk doesn’t get reported here. It’s...

I’ve been having too much fun and doing too much work lately to post anything here. On the work side, our proposal to teach first-year logic in an interdisciplinary way as a “breadth” subject to all students in the “new generation” degrees from 2008, has passed the first hurdle. We have a bucket of money to develop the course over the next year....

My son, Z, asks me Dad, what is Kantian freedom? some time later Dad, what is a conceptual repertoire? No, he’s not a philosophical prodigy. He was curious about what I was reading, and I explained that I had an essay written by a student, and I had to figure out how good it was. It happened to be an essay about John McDowell’s Mind and World,...

Two bits of horn tooting for today: First, from the famous and notorious Philosophical Gourmet Report. Brian Leiter pointed out that the report hit the newspaper here in Australia. The point of the little note in the Higher Education section of The Australian was that the ANU topped the rankings of Australian philosophy departments (as it has in...

I’d like to guage some philosophical opinions. (I don’t have many of my own. Most of them have been worn down by years of logical abuse.) First, some pre-requisites: Let’s understand ‘possibly’ as a metaphysical sort of possibility. If it helps, think of it as truth in some possible world, no matter how outlandish. Let’s understand a priori...

You’re all invited to a party on Tuesday, October 17 (5:30pm for 6pm) at the Melbourne University Bookshop to celebrate the publication of five books in Logic and Philosophy here in the Philosophy Department at Melbourne. Here are the books: Models, Truth and Realism, Barry Taylor. Doubt Truth to be a Liar, Graham Priest. In Contradiction, Graham...

Here’s my (much delayed) answer to the second of Vincent Hendricks and John Symons’ five questions about Formal Philosophy. What example from your work illustrates the role formal methods can play in philosophy? I’ll focus on one example from some of my recent work. In the last few years I have been working on topics in proof theory and...

I just had an Idea today. From here, it seems like a Really Neat Idea. (Having the idea made me remember what it feels like to prove something you’ve been struggling with for a long time: a mix of excitement, wonder, awe, relief, and much else besides. It’s welcome to be reminded of why I like working in logic.) This idea isn’t a new theorem, but...

In the Philosophy Department we’re pleased to be hosting some short visits from Gillian Russell, and Jon Cohen. It’s neat to be in a place where smart people come to visit, think and talk to you. Last week we had a couple of logic seminars from neat west-coast of the USA types: Mike Titelbaum from Berkeley and Stanley Peters from Stanford. At...

Since Jo asked so nicely, I’ll add my answers to the one book meme that’s going around the place. One book that changed your life Robert C. Roberts, Spirituality and Human Emotion. It’s because of this book that I’m a philosopher, believe it or not. Reading it, I saw that the philosophy needn’t be self-contained, but could be used to say...

I’ve listened to the interview, and I’m pretty happy with how it went. The ABC team did a good job with the editing (I think the interview I recorded was a bit over 30 minutes). I never thought that I’d live to hear the day that someone explained the semantics of first degree entailment on national radio, and I was especially grateful that my...

In the car this evening, Z (our five-and-a-bit year-old son) says, unprompted, Dad, I’ve been thinking … I reply “yes …” … why does Kim Beazely want to be Prime Minister? It’s nice to know that he’s keeping up with his world. It’s telling that we found it difficult to answer the question.

This morning I trooped down to the ABC Melbourne studios in Southbank, to sit in a ‘Tardis’ booth to talk to Alan Saunders of The Philosopher’s Zone on logic, the liar paradox and other stuff I think about. Alan was feeling unwell and suffering from a croaky voice, so the interview that goes to air might be more of a monologue than what took...

It’s been difficult to get back into the swing of work, but I’m slowly clawing my way through. Jetlag has been much worse on my return than on the European end of the trip. I’ve also been concentrating on my parental duties, as my Significant Other is taking her conference trip. Playing with your son is much more fun than doing niggly...

I’m back in Melbourne, after my whirlwind jaunt in Nancy. I was in too much of a rush on Day 4 of the conference to post thoughts on Day 3 or Day 4. I promise I’ll do that once I recover from my jetlag and deal with my growing pile of mail, both snail and electronic. In other news, the nicest thing about reading this article on blogging in this...

Nancy Day 2 was a quiet as far as the official program went. Talks were scheduled in the morning leaving the afternoon free. Michael Lynch and I took in the Musée des Beaux-Arts and talked philosophy and much else with Peter van Inwagen, Scott Shalkowski and others into the evening and late in the night. The morning featured a well-put-together...

I’m conference blogging here in Nancy at the Realism/Anti-Realism conference. It’s been neet, chatching up with people I’ve not seen for a while. Today, after a not-completely-rested-night as I tried to sleep through a rather rowdy French community beeping car horns after their 3-1 victory in the round of 16, I went to five talks. Here’s the...

Today I’m flying off to Nancy for (Anti)Réalismes Logique & Métaphysique. It should be an interesting meeting: the program is here. If I get time to edit my paper on the plane, I’ll try posting the text of the paper before I give it, internet access permitting.

In Semester 2, which starts on July 31, I’ll be teaching an honours seminar 161-438 Logic and Philosophy, in which we cover proof theory and its applications to semantics.

Now that my undergraduate teaching is done for the semester, I can devote more time to research. I’m going to use this place to post some material from my proof theory project. My goal is to present some key ideas in an accessible way. Today’s idea is the duality between proofs and counterexamples. Proofs: You can think of a valid argument as...

When the team are 0–1 down at the eighty-fourth minute, you don’t think they’ll win 3–1. Update: I’m glad I don’t have to detail the match, and can point you to this excellent piece of writing instead. It’s a reflection on the match by Jeremy, a first-year Arts/Engineering student here at the University of Melbourne. He’s one of the contributors...

This afternoon I was interviewed by Lisa Mitchell from The Age about academic blogging. She’s writing an article for the education supplement (published on Mondays). It’s a piece with a long lead time. I wonder if I’ll recognise anything I said in the article, and if she’ll quote me. (I blabbed on for 25 minutes. I hope there was some useful raw...

We’ve finished lectures for the semester, and I’m officially recovering. It was fun teaching Logic and Non-Classical Logic, but it was also a hard slog. Next semester I have a light teaching load, with my honours logic seminar. The highlight last week was Richard Zach’s visit. He gave two nice talks. One on vagueness and logic – setting out...

Here’s a silly puzzle for you. Regret seems like a factive emotion. You can’t truly regret that you forgot to feed the cat today if, indeed, you did feed the cat. If you did feed the cat and you forgot that you did, then it seems to you like you’re regretting not feeding the cat, but you’re as mistaken about your regret as you are about feeding...

Have you ever waited for a tradesperson to come to your place? Alan Hájek uses this example in an article entitled “The Cable Guy Paradox.” The issue is straightforward. You and I are waiting for the cable guy who has given you a window between 8am and 4pm for his arrival. He will arrive after 8am, and before 4pm. We while away our time with a...

As I mentioned before, I’ve been thinking about Vincent Hendricks and John Symons’ five questions about Formal Philosophy. This seems like as good a place as any to answer them. So, today, I’ll have a crack at the most autobiographical of the questions: Why were you initially drawn to formal methods? I suppose the natural way to interpret this...

Happy fifth birthday, Z! Today it’s unwrapping presents, a quiet family breakfast and lego-making, talking to grand-dad on the telephone, a little practice on the new bike, some school, and dinner together with more fiddling around with the new presents. The Party is on Saturday. (Wish us luck. We’ve not hosted a fifth birthday party before.)

Sometimes technologies can be use for purposes the inventors didn’t really intend. I’m sure that when the designers of the iTunes music store set the thing up, they didn’t expect that you’d be able to use it to download esoteric papers in philosophical logic. But you can. All I had to do was submit the RSS feed of my papers to the iTunes store on...

Su Rogerson has brought to my attention a lovely rendition of Curry’s paradox, due to Peter Geach, in his Reason and Argument (Blackwell, 1976), pages 93–95. The discussion takes place at a car yard. I’ll quote the discussion, interspersed with some commentary. (I’m quoting from a draft of Su Rogerson’s thesis, and not from the text. I’ll check...

I’ve finally added enclosures to my RSS feed of papers. This means that if you subscribe to my papers page using that feed, and you’re using an RSS reader that handles enclosures (this feature is primarily used for podcasts), then you can get it to download my papers automatically. This has the side effect that you can subscribe to me in iTunes:...

I’m trying to neaten up this place a bit, and I need your help and advice. Have a look here and let me know what you think of it. I’m trying to make it easier to see what’s new, what’s changed, etc. In particular, you look down to find links to other new stuff on the site. This opens up the sidebars for four things. The most recent picture, my...

This morning I uploaded a few new papers to the Australasian Journal of Logic, one of the projects I (mostly!) enjoy working on. It’s an open access, fully refereed, online journal in logic. If you’ve not seen it before, browse around and check it out. Let me know what you think. One thing that an online journals make possible is the freedom from...

Today in Logic I talked about vagueness and the sorites paradox. Then when I get back to the office, I find that this Saturday, Alan Saunders on The Philosopher’s Zone has a program on – you guessed it – the sorites paradox. Is that a spooky coincidence or what? No, it’s not spooky. It’s just a coincidence. Anyway, from the little outline, it’s...

I forgot to mention that I have written another paper recently. It’s a proof theory paper, putting down some thoughts on modal proof theory that I formulated when giving the S5 paper around and about in the last six months or so. In “Comparing Modal Sequent Systems” I look at different ways to understand modal deduction. In particular, I argue...

