Science & Logic

PHIL20030: Meaning, Possibility and Paradox

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 look at the different ways that this idea has been applied in logic throughout the 20th Century and into the present day. ¶ In the first part of the subject, our focus is on the concepts of necessity and possibility, and the way that ‘possible worlds semantics’ has been used in theories of meaning. We will focus on the logic of necessity and possibility (modal logic), times (temporal logic), conditionality and dependence (counterfactuals), and the notions of analyticity and a priority so important to much of philosophy. ¶ In the second part of the subject, we examine closely the assumption that every statement we make is either true or false but not both. We will examine the paradoxes of truth (like the so-called ‘liar paradox’) and vagueness (the ‘sorites paradox’), and we will investigate different ways attempts at resolving these paradoxes by going beyond our traditional views of truth (using ‘many valued logics’) or by defending the traditional perspective. ¶ The subject serves as an introduction to ways that logic is applied in the study of language, epistemology and metaphysics, so it is useful to those who already know some philosophy and would like to see how logic relates to those issues. It is also useful... -

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PHIL30043: The Power and Limits of Logic

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 Theorem, Compactness, Cantor’s Theorem, the Downward Löwenheim–Skolem Theorem, Recursive Functions, Register Machines, Representability and ending up at Gödel’s Incompleteness Theorems and Löb’s Theorem. Kurt Gödel, seated ¶ The subject is taught to University of Melbourne undergraduate students (for Arts students as a part of the Philosophy major, for non-Arts students, as a breadth subject). Details for enrolment are here. I make use of video lectures I have made freely available on... -

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Materiality revisited

I’ve long been puzzled by materiality. ¶ Here’s a thought: What if materiality isn’t characterized by anything deeply metaphysical, but by a physical quality? Perhaps to be material just is to have something like inertia, or mass, or energy? ¶ (I think that to have zero of some quality... -

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Accommodation, Inference, Generics and Pejoratives

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... -

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Materiality revisited I’ve long been puzzled by materiality. Here’s a thought: What if materiality isn’t characterized by anything deeply metaphysical, but by a physical quality? Perhaps to be material just is to have something like inertia, or mass, or energy? (I think that to have zero of some quality like mass is still to have mass. A mass of x is a determinate of the determinable mass even if x = 0. Photons have mass, while numbers don’t.) Alexander Pruss -


Accommodation, Inference, Generics and Pejoratives 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 behaviour: Why is it, for example, that “birds lay eggs” seems true, while “birds are female” seems false, despite the fact... Consequently.org -


Accommodation, Inference, Generics and Pejoratives 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 behaviour: Why is it, for example, that “birds lay eggs” seems true, while “birds are female” seems false, despite the fact... Consequently.org -


Negation on the Australian Plan 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 incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing... Consequently.org -


Proof Theory, Rules and Meaning — an introduction 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. Consequently.org -


Defining Rules, Proofs and Counterexamples 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 models, and the relationship between proof-theoretic and model- theoretic analyses of logical consequence. This is a talk for... Consequently.org -


PHIL20030: Meaning, Possibility and Paradox 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 look at the different ways that this idea has been applied in logic throughout the 20th Century and into the present day. In the first part of the subject, our focus is... Consequently.org -


PHIL30043: The Power and Limits of Logic 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 Theorem, Compactness, Cantor’s Theorem, the Downward Löwenheim–Skolem Theorem, Recursive Functions, Register Machines, Representability and ending up at Gödel’s Incompleteness Theorems and Löb’s... Consequently.org -


What Proofs are For 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 informal notion of of validity and the notions formalised in our accounts of proofs and models, and... Consequently.org -


Truth Tellers in Bradwardine's Theory of Truth 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 papers, I have developed a model theory for Bradwardine’s account of truth. This model theory has distinctive features:... Consequently.org -


Isomorphisms in a Category of Propositions and Proofs 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 \(q\land p\); \(p\) and \(\neg\neg p\); or \(\neg(p\land q)\) and \(\neg p\lor\neg q\). Another relation is more coarsely grained, and... Consequently.org -


Accommodation, Inference, Generics and Pejoratives 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 behaviour: Why is it, for example, that “birds lay eggs” seems true, while “birds are female” seems false, despite the fact... Consequently.org -


Accommodation, Inference, Generics and Pejoratives 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 behaviour: Why is it, for example, that “birds lay eggs” seems true, while “birds are female” seems false, despite the fact... Consequently.org -


What Proofs are For 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 informal notion of of validity and the notions formalised in our accounts of proofs and models, and... Consequently.org -


Isomorphisms in a Category of Proofs 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 \(\neg\neg p\); or \(\neg(p\land q)\) and \(\neg p\lor\neg q\). Another relation is more coarsely grained, and gives the... Consequently.org -


Isomorphisms in a Category of Proofs Abstract: In this talk, I show how a category of formulas 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 \(q\land p\); \(p\) and \(\neg\neg p\); or \(\neg(p\land q)\) and \(\neg p\lor\neg q\). Another relation is more coarsely grained, and... Consequently.org -


Accommodation, Inference, Generics and Pejoratives 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 behaviour: Why is it, for example, that “birds lay eggs” seems true, while “birds are female” seems false, despite the fact... Consequently.org -


Accommodation, Inference, Generics and Pejoratives 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 behaviour: Why is it, for example, that “birds lay eggs” seems true, while “birds are female” seems false, despite the fact... Consequently.org -


Accommodation, Inference, Generics and Pejoratives 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 behaviour: Why is it, for example, that “birds lay eggs” seems true, while “birds are female” seems false, despite the fact... Consequently.org -


Isomorphisms in a Category of Proofs Abstract: In this talk, I show how a category of formulas 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 \(q\land p\); \(p\) and \(\neg\neg p\); or \(\neg(p\land q)\) and \(\neg p\lor\neg q\). Another relation is more coarsely grained, and... Consequently.org -