Metaphysics

Vasubandhu’s Twenty Verses and Comparative Philosophy, Part One

In this duology of posts I’m going to respond to Sonam Kachru’s friendly criticism of my own work on Vasubandhu’s Twenty Verses (Vimśikākārikā). But instead of the usual academic practice of arguing against Kachru’s criticisms, I’m going to suggest that Kachru may be right. Or maybe half-right. In any case, his work has helped my own thinking move toward a new insight: I have come to suspect that I made some mistakes in my own earlier work—and maybe these errors are iterations of deeper mistakes that often occur under the banner of “comparative philosophy.” ¶ In this first post, I’ll discuss my own previous work and Kachru’s criticisms of it, and in part two I’ll say more about what I think all this has to do with comparative philosophy and how we 21st century scholars approach classical Indian texts like the Twenty Verses. ¶ In my 2017 article, “External-World Skepticism in Classical India: The Case of Vasubandhu,” I laid out the debate about whether Vasubandhu’s Twenty Verses should be understood as advocating a form of metaphysical idealism or a kind of epistemological phenomenalism, and I came to the (appropriately cagey) conclusion that in either case, Vasubandhu might be read as providing an invitation to consider something like the issue of external-world skepticism. ¶ In his excellent 2021 study of Vasubandhu’s Twenty Verses, Other Lives: Mind and World in Indian Buddhism, Sonam Kachru develops a novel account of the text that moves away from the contemporary debate about whether Vasubandhu... -

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PY4601: Paradoxes

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 semantic paradoxes. Here’s what we’re covering. A paradox is a plausible argument for an absurd conclusion. Better still: a paradox is an apparently plausible argument, with apparently plausible premises, which leads to an apparently absurd conclusion using apparently valid reasoning. In this module, we are going to look at three groups of paradoxes (and the connections between them): Epistemological Paradoxes (e.g. various forms of Scepticism, Lottery Paradox, Dogmatism Paradox). Paradoxes of Vagueness and Indeterminacy (The Sorites Paradoxes, The Problem of the Many, The Open Future, The Ship of Theseus, The Chicken and Egg Paradox).... -

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Chat GPT and Student Writing: Some Practical Reflections

ChatGPT: What it is, how it works, the challenge it presents Developed by OpenAI, ChatGPT is an AI text generator that uses a large language model (LLM) to create responses to queries. In many ways it is like your phone’s autocomplete function—when you type a sequence of words into your... -

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PY1012: Reasoning

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... -

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Chat GPT and Student Writing: Some Practical Reflections ChatGPT: What it is, how it works, the challenge it presents Developed by OpenAI, ChatGPT is an AI text generator that uses a large language model (LLM) to create responses to queries. In many ways it is like your phone’s autocomplete function—when you type a sequence of words into your phone, the autocomplete makes a […] Blog of the APA -


PY4601: Paradoxes 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 semantic paradoxes. Here’s what we’re covering. A paradox is a plausible argument for an absurd conclusion. Better still: a paradox is an apparently plausible argument, with apparently plausible premises, which leads to an apparently absurd conclusion using apparently valid reasoning. In this module, we... Consequently.org -


PY1012: Reasoning 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 premises? In addressing these questions, we will also cover topics such as ambiguity, argument forms and analyses, induction compared to deduction, counterexamples, truth-tables, natural... Consequently.org -


Come and See! (John 1:29-42) 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 the text... Consequently.org -


Time for a little grease and oil change 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 time to clean up a bit of the mess... Consequently.org -


True Contradictions in Theology? 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 involved in each claim. Since to say that Christ is impeccable is to say that Christ is not... Consequently.org -


Natural Deduction with Alternatives: on structural rules, and identifying assumptions 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 restrictions of these systems. Each of these proof systems have identical connective rules. As we expect in substructural logics, different logical systems are given by varying the structural... Consequently.org -


Natural Deduction with Alternatives: on structural rules, and identifying assumptions 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 restrictions of these systems. Each of these proof systems have identical connective rules. As we expect in substructural logics, different logical systems are given by varying the structural... Consequently.org -


PY4638: Philosophy of Religion 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 science. In 2022, we will be exploring one important topic in the philosophy of religion from three different perspectives. We will explore the notion that ultimate reality—or God—is... Consequently.org -


Classical Logic and Intuitionistic Logic: looking both ways 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 might mean, from the perspective of partisans of one side or other of the divide, and what kinds of pluralism might be tenable, in the... Consequently.org -


The Many Uses of Proofs: logic and philosophy, language and more 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 talk is a face-to-face presentation at the University of St-Andrews Computer Science Department’s Research in School day. The slides... Consequently.org -


True Contradictions? Why, and Why Not? 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 Christology as one such motivation, and discuss some attractions of the view, as well as some shortcomings to be further explored. The... Consequently.org -


Collection Frames for Distributive Substructural Logics 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 are modeled by varying the kinds of collections used: they can be sets, multisets, lists or trees. We show that collection frames on... Consequently.org -


Exploring Three-Valued Models for Identity 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 logic, because for that, you need to determine how models are used to provide a counterexample to a sequent.... Consequently.org -


Proofs and Models in Philosophical Logic 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 general notions of proof and of models, I introduce and motivate a simple natural deduction system, and present the... Consequently.org -


Natural Deduction with Alternatives: on structural rules, and identifying assumptions 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 restrictions of these systems. Each of these proof systems have identical connective rules. As we expect in substructural logics, different logical systems are given by varying the structural... Consequently.org -


Questions, Justification Requests, Inference, and Definition 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 weak assertion, and the distinct way that these speech acts interact with the common ground. In addition, once we pay attention to the... Consequently.org -


Justification Requests, Inference and Definitions 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 distinction between strong and weak assertion, and the way that these speech acts interact with the common ground. In addition, we can give... Consequently.org -


PY4634: Philosophical Logic 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 logics. Consequently.org -


PY1012: Reasoning 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 premises? In addressing these questions, we will also cover topics such as ambiguity, argument forms and analyses, induction compared to deduction, counterexamples, truth-tables, natural... Consequently.org -