I’m sorry, I truly am. Back in the period 1990-1992, I wrote a couple of papers on the semantics of relevant logics. I thought they were pretty nifty, and I submitted them to a prestigious journal. They got accepted. The first of these papers is “Simplified Semantics for Relevant Logics (and some of their rivals).” Unfortunatley, there’s a hole...

This little spot called Melbourne Is the city of my birth It’s not as hot as Brisbane or as far away as Perth, It’s not as small as Adelaide, Compared to Canberra, it’s bliss, And if you’ve been to Melbourne, You can give Sydney a miss… As the world gets scarier, It’s a pretty decent area Melbourne The envy of the world. I think that was a...

Z and I – together with around 80,000 other people – filled the MCG to watch the track and field portion of Day 9 of the Commonwealth Games here. Some highlights: The completed renovations at the MCG make the huge stadium very easy to navigate. We got there early, so had no long queues to deal with (once we were at the ground itself – it was...

Z and I went in to the city to have a look at the Women’s and Men’s Marathon held here for the 2006 Commonwealth Games. The city was buzzing, the crowds friendly, and it was great to get a glimpse of the lead runners: especially Kerryn McCann and Hellen Cherono Koskei who raced neck-and-neck right into the stadium. No matter how you cut it, 42+...

It’s a happy day for us logicians at Melbourne. Greg Hjorth is going to be joining the Department of Mathematics and Statistics later in the year, taking up a five-year, professorial fellowship. He’s a super-smart set theorist and model theorist, and I’m looking forward to having him around on campus.

The paper reviews a number of approaches for handling restricted quantification in relevant logic, and proposes a novel one. This proceeds by introducing a novel kind of enthymematic conditional.

An historical essay, sketching the development of relevant and substructural logics throughout the 20th Century and into the 21st.

My entry in a book of interviews of philosophers who work on the more formal side of the discipline. It gives an account of how I got into this area, what I think logic is good for – when it comes to philosophy – and where I think we should head.

The notion of that information is relative to a context is important in many different ways. The idea that the context is small – that is, not necessarily a consistent and complete possible world – plays a role not only in situation theory, but it is also an enlightening perspective from which to view other areas, such as modal logics, relevant...

Vincent Hendricks and John Symons are working on a sequel to their book Formal Philosophy, in which philosophers who use “formal methods” talked about their work, their motivations, and their take on the state of philosophy. For the sequel, they are opening things up for others to take an “interview” with five questions, to appear in the next...

Toby Ord (a former student of mine, now taking Oxford by storm), has written up a nice short essay on degrees of truth and degrees of falsity. It shows how you can get a very nice little algebra if you extend the usual non-classical idea of a 4-valued logic in which truth and falsity are somewhat independent with the “fuzzy” idea of degrees of...

I’ve finally joined the ranks of the zombies with white earbuds. My trusty 2GB black iPod nano was acquired on the way home from our Sabbatical, in a duty free store at Changi Airport. I’ve had a little while to experiment with it, and so far, it’s been working better than I’d expected. I take it with me on my early morning walks, sometimes...

Today is the first day of the new phase of our lives – Zachary Luke Parker Restall had his first day of school today. Well done, Zachary!

This morning found Z and me in the grocery store, doing yet more re-stocking of the pantry. Here are some hastily selected observations. Organic and fairtrade food has significantly higher market presence in the UK than in Australia. Our nearest Sainsbury’s had many more organic products than can be found in either of the two major chains here in...

I’m back in the teaching saddle for 2006. In Semester 1, I teach two undergraduate courses. 161-115: Logic and 161-212: Non-Classical Logic.

Happy New Year, my readers! We’ve landed in Melbourne (to a hot 8pm at around 42 degrees Celcius), and are slowly reconstructing our household bit by bit. The internet connection seems to work at least. We’ve managed to change lightbulbs, unpack bags, look at a bit of our large pile of mail, get the boy to bed (and even to sleep) and have some...

This is our article on logical pluralism. We argue that the notion of logical consequence doesn’t pin down one deductive consequence relation, but rather, there are many of them. In particular, we argue that broadly classical, intuitionistic and relevant accounts of deductive logic are genuine logical consequence relations. We should not search...

This is an introductory textbook in logic, in the series Fundamentals of Philosophy, published by Routledge. I use the text in my Introduction to Formal Logic class at Melbourne. It’s available at Amazon UK and Amazon US. The book was translated into Chinese in 2024. The book has a dedicated website at http://consequently.org/logic.

We’re in the middle of packing up our Oxford home, to start the short trip back. We land in Melbourne on New Year’s Eve, after some stops in Köln (for the Christmas Markets), Augsburg (for Christmas with friends), Frankfurt Airport (to get on the plane), Singapore (to break the journey, and give us some summer in close proximity to air...

A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline).

I’ve given my two talks here in St. Andrews, with really useful discussion in both of the talks. In the philosophy talk, questions ranged from matters of meaning theory, metaphysics and epistemology of possibility and necessity. Thanks especially to Daniel Nolan, Carrie Jenkins, Marcus Rossberg, Ole Thomassen Hjortland, Crispin Wright, Stephen...

… you’re on sabbatical. I’m now in St. Andrews visiting Arché for what can only be described as “November Madness.” I’m giving a seminar this afternoon in Arché/Philosophy (in the wonderful Edgecliffe building) and then tomorrow, I’m giving a seminar in computer science tomorrow. This means I’ll miss the Vagueness Seminar and a Philosophy...

We’re now in the second day of “week 1” of Michaelmas, here in Oxford, and the philosophy faculty library is considerably busier than it was in week 0, let alone the negative weeks. It’s just as well that I’ve got some writing done already. Today I’m heading off to Nottingham to give two talks. The Philosophy Department will get the first outing...

This post is a change of scene for those of you that have come to expect gentle meditations on matters personal. I’m going to experiment with posting some of my work scribblings as an irregular record of thoughts I’m having while working on sabbatical. It may well confirm the impression that you might have that I’m crazy, but hey, I have tenure,...

Here’s the second part of my reflections on our week on Iona. If you’re interested in that kind of news, read on. I haven’t mentioned the most significant thing about our time on Iona – the week was tempered by an event just before we left for the island. The story started on the Friday before we left Edinburgh on Saturday. It was my last day...

This is an extended post reflecting on the week in Iona. Read on if you want to find out what we did for a week on a small Hebridean island. It’s not immediately straightforward to get to Iona, when you start from our B&B in North Queensferry. Our day’s journey started early with a taxi ride to Edinburgh Waverley, and then a train to Glasgow...

The paper examines what its title says. Constant domain modal frames seem to be the natural semantics for quantified relevant logics and their cousins. Kit Fine has shown us that things are not that simple, as the natural proof theory is not complete for the natural semantics. In this paper I explore the somewhat simpler case of one-place modal...

Phew! We’re back in Oxford, and arrived in our house today. We’re in a cute little 2 bedroom house in the northern outskirts of Oxford, a quick busride down Banbury Road into Wolfson or the centre of town. I’m currently dealing with some of the backlog of email in a Starbucks (of all places!) with a wireless network. The week at Iona was great....

Too many things are happening for me to spend any time posting here until the whirl of activity settles down. Still, people have been wondering what’s going on, so here’s a bit of a run-down. After Logic Colloquium, I went back to Denmark to rejoin the family, to have a holiday in Blokhus with close friends. Much fun was had, involving sand...

Today is Day 4 of the colloquium. Yesterday was a day of rest, which for me involved a visit to the Byzantine and Christian Museum, in the morning, a lazy afternoon restructuring the order things in my ESSLLI course while staying in the shade, and visiting the Herakleidon Museum which featured an exhibit of Escher prints (the detail in some of...

It’s another busy day with lots of things to learn. Here’s my impressions so far, updated through the day. 9:20: Phokion Kolaitis is giving his second lecture — he’s good, and it’s been interesting to learn about dichotomy theorems in CSPs. Schaefer’s dichotomy results cast in terms of constraint satisfaction problems, are really interesting. The...

9:25: There’s wireless access in the large lecture theatre, so I’ll take notes and upload comments occassionally through the day. At the moment, Phokion Kolaitis is giving his first short course lecture on constraint satisfaction problems. So far he’s talking about examples of CSPs (graph colourings and 3-SAT are his first examples) and he’s just...

I’ll try this conference blogging thing, to see how it goes. Logic Colloquium has started, with the opening address by Charles Parsons from Harvard. His talk was on Paul Bernay’s later philosophy of mathematics — a subject of which I knew nothing. So I learned a bit. After Bernays’ collaboration with Hilbert at Göttingen, he left Germany because...

Remind me to check legroom on airlines before I book them for the first time – especially if I’m planning to write on the plane. Maersk Airlines has an interesting policy of offering seats in S/M/L sizes. S seats have a tight pitch of 29 inches (73-and-a-bit centimetres). You can upgrade to a roomier seet for a price–a fact that the stewards make...

I’m off to Athens tomorrow. Tonight I catch the train to København, where I stay overnight in a cheap hotel near the airport, to get my 7:30am flight. Logic Colloquium 2005 looks like it will be lots of fun. I’ve been busy writing slides, and I should use the time on the train to put the finishing touches on Day 2. Once they’re done, I’ll post...

I’ve been experimenting with a map using plazes, a neat little doodad that keeps track of where you are when you use a computer to access the net (if you explicitly log in yourself—it’s not spying on you without your consent). It powers the map on the main page here, and you can use it to generate a map of where you’ve been. Read on if you want...

