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Here’s August’s book haul: This month I enjoyed three novels.

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.

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.

In this paper, I examine connections between the speech acts of assertion, denial, polar questions and justification requests, and the common ground.

Substructural logics are non-classical logics weaker than classical logic, notable for the absence of structural rules present in classical logic.

Martin Hägglund’s This Life is an important treatise on metaphysics, philosophical anthropology, and political philosophy.

June was also an enjoyable month for reading.

Abstract: In this informal talk, I will revisit some longstanding issues in philosophical logic in the light of some contemporary developments.

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.

May was a great reading month, but I forgot to upload my notes until June was nearly done.

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.

Earlier this month I got a lovely package in the mail.

Another month, and another pile of books I’ve managed to read.

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…

This is a translation into Chinese of my introductory textbook Logic.

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)

I’ve just emerged from two intense days 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)

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.

py4612: Advanced Logic applies the tools of formal logic to make logic itself the object of study.

We present a new frame semantics for positive relevant and substructural propositional 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…

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.

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.

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.

py2010: Intermediate Logic is a University of St Andrews undergraduate subject in which we cover important results in logic to philosophy students.

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.

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.

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?

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…

Natural deduction with alternatives extends Gentzen–Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives.

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.

Abstract: In this talk, I show how to incorporate insights from the model-theoretic semantics for negation (insights due to J.

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…

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.

py4601: Paradoxes is an honours Philosophy module at the University of St Andrews.

py1012: Reasoning introduces the essential concepts and techniques of critical reasoning, formal propositional logic, and basic predicate logic.

I grew up in Australia: my university training and my initial academic positions took place in the explicitly secular institution of the Australian 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.

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

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.

Today MIT Press releases our book, Logical Methods into the big wide world.

As the cover blurb says Logical Methods is an accessible introduction to philosophical logic, suitable for undergraduate courses and above.

2022 has been another big year, not that you’d know it from looking around the news section of this website.

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.

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)…

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.

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)…

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 justi…