We’re settled in Århus now, while Christine does work with a colleague on a research project. This gives Z and me lots of time for lots of fun. Yesterday’s fun was Legoland (Vibeke and Christine wanted to come too, so we all made a day of it). Z loved the rides, and the displays, and the Lego for sale. We bought a set for him to grow into....

We fly later today! The big study leave adventure starts later this afternoon. The first few weeks alternate holidays and work for Christine and for me, and it gives us lots of time to enjoy the company of our young son. Zachary and I are especially looking forward to Legoland in Billund and exploring the surrounds of Århus. Our apartment...

Sometimes music is best heard at volume. A case in point? The second movement of Shostakovich’s String Quartet No. 8. I recommend the Fitzwilliam String Quartet recording. (The Emerson Quartet’s recording is available on iTunes, but the Fitzwilliams’ isn’t.) (Apologies to our next door neighbours. I’m enjoying my last bout of loud music at home...

The Australasian Journal of Logic is firing on all cylinders again. As the managing editor, there was a period in this last semester where I wasn’t managing very well, and things piled up and got the better of me for quite some time. To speak overly frankly for a moment, I got quite depressed over the state that things were in and over my own...

A half hour of php hacking has finally produced a working archive page for the photos I’ve been posting from my phonecam. My little Sony Ericsson T630 phone has a terribly lo-res camera, but it’s fun to take shots now and then when you wouldn’t normally take photos. Now, instead of sliding off the front page when I upload another one, you can see...

I’m teaching some classes on proof theory at Logic Colloquium 2005 and ESSLLI 2005 soon. Spurred on a little bit by discussion of commentary at conferences, I’ve wondered a little bit about how I can get interesting feedback going during/after the presentations. (The material I’ll be teaching is from the book, which is a Work very-much-in...

I’m rearranging stuff around here, in preparation for the Big Trip. Let me know if anything broke in the transition.

This Queen’s birthday holiday moning, cool and clear, was a perfect time for Zachary and me to fly our hot-air balloon. The flight was short but glorious. Flying a balloon like this is not completely straightforward. You need to unfurl the balloon carefully, and make sure no bit touches the little burner on the ground (fuelled with cotton wool...

Since I’m on study leave from July, I’m not doing any teaching in Semester 2 this year. Hooray! (I need a break.)

Next travel thing: I’ve signed up at skype.com and I have an account to make super-cheap voice calls home and almost anywhere else from the computer while overseas at least, when I’m connected to the internet. It looks very well executed. There are clients for Mac OS X, Windows and Linux, and at 1.7 euro cents a minute for calls to any landline...

I’ve taught my last classes for 2005. I’m officially on study leave from July 1, until December 31. We’re off on our journey from July 13. First, Denmark, where I’ll be looking after Z, while Christine works with a colleague. (Z and I plan to have some fun in our time there.) Then I’m off to the Logic Colloquium 2005, in Athens, and ESSLLI2005 in...

Like almost everyone else, I’ve installed Mac OS X 10.4 Tiger, and it’s a really very good upgrade to the operating system. The system-wide search will be really handy. It’s indexed all of my documents (which includes a 2.3GB library of PDF files of other people’s papers), so being able to find the 29 papers that mention hypersequents (together...

Tomorrow I’m presenting a paper at the staff seminar in the Philosophy Department at the University of Otago. Given Charles Pigden’s delightful account of seminars at Otago, I’m not quite sure what to expect. Wish me luck!

I think that Google’s new search-inside-the-book service will prove to be quite handy to a researcher like me. It’s not satisfactory to read through a book like that on the screen (especially when copyright restrictions do not permit you to keep going after a couple of pages of continuous reading), but it will be a boon to research to be able to...

If you’re like me, you do research on the web, and you browse around different sites for journals, seeing what’s been published, and what you should read. Our library has online subscriptions for lots of these journals, so I can download the papers, file them, read them, etc. It’s all very nice. But it’s not always easy to get from the site to...

Here’s one thing I find comments on a website really good for: trawling for information. My spouse and I were talking over dessert this evening, over some lemon delcious pudding that she had made. She asked the question she asks every couple of years (when a self saucing pudding is made): How do self-saucing puddings work? They really are...

At logicandlanguage.net the author talks a little bit about comments on weblogs. On why one might allow them, or do without them. As you can see, I leave comments open here. (Behind the scenes there is a hardworking comment spam filter. Without that, this place would be deluged with spam.) I can understand why one would want the place to yourself...

I sometimes catch the tram to get to or from the office, and usually it’s a not unpleasant experience. This evening was not one of the usual reasonably relaxing fifteen minute trips down Flemington Road and through Royal Park. It’s remarkable how a violent scuffle between passengers can change the feeling throughout the tram. There was pushing,...

In this paper, we introduce a new natural deduction system for the logic of lattices, and a number of extensions of lattice logic with different negation connectives. We provide the class of natural deduction proofs with both a standard inductive definition and a global graph-theoretical criterion for correctness. We show how normalisation in...

According to the “knowability thesis,” every truth is knowable. Fitch’s paradox refutes the knowability thesis by showing that if we are not omniscient, then not only are some truths not known, but there are some truths that are not knowable. In this paper, I propose a weakening of the knowability thesis (which I call the “conjunctive knowability...

I argue for the following four theses. (1) Denial is not to be analysed as the assertion of a negation. (2) Given the concepts of assertion and denial, we have the resources to analyse logical consequence as relating arguments with multiple premises and multiple conclusions. Gentzen’s multiple conclusion calculus can be understood in a...

In this paper we introduce a distinct meta-ethical position, fictionalism about morality. We clarify and defend the position, showing that it is a way to save the “moral phenomena” while agreeing that there is no genuine objective prescriptivity to be described by moral terms. In particular, we distiguish moral fictionalism from moral...

Minimalists about truth say that the important properties of the truth predicate are revealed in the class of T-biconditionals. Most minimalists demur from taking all of the T-biconditionals of the form “ is true if and only if p”, to be true, because to do so leads to paradox. But exactly which biconditionals turn out to be true? I take a leaf...

Two short entries on two great philosophers of logic (and philosophical logicians) of late 20th and early 21st Century American philosophy, Nuel Belnap and Karel Lambert.

In this paper I consider an interpretation of future contingents which motivates a unification of a Łukasiewicz style logic with the more classical supervaluational semantics. This in turn motivates a new non-classical logic modelling what is “made true by history up until now.” I give a simple Hilbert-style proof theory, and a soundness and...

The wiki is lots of fun. Being able to edit the page you’re on, and freely create new pages by making new links, does seem to foster a new way of writing. It’ll be fun to see if any of my students catch on. If you’re interested in typesetting manuscripts in LaTeX, you might be interested in the notes I wrote up this evening. One on page layout,...

I’ve been pretty busy getting courses up and running for Semester 1. Some of this has involved starting writing my book, and setting up a wiki as a place to encourage feedback on the book and other things. Go and play there… (I’ll be interested to see how this goes.)

… when you fiddle with your book draft and manage to get it to compile with no overfull \hboxes and no underfull \vboxes.

Our friend Darren Rowse is blogging for tsunami relief over a 24 hour period. To make things interesting for him, we’re sponsoring him with a small amount for each different top level domain he uses in a post. It should make his posting nice and eclectic.

Matt Carter and Nick Trakakis are arguing over dialetheism. What’s dialetheism? It’s the view that some contradictory pairs of statements are true. It’s interesting that Nick is trying the line that contradictions (conjunctions of the form ‘p and not-p’) are meaningless. I always find it hard to judge claims of meaninglessness (since I don’t have...

I’m enjoying being back at work, but I seem to be procrastinating rather badly. Instead of writing my grant application and getting through my growing pile of emails, I’m doing research. I blame this on three things: I just don’t want to deal with my emails and my grant application. I’ve recently purchased two black-cover 100 page A4 spiral bound...

Tomorrow I’m back in the office, and back at work after my short Christmas/New Year break. It’ll be time to plough through that 45-email inbox, and see what else is waiting for me. I’ve started converting the news item archive pages to the new template. Expect more fiddling as I try to get them looking clearer. (They seem a bit too busy right...

This semester I am teaching the first-year subject Introduction to Formal Logic and an honours (fourth-year) seminar Logic and Philosophy. I’ll teach the honours class from draft material from my (as yet only in scribbles in my notebooks) draft book.

My redesign for 2005 is in progress now. After some problems (I managed to delete the writing page in a fit of cutting-and-pasting) I have some things on the way. There are lots of changes behind the scene. The linklist in the right column is now powered by del.icio.us, which is wonderful. The sidebars (left and right) contain other information,...

I’ve been rather busy for the last little while, as the absence from the website might indicate. Here is a list of what’s been happening, which involves not a little bit of trumpet-blowing, because a lot of the news has been good and it’s time for me to share. Last week I spent an enjoyable (if rather wet) week in Canberra, touring the sights...

Take these shoes Click clacking down some dead end street Take these shoes And make them fit Take this shirt Polyester white trash made in nowhere Take this shirt And make it clean, clean Take this soul Stranded in some skin and bones Take this soul And make it sing. That’s not a bad album, and not a bad song.

I’ve just bought some sheet music for the first time in 18 years or so. Let’s hope my violin technique is up to this. I know I can play the notes (or close approximations to them). It’s sustaining the technique for 10 minutes that I’m not so sure about.

In the second half of 2005 we’re planning to travel, on sabbatical. The C, G and Z show will be based in Oxford for Michaelmas. Before arriving in Oxford, we’ll be doing some European touring. C will be visiting a colleague in Denmark. I’ll hopefully be presenting at Logic Colloquium 2005 in Athens (July 28 to August 3), and ESSLLI2005 in...

One stroke of good fortune today. In a shopping trip with Z this afternoon, while looking for a Super Secret Present at JB Hi-Fi I found a set of Sennheiser HD 497s on sale. Picking these sweet headphones up for $15 was very very nice. Especially considering that this was approximately 80% off the list price. Oh, and they’re very nice headphones.

Oh well. Sad news tonight, with the conservatives returned with an increased majority here in Australia. Most worrying is the fact that their representation is increased in the Senate. We’re going to have an interesting few years ahead. (Let’s see how the forces for succession develop: Costello, Abbott, Turnbull…)

Stephen Neale, in Facing Facts takes theories of facts, truthmakers, and non-extensional connectives to be threatened by triviality in the face of powerful “slingshot” arguments. In this paper I rehearse the most powerful of these arguments, and then show that friends of facts have resources sufficient to not only resist slingshot arguments but...

In case you were wondering where this site was over the last couple of days: it turns out that both of the domain name servers that were registered for this site are in Florida. Not the best place to be over the last few days. I’ve now got three DNS machines registered for this domain, and they’re not all in the same continent, so hopefully it’s...

Our Federal Election is to be held on October 9. Our current Prime Minister says that this election is about trust. Well, I’m glad that the unannounced election campaign is over and the announced one is on its way. I don’t think that we’ll get a government that we can, or should trust in the result of this election, and I think that trust is...

I’ve been feeling like redesigning this site, yet again. There’s a lot about the design here I like, yet it’s not quite right for some of what I want to do. If you have any likes or dislikes about this place, please leave a comment here. I’ve got some ideas of what the redesign might feature, but I don’t want to get rid of anything that my three...

I suppose I should post something, even though the urge to post seems to have gone for a while over the last months. Let me fill you in on what’s been happening around here. I’ve been doing work with Mark Lance, who’s been visiting the Philosophy Department for a couple of months to do research with me. This has been immensely productive. We seem...

This morning I had my first ever “parent/teacher interview,” with Z’s carers at childcare. They seem to like him, and he generally likes them (though Z is choosy when it comes to who counts as his friend: the select group is pretty small at the moment). So now I know how they take him to be going on emotional, social, cognitive and motor...

There is widespread agreement that the law of non-contradiction is an important logical principle. There is less agreement on exactly what the law amounts to. This unclarity is brought to light by the emergence of paraconsistent logics in which contradictions are tolerated (in the sense that not everything need follow from a contradiction, and...

I’m not here, because I’m elsewhere. Elsewhere is lots of fun, and 1/3 of the way through, we seem to be having a very good time. I’ll report back with some highlights later. But now I’m off to another talk.

This last couple of weeks has been super-busy-hectic. Z and I fly up north this afternoon for a family visit. On Sunday I go off to the AAP Conference at South Molle, and Z stays with his Granddad for a couple of days, to be joined by his mum who returns from her little Europe conference trip. One piece of advice: If you’re preparing a conference...

Is there anyone who wants a GMail account that doesn’t have one by now? If you do, let me know in the comments. I have a few invitations I can burn. Update: This batch of invitations are gone.

Now this is a question which is much more sensible to ask than you might otherwise think: “Why can’t I manage academic papers like MP3s?” (the link is to a pdf of a paper by James Howison and Abby Goodrum). My “paper archive” is a fairly large 2GB (not as big as my “music archive”, I suppose) with about 6000 papers, and it’s catergorised under...

It’s going to be a slow period on the ’net for me in the next little while. My creaky powerbook seems to have developed yet another fault (now its AirPort connection is completely bung, so I’m only online at home when I directly plug in to the ADSL modem, which boots off the other users of the connection). This, together with the wonky right...

There’s no accounting for musical taste. This morning Z was a little upset. I decided to put on some music for him. First selection: Big Red Car. A little voice responds, with a tremor. “Dad.” I ask, “Zack, what is it?” “I don’t want this on. I want your music.” “OK.” Takes CD out. Replaces it. “Is this any better?” He sounds much brighter. “Good!”

I never thought I’d comment on Big Brother, but when I learned that the inmates aren’t even allowed writing implements inside, I am convinced that the place is completely inhumane. I can’t imagine a life where I can’t write, whether on paper or on the computer. I suppose that the restriction serves a couple of goals of the producer. (1) no...

Great Ocean Road, May 29, 2004. [Larger Version]

Assertion, Denial, Accepting, Rejecting, Symmetry, Paradox, and all that (the paper with the ridiculously long name) has been given a few more paragraphs in preparation for an outing. Comments, as always are welcome.

If you browse my academic genealogy, you’ll notice that my ancestry goes back to Hardy (a great-great-great-great-great grandfather: hereafter a great^5 grandfather), Schur (another great^5 grandfather), Cayley (a great^8 grandfather), Frobenius (a great^6 grandfather), Weierstrass (a great^7 grandfather) and Gauss (a great^9 grandfather). I just...

Greenfleet’s Tree Totaller is a simple way to estimate your annual greenhouse emissions from your use of a car, your household and your air travel. As a household, we’re running at an annual rate somewhere between 30 and 40 tonnes. (The indeterminacy here is chiefly due to my ignorance about the number of flights we’re making this year.) Our car...

Oh, and you’re wondering where I am? This is the last teaching week of semester, and I’m busy teaching, organising a couple of conferences, writing papers and doing a bundle of other stuff. Expect to see some more things in the pipeline very soon.

Who are Boole, Fitch, and Tarski? That’s Richard Zach’s short story about the history of logic. His long (and interesting) story is here. It looks very good.

Doing anything from July 12 to July 14? No? Well, why not come to my little conference. It should be lots of fun, if you like philosophy, meaning theory, logic and that kind of thing.

I haven’t been able to write about the prisoner abuse scandal in Iraq, and the brutal murder of Nicholas Berg. However I do wish that I had written what Toby has. (See his entry for May 8.)

“Not Every Truth Can Be Known” is now up to version 0.9, and it’s having its first public beta test on Friday morning in the local logic seminar. Come along (Cussonia Court Room 1, University of Melbourne, Friday 11am) and enjoy the ride if you like that kind of thing. Christine reminded me that when talking about epistemic logic one should, of...

This looks very nice indeed: The Haskell Road is a textbook on elementary logic, mathematics and programming, based around my favourite programming language Haskell. I’m glad that this wasn’t the textbook in my introductory computer science course, long ago in 1986. If it were, I may have fallen in love with computing and never become a...

Christine received an early Mother’s Day present. The NAD C521BEE sounds gorgeous. A weclome bonus is that it plays every CD we feed it, unlike our dearly departed Yamaha CD player, which served us well for the last 10 years or so, but it started giving up the ghost (being very picky about what CDs it felt like playing) over the last couple of...

“Not Every Truth Can Be Known” has been updated with some brand spanking new theorems for your delectation. Comments are, of course, welcome over there.

Bernhard Bolzano (1781-1848) Bolzano was a philosopher, mathematician and logician who had important things to contribute in each of these fields. He’s probably best known for what he has done in mathematics: the precise definition of continuity when it comes to real-valued functions. But for my money (and in my discipline) Bolzano was worth much...

I’ve fiddled with the colours for winter. Let me know if in mucking around I’ve made anything worse for you.

I’m pleased to point you to the next article published in our little ejournal. Max Cresswell’s paper “Possibility Semantics for Intuitionistic Logic” was uploaded earlier today.

Well, it’s taken me longer than I wanted to, from conception to first rough draft, but here it is: ``Not Every Truth Can Be Known: at least, not all at once.’’ Comments are most welcome over there.

I’ve just heard that the AJL will soon appear in the DEST Register of Refereed Journals. This makes me happy. If you are an editor of a refereed journal, please take the time to get your journal registered on this list. (It’s not difficult. The submission process is straightforward.) If you are on this list, then Australians who publish in your...

Do you want to come to the Melbourne Philosophy Department and teach my Reasoning and Uncertainty course for me for Semester 2, 2004? I’ve got some research money, and I’m using it to buy out some teaching to give me more time to write. Check the details if you’re interested in applying for the position. If you’ve got any questions, contact me....

Now that Christine’s back from overseas, I seem to have entered another busy/quiet period. In the last week we have had Z’s birthday (he’s now a precocious three-year-old), Easter, our midsemester break, various small house renovation things, and catching up on previously unattended email. (The inbox is down to two items as of this afternoon,...

In between teaching, looking after Zack, keeping a house in order and occasionally getting some sleep, I am thinking about Fitch’s Knowability Paradox. This thinking seems to be turning into a little paper entitled “Not Every Truth Can Be Known: at least, not all at once.” I’ll post the thing on this site as soon as it’s a rough draft.

The University administration made some decisions today on funding and access changes for 2005. There were student protests on campus today, over the decision. The University’s council chambers are in our building, and the building was locked down from 11:30 this morning, in preparation for the protests. (We were asked to leave the building for...

Are computer technical “support” positions staffed by robots? Or are they simply underqualified, underpaid people in call/email centres? Probably the latter, as far as my experience (limited to just one case, of course) is concerned. Let me cast my support request out to cyberspace to see if I receive a more useful response. I have just purchased...

Castlemaine, January 2004. [Larger Version]

Once the “underworld shootings” started in Rathdowne Street it felt close to home. But when it occurs just a few blocks down the road …

Here’s a research project for you. Look at the physical interpretation of intuitionistic logic in the Markopoulou and Bell papers I mentioned yesterday, mix in Nuel Belnap’s really interesting account of an indeterministic relativistic universe in “Branching Space-time” and the Thomason point/history semantics for temporal logic motivated and...

The mathematically/logically/physically minded among you should take a look at “The internal description of a causal set: What the universe looks like from the inside” by Fotini Markopoulou. (Found from a reference to in two papers by John Bell, which was found in turn by way of Brian Weatherson.) This is interesting, deep material at the...

If I post anything here between now and Easter, consider yourself lucky. Christine (my omnicompetent spouse) is enjoying well-earned time away from the house while taking a research/conference/catch-up-with-friends trip to London, Oxford and Glasgow. I, therefore, am enjoying even more time with my son. It follows that any posts here are either...

Robert Brandom recently addressed the trustees at the University of Pittsburgh (where he works). His talk addressed different issues, including the history of the Pitt philosophy department, the role of a research university, and how we ought to conceive of the relationship between the university and its students. Go read this extract of the...

Today I received offprints of “Paraconsistency Everywhere,” an article I wrote quite some time ago (it was essentially finished in 2001). It appears in the 2002 issue of the Journal, yet it has only just appeared on my desk. This comical state of affairs continues when you look at the bottom of the published article where it indicates that the...

Canberra, January 2004. [Larger Version]

On Saturday night I went to see Fog of War with my brother-in-law, who is visiting Melbourne for a few days. I was absolutely knackered (must have been something to do with staying up until 1:30 that morning getting the book away to the publisher), but I managed to stay conscious for 95% of the movie. It was a striking movie in a number of...

Kai von Fintel has plans like mine on academic book publishing. Maybe we can kick the revolution along just a little.

Home, February, 2004. [Larger Version]

On and off, I've been thinking about what I'm going to do with my next book. I mean, I'm planning to write the thing, and to see to it that it is published by a decent publisher. So much is required for it to get the kind of institutional recognition that is necessary for people in a position like mine. However, I'm looking for something more...

My iTunes library filtered on the word “wind”: Messenger Wind: Bruce Cockburn (You’ve Never Seen Everything). Child Of The Wind: Bruce Cockburn (Nothing But A Burning Light). The Wind: Keith Jarrett (Paris Concert). A Cool Wind Is Blowing: Kronos Quartet (Released 1985-1995). I Envy The Wind: Lucinda Williams (Essence). An interesting collection....

Entries for both the news and snippets section from my pre-hiatus website have now appeared in the new design. You can browse through the recent past here and here.

Home, February, 2004

Reading the paper with this title at an online journal got me thinking ... The author concludes: The consequence for philosophy of religion is quite simple--that if God is an agent, his hands must be bound by logic. To many, this might seem to be a conclusion which is so trivial as to be scarcely worth stating--apart from Descartes, and a few...

The Australasian Journal of Logic's Volume 2 is beginning its gradual release into the wider world. We have some other interesting papers in the pipeline for 2004, so stay tuned.

Canberra, February, 2004

Teaching for 2004 Semester 1 is now well underway. My classes for this term have been enjoyable in different ways: Non-Classical Logic is a second/third level logic class. I've decided to follow Graham Priest's book An Introduction to Non-Classical Logic rather closely, which means I don't need to make too many further decisions. (It's designed...

October, 2003

This site has been sitting fallow for eleven months. That's far too long in short-attention web land, so no doubt I've lost my vast readership. It's time to reboot it, so here we go. There are a few changes that have been on my mind for some time. The look. Tired of white, tired of websafe colours, I've gone to earth tones for a change. Sterility...

It is well known that contraction-related principles trivialise naïve class theory. It is less well known that many other principles unrelated to contraction also render the theory trivial. This paper provides a characterisation of a large class of formulas which do the job. This class includes all properly implication formulas known in the...

I defend logical pluralism against the charge that One True Logic is motivated by considerations of warrant preservation. On the way I attempt to clarify just a little the connections between deductive validity and epistemology.

Published in a special issue of Logique et Analyse, on Truthmakers, edited by Peter Forrest and Drew Khlentzos. This expands on my paper “Truthmakers, Entailment and Necessity" by showing that the theses on truthmaking given in that paper are mutually consistent. It does this by providing a model in which each thesis is true. This model is an...

Zachary and Erasmus facing off: April 2003. Happy second birthday, Zachary! Here’s to many more happy years of growing up.

Having a young child gives you lots of new examples about language learning and concept acquisition. (It also provides you with many opportunities for experimentation, but I will set that to one side, for the moment.) Here is one such example: On Friday morning, I was changing Z’s nappy and getting him dressed. He was in a happy mood, and I asked...

I have refrained from making any public comment about the coming war with Iraq that Australia is about to enter. Partly out of general reticence, partly because the whole matter is very depressing, and partly because my own thoughts and feelings are inarticulate. However, one way to deal with inarticulate thoughts and feelings is to attempt to...

Zachary helping Christine in the Kitchen. March 2002. Zachary had a difficult day today, missing his afternoon sleep, and getting a bit cranky as a result. This evening, as I was cooking dinner for Christine and myself, and supervising Zachary eating his dinner, he decided he’d had enough of his meal (i.e., he had fingered it a bit, no more),...

Mark Balaguer has, in Platonism and Anti-Platonism in Mathematics, given us an intriguing new brand of platonism, which he calls, plenitudinous platonism, or more colourfully, full-blooded platonism. In this paper, I argue that none of Balaguer’s attempts to characterise full-blooded platonism succeed. They are either too strong, with untoward...

A sign on the docks on the Yarra. December 2002. It’s time for a new picture. This picture was taken last December on the infamous Williamstown Ferry trip. Classes start next week, and I’m looking forward to them, even though preparation has been a bit tight. I am especially interested to see how my fourth year honours class enjoy what I have in...

Zachary with spots. February 2002. Zachary’s chicken-pox spots are fading now, so he is probably past the most infectious stage. This photo is from the first seriously full-on day of spots, last Thursday.

February pictures of Zachary are here. They were taken on our day trip to the Dandenongs with Uncle Martin. Zachary was pretty keen on that straw. Unfortunately for him, and for us, Zack’s come down with chicken-pox. The photos are all pre-pox, so there are no pictures of spots. Or of fots as he calls them.

Sometimes it seems like there are too many thoughts to think and too little time in which to think them. Here’s an example: I really ought to think of a detailed response to Brian Weatherson’s comments on my two envelopes paper co-authored with Graham, but that detailed response will have to wait a little while. However, let me write a little...

Zachary, at a café in Sassafras. February 2002.

Details are out for the Brunswick Music Festival for 2003. Looks like it will be fun. The Sensitive New Age Cowpersons (gig details, their own site) are good for a laugh.

Both News and Snippets sections have corresponding RSS feeds, which you can use with feedreaders like NetNewsWire or AmphetaDesk. (Some of the five readers of this site already use these tools, but I never publicised the links. Now you can all know they’re there.)

Butterfly, at the Zoo, December 2002. Here’s the 2003 redesign for the site. It’s late, if you count calendar years, but it’s early, if you count our teaching year. Classes don’t start for a couple of weeks. The design includes the ‘Snippets’ section, which will include links I find in day-to-day browsing. This news section will contain photos...

Mac OS X users might be interested in Meteorologist, a menubar or dock thingy which tells you current weather and forecasts for the locations you suggest. Just the thing for me, as I'll be off in Dunedin at a conference next week. At least I'll be prepared for the wet and cool weather.

Jazz at the Zoo. January 11, 2002. The place was packed with easily more than 4000 people crowded in to the Zoo grounds to hear Don Burrows and Nina Ferro in the Zoo Twilights music program. They were in good form, and a fine night was had by all.

John Baez’s Crackpot Index seems to me to be a pretty good measure of the difficult to define phenomenon of crackpottedness. Notice the relatively low cost of outright inconsistency compared to nearly everything else. That warms my heart.

Quantum mechanics is just plain weird. I don’t really understand it at all, partly because of the strange nature of the probabilities in QM. They certainly seem to fit observation (so physicists say), but what do they mean? Well, it just might be that they are traditional probabilities after all. That is, Gerard ’t Hooft has proposed a new...

Brett Lee in delivery stride at the MCG today. Today was spent at the MCG, on the second day of the Boxing Day Test. My brother, my nephew and I spent a delightful day soaking up the atmosphere, enjoying some fine batting (especially Justin Langer and Martin Love) and some fine bowling (each of McGrath, Gillespie, MacGill and Lee were in...

Chairs on the Williamstown Ferry. December 2002.

The Wired article on the upcoming movie adaptation of Stanislaw Lem’s novel, Solaris is surprisingly good. It doesn’t encourage me to go and see the movie, but it does make me want to go back and reread my Lem novels and short stories.

I just found a very insightful interview with Philip Pullman, the author of the His Dark Materials trilogy. I haven't read the trilogy yet, but I probably will before I get to Harry Potter. Third Way, the mob who published the interview, produce some of the best (Christian) theologically informed social comment around. Sadly, that's not saying...

I love the way the BBC news report about the High Court of Australia's interesting decision on defamation and internet sites leads with a really nice picture of the National Library of Australia. The library is next door to the High Court, which is a very different building.

I have to let you know that I really don't enjoy marking first year logic exams. I love teaching the subject, but the marking is just a hard slog. And it's depressing in the cases of failures. The bright spots are the cases of really excellent work. But the tedium is pretty tedious.

Richard Jeffrey died on November 9. Now both authors of my favourite text on Gödel’s theorem and computability theory have left us. (After November, the link to this story on the Princeton news page will expire. The archived news item should appear here, with any luck.)

More reason to be thankful that The Age publishes Peter Roebuck’s commentary on the cricket too. It makes breakfast newspaper reading enjoyable. Here is one example: Lehmann will be popular with spectators because he is an antidote to the prevailing fashion, a throwback to the days of blue-collar cricketers. As far as this column knows, he spends...

I sometimes complain about grade inflation, the phenomenon of too many students being given high grades. According to Alfie Kohn (whose work I respect) maybe I shouldn’t worry so much.

Strangely apposite text at church yesterday. Matthew 6:19ff: “Do not accumulate for yourselves treasures on earth, where moth and rust destroy and where thieves break in and steal...”

There'll be no new photos here for a little while. Our house got broken into yesterday, and a few things -- including the camera -- were nicked. Everyone's OK, however. A little bit shaken, but OK.

Zachary playing in the back garden today. October 2002.

The terrible shooting at Monash University took place in the building housing the Philosophy Department, and at which I gave a seminar in one month ago. No-one I know was physically hurt, but I'm sure everyone who works in that building will find it hard to go back to work tomorrow.

I was searching for the current bibliographic reference for Reinhardt Diestel's canonical text Graph Theory, and lo and behold, the entire text available online for my perusal.

Be sure to gaze at the amazing checkershadow illusion. Go now, then come back here. A cursory check with a little computer program I have (Digital Color Meter in /Applications/Utilities/ for those of you with MacOS X) verifies that the two squares which look so different are, in fact, the same 42% grey. But the surely don't look the same. The...

The bugs aren't ironed out yet, but I've enjoyed playing around with iCal, and Movable Type in order to automatically send my calendar of logic seminars (maintained locally on my own computer in my diary) to a web page which announces them to the world. It's not quite finished yet, but it gives you an idea of what we're doing.

A happy boy. September 2002.

There's a robust, freely available implementation of Prolog available for lots of platforms: GNU Prolog. It looks like it might be quite useful to me.

We went to the Zoo on Sunday afternoon. It was very busy, dodging all of the other prams and strollers. The zoo is only a couple of minutes (drive) away from our place: it’s halfway between our house and the university. So, we’ve become “Friends of the Zoo”. It’s great to visit during the week, when it’s much quieter.

If I stand really close to a window of my office, I can just get a tiny signal from my Campus wireless network.

With the arrival of iChat, I now have an instant messaging client. My AIM (AOL Instant Messenger) username is cutelimination. If you have a chat client and you want to contact me that way, you could always check if I'm online. I'm not online that often, but you can try your luck.

zerotothree.org is a helpful resource for people like us, with little kids. I especially like the mix of information for parents and early childhood ‘professionals’.

Sorry for the lack of updates lately. We've been slowly settling in to Melbourne. Zack loves his childcare, but settling in has meant a range of new infections in quick succession. (Conjunctivitis, a severe ear infection and gastroenteritis.) The latter, he managed to give to me, and this has meant that I now have new insight into the etymology...

This is seriously elegant: Apparently, three Indian mathematicians have shown that you can test primality (deterministically) in polynomial time. That's incredible. More incredible, I seem to understand the paper. (The authors seem proud as punch, as you'd expect, cracking a centuries old problem.)

Paul Kelly has written a song I Guess I Get A Little Emotional Sometimes in response to the plight of the refugees in detention in Australia.

I'd heard that the new Archbishop of Canterbury was about to be appointed, but I hadn't heard the result: Rowan Atkinson has been appointed the 104th Archbishop of Canterbury.

Campus is a whole lot more crowded now that classes have started.

As Australians are only too aware, the ABC, our national broadcaster, is a political football. Liked by neither of the major parties in the Federal Parliament, it suffers regular funding cuts. Tim Bowden's analysis of the situation is the best I've read for a long time.

It's come to my attention that my old Macquarie Uni email address is bouncing. If you want to email me about personal things, use my consequently.org email address: greg@consequently.org. If you want to email me about work things, use my University of Melbourne email address "restall at unimelb.edu.au". (Convert that text into the obvious email...

This looks like the course for me: Visit Sydney Road (warning, it's a PDF file). The Centre for Adult Education offers a one-day course on the main road just near my place. Looks like a nice way to spend 11 to 2 on Saturday.

Here is a helpful short history of Brunswick, our new home.

Moving house is tiring. Moving house with a young child is exciting, but very tiring. Moving house to a new city, and rewiring your brain to cope with the changes in weather, shopping, driving, childcare, work, and the innumerable other habits which need to be unlearned and relearned, is very very tiring. Moving house and waiting five days for...

South Korea's victory did not go down too well in Lygon Street in Melbourne. Next week we'll be living a stone's throw from there.

Even more strangely, some parts of the building seem to be on the M2 Motorway, and others are in Epping. Space warps strangely in Building W6A. I will miss it.

According to my new mobile phone, different floors of my office building here at Macquarie are respectively in Denistone, North Ryde and Marsfield.

Zack loves his car, which he gets to drive at playgroup. Alas, next Wednesday is his last time at playgroup before we move to Melbourne.

Don Mannison's Notes on the Existence of God. It is to my eternal dismay that Don passed away before I was a postgraduate student in Philosophy at Queensland, because I would have loved talking with him about this material.

Success! We'll soon be signing a lease to live in this house: It's a sweet three bedroom cottage, with a little backyard and front garden. Room enough for visitors, so come and visit sometime. We move in when we arrive in Melbourne: in around two week's time. (I never thought I'd live in a house with a picket fence, but there you go.)

I'm spending most of my time and emotional energy finding a place to live in Melbourne. It's now possible to do a fair bit of this at a distance, due to websites listing available properties, but of course you have to be there to inspect properties. Timing, as usual, is almost everything. In this business money is also almost everything. It...

A helpful summary article in the Chronicle on the proliferation of biographies of philosophers. The central question is whether biography of philosophers illuminates the philosophy itself. Lots of people say there's nothing one can say about there other. Others say that all philosophy is biography. Here's one case where I steer a middle path. I'm...

Today's listening: those tracks in my playlist featuring God: Rejoice in God O Ye Tongues [Benjamin Britten] ¶ God Rest You Merry, Gentlemen [Bruce Cockburn] ¶ Play God [Chagall Guevara] ¶ God's tender mercy knows no bounds (solo soprano) [George Frederic Handel] ¶ That God is great (solo baixo) [George Frederic Handel] ¶ God's Dub [John Daly and...

For some reason, I seem to pay attention to news reports like this one. Real estate worrying is silly, but strangely compelling.

For future reference.

The famous obfuscated put-down "this book fills a much needed gap in the literature" has many, many friends.

not only is the bremsstrahlung ∑ lowercase audio site a blast from the past with its early macintosh system appearance -- lowercase audio provides for a challenging and rewarding listening experience. try it for yourself.

I've just been invited to give a lecture at the 12th International Congress of Logic Methodology and Philosophy of Science in Oveido, in August, 2003. This is Very Nice. The first really big international conference I ever attended to was the 10th LMPS Congress in Florence in 1995 (I was a postdoc then), and I had a truly wonderful time. I gave...

The Department of International Relations at the Australian National University's Research School of Pacific and Asian Studies publishes a lot of interesting material. Their "keynotes series" are intended for the general public. Keynote 1 is The Day the World Changed? Terrorism and the World Order, and Keynote 2 is Refugees and the Myth of the...

Epitonic.com advertises itself as providing "Hi Quality Free MP3 Music." The quality is variable, but the range provides hours of aural exploration. My music player now has a clutch of math rock songs.

The Drawing Board is, as it advertises, an Australian Review of Public Affairs. It contains accessible interesting articles on instituitions in Australian public life.

We are all boat people. Strategic information about the asylum-seeker issue, here in Australia.

Stephen Jay Gould, Biologist and Theorist on Evolution, Dies at 60.

East Timor becomes independent; Sir John Gorton dies.

Consequently.org now has a new home. It's no longer hosted from my desk at work. It's now hosted by professionals. This way, it will continue to exist even when I'm "between desks" in late June. Hopefully the transition has been unnoticed by you. (It was relatively painless here.)

Manly, January 2002

Here's the details of the Federal Budget, handed down just now. (Notice how the Treasurer likes talking about the "fiscal surplus" rather than the "cash defecit".) And here's the Sydney Morning Herald's commentary. For changes in Higher Education, we must wait for the currrent minister to come down with his grand plan.

Jobs in logic are pretty rare. So now that Auckland is advertising, you should hop to it and apply. Auckland has one of the largest and most diverse philosophy departments in Australasia, and it's a good place to be. Auckland University, New Zealand, Department of Philosophy. Lecturer (=USA Assistant Professor), tenure track; semester system, 1.5...

This makes me queasy.

... the Internet radically redefines a person's psychological relationship to time and space. Attention is rivetted on what is tangible, useful, instantly available; the stimulus for deeper thought and reflection may be lacking. Yet human beings have a vital need for time and inner quiet to ponder and examine life and its mysteries, and to grow...

Here's how to mark a book.

I like that flag, and I don't think that Australian white wines had anything to do with it.

This letter is an excellent piece of reasoning and rhetoric. It will be fun to see how Peru goes with Bill Number 1609, and what the other Bill does about it.

The current ASIO bill before federal parliament is a very big worry. No-one should be allowed to arbitrarily detain people on suspicion of having contact with a member of an what has simply been designated by the Attorney General as a terrorist organisation. As an academic who regularly comes into contact with hundreds of students on a daily...

Zachary, Martin, Christine and me. Blue Mountains, April 2002

I don't normally spend my time worrying about the monopolistic practices of that software company, but this case is too bizarre to go unremarked. In a nutshell, at this site Microsoft explain that if a computer is donated to a school, it's a legal requirement that the original software installed on the computer be donated with it. Notice that...

Not only do neutrinos have mass, they also come in vanilla, chocolate and raspberry.

Do you have bandwidth and a love of fine typography? If so, download this delightful movie about Firefly Press, and see the difference letterpress makes.

There are more rumblings about higher education and its funding here in Australia. Everyone agrees that universities are underfunded, but there is not a whole lot of agreement about what to do about it. The recent discussion paper, flagging increased deregulation for public universities, has sparked some debate. I notice a change in my own...

Zachary admiring the fish, April 2002

It's fun for all the family at John's Combinatory Logic Playground.

A review of three books on the intersection of politics and science, from Richard Lewontin, published in the NYRB.

It is not an exaggeration to say that many in Europe are in shock tonight...

Now you know what would happen if the Moon were made of Green Cheese.

The real estate market here in Sydney is insane.

Circular Quay, March 2002

In which a man is imprisoned for working on the subway in New York.

She said ‘Mommy, is that God singing?’ I said, ‘Simone, why would you think that?’ And she said, ‘Because his voice is funny, but it doesn’t make me laugh.’

James Pryor's guidlines on writing a philosophy paper: "Don't begin with a sentence like "Down through the ages, mankind has pondered the problem of...'" That's right. Please don't begin your essay like that.

You Are Here: public art inspired by algebraic topology. The algebraic topology of Brouwer's fixed point theorem is profound. The artists' explanation of the theorem isn't so inspired, but they're artists not mathematicians. The art is inspired. You are here. No, that's not right. I'm here, you're there...

Guess the context for this: "Personally, I would say 'Go to Australia'. At that stage anything else seems pointless." Now go here to find it. Surprised?

Scott Raymond points me to Pascal’s Wagering: the perils of a life of gambling. Banned from the casinos, Blaise rolled up huge debts with illegal existentialists, who set arbitrary odds and paid off arguments on a whim. After losing three times in a week to the idea that all of human consciousness is the precocious hallucination of a disembodied...

Happy Birthday, Zachary! You're the picture of a happy one-year-old.

The new design is online. Go to the archive page for past entries. If you have any comments on the new design post them on consequently.org/discuss.

Zack is learning object permanence. Just now he’s spent a couple of delightful minutes putting Shaun the Sheep on a cupboard shelf, closing the door. Waiting a while, opening the door, smiling, picking up Shaun, closing the door, then opening it again and repeating the process. Ad infinitum. I think he's getting the point that Shaun is still...

Bijan Parsia is reading Appiah's In My Father's House. From monkeyfist.com.

No Sugar: Greg Egan on asylum-seekers.

Do you like your science fiction with a social conscience? If you do, try these: Fifty Fantasy & Science Fiction Works That Socialists Should Read.

Browse the MoMA exhibit The Russian Avant-Garde Book 1910–1934 online. Makes me wish I were there myself.

Spend a few minutes exploring Bembo's Zoo. I love the giraffe, rhinoceros and octopus. (The koala is less than perfect, with that odd tail.)

Linotype have posted an excellent feature on Jan Tschichold for the 100th anniversary of his birth.

"The text is wonderfully clear and avoids the tedium of many introductory logic texts. The examples, exercises, and suggestions for further reading are all good. This is the only introductory text I know of that introduces students to some of the philosophical problems logic pertains to and intersects with. It is the type of book I would like to...

2002/03/21 I seem to be the 10th search result on AltaVista for "unthinking unmanned criticized submarine teletype." What on earth could this mean? 2002/03/20 Who wrote this? Theories of new types of inference, ignored or misunderstood by the traditional logic, have at the same time been discovered and worked out with true mathematical elegance....

A revision of the Handbook of Philosophical Logic essay on relevant logics, updating it to include work on display logic, relevant predication, Urquhart’s undecidability and complexity results, and connections with other substructural logics.

Paraconsistent logics are, by definition, inconsistency tolerant: In a paraconsistent logic, inconsistencies need not entail everything. However, there is more than one way a body of information can be inconsistent. In this paper I distinguish contradictions from other inconsistencies, and I show that several different logics are, in an important...

In this paper, I distinguish different kinds of pluralism about logical consequence. In particular, I distinguish the pluralism about logic arising from Carnap’s Principle of Tolerance from a pluralism which maintains that there are different, equally “good” logical consequence relations on the one language. I will argue that this second form of...

We consider the virtues of relevant arithmetic couched in the logic E of entailment as opposed to R of relevant implication. The move to a stronger logic allows us to construct a complete system of true arithmetic, in which whenever an entailment A → B is not true (an example: 0=2 → 0=1 is not provable) then its negation ~(A → B) is true.

2002/02/27 A two week absence from this site is pretty large, at least when its unannounced. As you can probably tell, I'm snowed under. Slowly digging through that inbox and the pile of administrative work which requires doing. You might even get a link recommendation or two from me in the next few days. But I'm not promising anything. First, I...

2002/01/31 Dave Scarratt sent me a link to the Ethical Philosophy Selector. Find out which philosopher you best match, when it comes to ethics. I managed to match Augustine, which struck me as not-quite-right, but then I don't think I match too many other people on the list anyway. Who do you match? ~ Zachary and I enjoyed a swimming lesson at...

2001/12/18 Zack reclining, by the pool (Fremantle, November 2001) Tomorrow, we pile into the car, and start the drive up to Brisbane to spend Christmas with family. We're looking forward to a relaxing and refreshing Christmas break, and I hope you have something similar to that too. See you sometime in 2002. 2001/12/13 Thanks to Robert King, I'm...

2001/11/30 Jon Barwise (1942-2000) Jon Barwise was a renaissance logician. He didn't know everything but his contributions ranged so widely that he approximated omniscience quite well. His work ranges from infinitary logic (an extension of Frege-style predicate logic to deal with infinitely long sentences, and infinitary quantifiers), the model...

2001/10/31 I have a change in store for you for next month. Instead of ceaseless worry about Federal elections, asylum seekers or a war on terrorism, I bid you to enjoy some solace in abstraction. For all of November, this site will be taken up with Great Moments In Logic. I hope to serve up one insight per day for thirty days, from thirty great...

Shapiro and Taschek have argued that simply using intuitionistic logic and its Heyting semantics, one can show that there are no gaps in warranted assertibility. That is, given that a discourse is faithfully modelled using Heyting”s semantics for the logical constants, that if a statement S is not warrantedly assertible, then its negation ~S is....

2001/09/30 2001/09/28 Ballot '01: With the CHOGM postponed, we'll almost certainly have an early federal election. It's going to be messy, with the "war" on terrorism, the collapse and possible resurrection of Ansett, and asylum seekers all as hot issues here. The polls give the conservatives a huge lead. Let's see how this short election...

2001/08/31 Last Monday, my last surviving grandparent, Johanna de Vries, my maternal Grandmother, passed away at 1:30am. Today I fly up to Brisbane to attend her funeral, and to grieve with my family. 2001/08/29 2001/08/27 Discussions like these, on the uniquely internet discussion phenomenon of flaming make me wish I knew more about rhetoric...

2001/07/31 From: yapasdequoi (yapasdequoi@excite.ca) Subject: Open Letter to Professor Levitt, Professor Sokal and Professor Bricmont Newsgroups: comp.ai.philosophy, sci.logic, sci.philosophy.meta, sci.math, alt.postmodern Date: 2001-07-28 10:48:02 PST Dear Science Warriors, Isn't "paraconsistent logic" as far removed from reality as the most...

A defence of logical pluralism against a number of objections, primarily from Graham Priest in his article “Logic: One or Many” in the same volume.

2001/06/31 2001/06/30 Creative energy is a crazy thing. It took me a while to hit my stride with my research back when I was starting, and it feels like a transition has come with Zachary's birth too. Now, time to think and write is more concentrated. More focussed. I can't tolerate timewasting to anywhere near the same extent as before....

2001/05/31 Some advice: If you're an undergraduate attempting to take the short-cut to a good grade on an essay, by plagiarising. For your own sake, attempt to plagiarise from someone writes no better than you do. There is something thoroughly disconcerting about the jump from turgid, knotted, ungrammatical prose to smooth, well written text....

2001/04/30 The wall of a terrace house in Dulwich Hill. (February 2001) 2001/04/29 Interesting things are to be found at xrefer, a compendium of decent reference materials cross-referenced and freely searchable here on the net. For example, here is Steve Read's article (from the Oxford Companion to Philosophy) on relevant logic which explains...

2001/03/31 2001/03/30Hmmm. The Mac OS X implementation of PDF allows you to print PDF files which have been marked as "for viewing and not for printing" by Adobe Acrobat. That's one part of the specification that I think I'm glad they didn't implement correctly. I doubt that Adobe will be happy about that, though. ~ Those of you who are following...

(These are entries from my blog from 2000 and early 2001. They were originally hosted on a small server at Macquarie University. Most of the links are dead now, but I have kept them as they are here, for nostalgia’s sake.) Thursday, March 1 The action is no longer at http://www.phil.mq.edu.au/staff/grestall/log. It is now all happening at...

(These are entries from my blog from 2000 and early 2001. They were originally hosted on a small server at Macquarie University. Most of the links are dead now, but I have kept them as they are here, for nostalgia’s sake.) Wednesday, February 28, 2001 3:23 PM ~ That's all folks! This is my last post here using blogger. Tomorrow, I'll be somewhere...

(These are entries from my blog from 2000 and early 2001. They were originally hosted on a small server at Macquarie University. Most of the links are dead now, but I have kept them as they are here, for nostalgia’s sake.) Wednesday, January 31, 2001 3:19 PM ~ keaggy.com/30/ is another regular photography project, this time from Bill Keaggy. He's...

(These are entries from my blog from 2000 and early 2001. They were originally hosted on a small server at Macquarie University. Most of the links are dead now, but I have kept them as they are here, for nostalgia’s sake.) Friday, December 22, 2000 1:47 PM ~ Here's a parting gift. Spend those lazy summer Christmas days reading wonderful...

(These are entries from my blog from 2000 and early 2001. They were originally hosted on a small server at Macquarie University. Most of the links are dead now, but I have kept them as they are here, for nostalgia’s sake.) Thursday, November 30, 2000 8:51 PM ~ I'd like to see that. 5:02 PM ~ If I thought T-Bone Burnett sounded good on those...

(These are entries from my blog from 2000 and early 2001. They were originally hosted on a small server at Macquarie University. Most of the links are dead now, but I have kept them as they are here, for nostalgia’s sake.) Tuesday, October 31, 2000 10:33 AM ~ Meditate on this interesting snippet: Sun's chief scientist John Gage told us back in...

In his paper “Generalised Ortho Negation” J. Michael Dunn mentions a claim of mine to the effect that there is no condition on `perp frames’ equivalent to the holding of double negation elimination (from ~~A to infer A). That claim of mine was wrong. In this paper I correct my error and analyse the behaviour of conditions on frames for negations...

(These are entries from my blog from 2000 and early 2001. They were originally hosted on a small server at Macquarie University. Most of the links are dead now, but I have kept them as they are here, for nostalgia’s sake.) Tuesday, September 19, 2000 5:45 PM ~ Christine and I are heading off to Toronto tomorrow. This log is going on hiatus for a...

(These are entries from my blog from 2000 and early 2001. They were originally hosted on a small server at Macquarie University. Most of the links are dead now, but I have kept them as they are here, for nostalgia’s sake.) Thursday, August 31, 2000 10:14 PM ~ I was delighted to find that someone had trawled through pages of search engine entries...

(These are entries from my blog from 2000 and early 2001. They were originally hosted on a small server at Macquarie University. Most of the links are dead now, but I have kept them as they are here, for nostalgia’s sake.) Monday, July 31, 2000 4:31 PM ~ The PJ Harvey & Björk rendition of Satisfaction is the most menacing piece of music I've...

(These are entries from my blog from 2000 and early 2001. They were originally hosted on a small server at Macquarie University. Most of the links are dead now, but I have kept them as they are here, for nostalgia’s sake.) Thursday, June 29, 2000 11:59 AM ~ Do you have a Macintosh? Download this, the Alias|Wavefront paint effects demo. 11:54 AM ~...

(These are entries from my blog from 2000 and early 2001. They were originally hosted on a small server at Macquarie University. Most of the links are dead now, but I have kept them as they are here, for nostalgia’s sake.) Wednesday, May 31, 2000 6:06 PM ~ Sometimes the whole is much better than the sum of its parts. Megnut supplies eminenya.mpg,...

(These are entries from my blog from 2000 and early 2001. They were originally hosted on a small server at Macquarie University. Most of the links are dead now, but I have kept them as they are here, for nostalgia’s sake.) Saturday, April 29, 2000 11:52 PM ~ The Coffee FAQ. Know what you ingest. You might like a t-shirt to go with that coffee....

(These are entries from my blog from 2000 and early 2001. They were originally hosted on a small server at Macquarie University. Most of the links are dead now, but I have kept them as they are here, for nostalgia’s sake.) Friday, March 31, 2000 10:03 AM ~ OK. Just a little browsing while the cake is baking. Hermenaut is an interesting browse:...

This book is, as the title says, an introduction to substructural logics. Think of it as a book which tries to do for substructural logics what Hughes and Cresswell’s New Introduction did for modal logics. This book was published by Routledge in January 2000. It’s available at Amazon and many other bookstores.

Negation raises three thorny problems for anyone seeking to interpret relevant logics. The frame semantics for negation in relevant logics involves a point shift operator *. Problem number one is the interpretation of this operator. Relevant logics commonly interpreted take the inference from A and ~AvB to B to be invalid, because the...

Many logics in the relevant family can be given a proof theory in the style of Belnap’s display logic. However, as originally given, the proof theory is essentially more expressive than the logics they seek to model. In this paper, we consider a modified proof theory which more closely models relevant logics. In addition, we use this proof theory...

I show that the believer in possible worlds can have impossible worlds for free, as classes of possible worlds. These do exactly the job of ways that things cannot be, and they model the simple paraconsistent logic LP. This motivates a semantics for paraconsistent logic that even a classical logician can love.

This is an introductory essay on the notion of a “Logical Law.” In it, I show that there are three important different questions one can ask about logical laws. Firstly, what it means to be a logical law. Secondly, what makes something a logical law, and thirdly, what are the logical laws. Each of these questions are answered differently by...

In classical and intuitionistic arithmetics, any formula implies a true equation, and a false equation implies anything. In weaker logics fewer implications hold. In this paper we rehearse known results about the relevant arithmetic R#, and we show that in linear arithmetic LL# by contrast false equations never imply true ones. As a result,...

Ideas on the extension of intuitionistic propositional and predicate logic with a ‘subtraction’ connective, Galois connected with disjunction, dual to the implication connective, Galois connected with conjunction. Presented to an audience at Victoria University of Wellington, July 1997. I like this material, but it does not contain any ideas not...

I respond to an interesting argument of Hartley Slater to the effect that there is no such thing as paraconsistent logic. Slater argues that since paraconsistent logics involve interpreting a sentence and its negation as both true at points in a model structure, it is not really negation that is being modelled, since negation is meant to be a...

Combining non-classical (or ‘sub-classical’) logics is not easy, but it is very interesting. In this paper, we combine nonclassical logics of negation and possibility (in the presence of conjunction and disjunction), and then we combine the resulting systems with intuitionistic logic. We will find that some of Marcus Kracht’s results on the...

This paper is a revised version of a talk given at the Logic and Logical Philosophy conference in Poland in September 1995. In it, I sketch the connections between Nuel Belnap’s Display Logic and J. Michael Dunn’s Gaggle Theory.

A truthmaker for a proposition p is an object such that necessarily, if it exists, then p is true. In this paper, I show that the truthmaker thesis (that every truth has a truthmaker) and the disjunction thesis (that a truthmaker for a disjunction must be a truthmaker for one of the disjuncts) are jointly incompatible with the view that the if in...

In this paper we consider the implications for belief revision of weakening the logic under which belief sets are taken to be closed. A widely held view is that the usual belief revision functions are highly classical, especially in being driven by consistency. We show that, on the contrary, the standard representation theorems still hold for...

Peano arithmetic formulated in Łukasiewicz’s infinitely valued logic collapses into classical Peano arithmetic. However, not all additions to the language need also be classical. The way is open for the addition of a real truth predicate satisfying the T-scheme into the language. However, such an addition is not pleasing. The resulting theory is...

This paper generalises Girard’s results which embed intuitionistic logic into linear logic by showing how arbitrary substructural logics can be embedded into weaker substructural logics, using a single modality which ’encodes’ the new structural rules.

I introduce Nietzsche’s critique of religious belief, for an audience of thinking Christians. I show that his criticism cannot and ought not be simply shrugged off, but rather, it can form the basis of a useful self-critique for the religious believer. I also argue that any response to a Nietzschean critique of religious belief and practice must...

John Perry, one of the two founders of the field of situation semantics, indicated in an interview in 1986 that there is some kind of connection between relevant logic and situation semantics. I do know that a lot of ideas that seemed off the wall when I first encountered them years ago now seem pretty sensible. One example that our commentators...

This paper gives an outline of three different approaches to the four-valued semantics for relevant logics (and other non-classical logics in their vicinity). The first approach borrows from the ‘Australian Plan’ semantics, which uses a unary operator ‘*’ for the evaluation of negation. This approach can model anything that the two-valued account...

Once the Kripke semantics for normal modal logics were introduced, a whole family of modal logics other than the Lewis systems S1 to S5 were discovered. These logics were obtained by changing the semantics in natural ways. The same can be said of the Kripke-style semantics for relevant logics: a whole range of logics other than the standard...

I defend the extension of the lambek calculus with a distributive extensional conjunction and disjunction. I show how it independently arises in linguistics, information flow and relevant logics, and relation algebra. I give the logic a cut-free Gentzenisation and show that it is decidable.

My Ph.D. Thesis, completed in January 1994. I was supervised by Prof. Graham Priest, at the University of Queensland. The thesis is 292 pages of work on logics without the contraction rule.

I show how Priest and Sylvan’s simplified semantics extends from basic relevant logics to a large class of stronger logics. The completeness proof is a little tricky, given the different behaviour of the normal world in the models. This is the first paper from my Ph.D. thesis.

I show that any finitely valued logic of a simple kind fails to support naïve comprehension, if it has a conditional. I then go on to show how some infinitely valued logics also fail to be robustly contraction free. Then I make a bold conjecture that robust contraction freedom is sufficient to support naïve set theory. This conjecture was later...

I argue that the extant reasons for sticking to classical logic in the face of the paradoxes of self reference are not good reasons. The paradoxes are really difficult and we should use all of the weapons at our disposal.

My first publication. It stems from work I did in my Honours year (1989) with Graham Priest, on paraconsistent logic. I explain a particularly simple yet powerful technique for constructing models of naïve set theory in the paraconsistent logic LP. This can be used to show the consistency of the theory, and to construct models invalidating some...