Robert Trueman

My aim in this paper is to offer a novel justification for β-Equivalence. β-Equivalence is a standard principle of higher-order logic, but it is metaphysically controversial. My argument for β-Equivalence is based on a distinctively Fregean conception of predication. I argue that the Fregean conception motivates a non-standard notation for predicates, which can then be used to show that β-Equivalence is trivial on that conception. I also argue that the Fregean conception motivates a functional individuation of properties, which we can use to extend the Fregean justification for β-Equivalence to cover a more general principle, β-Conversion.

There is a widespread intuition that mereology should be ontologically innocent. In this paper, we compare two attempts to deliver this innocence. They both identify a fusion with the plurality of its parts, but they disagree over the logical status of the fusion: according to Composition as Identity (CAI), the fusion is a genuine individual, and in this sense it is both one and many; according to manyism, the fusion is not an individual, and so is merely many. We argue that no version of CAI can make mereology ontologically innocent without violating some independently attractive desiderata. But manyism can. In fact, when the details are appropriately filled out, manyism yields (what we call) mereologicism, the result that all of the axioms of Classical Mereology are logical theorems. Given manyism, mereology is innocent because logic is.

이 책자는 형식 논리의 일종인 양상논리에 입문하고 싶으신 분들을 위한 짧은 교재입니다. “양상논리 맛보기” 라는 말마따나, 이 책자는 양상논리에 관심은 있지만 아직 본격적으로 공부를 시작하진 않은 분들께서 ‘맛보기’를 하기에 적합한 안내 책자입니다. 아무쪼록 이 책자가 양상논리를 공부해나가시는데 유용한 첫 발판이 될 수 있기를 바랍니다. / This booklet is a Korean adaptation and translation of Part VIII of forall x: Calgary (Fall 2021 edition), which is intended to be introductory material for modal logic. The original text is based on Robert Trueman's A Modal Logic Primer, which is revised and expanded by Richard Zach and Aaron Thomas-Bolduc in forall x: Calgary. (forall x: Calgary is based on forall x: Cambridge by Tim Button, which is in turn based on forall x by P. D. Magnus, and also includes material from forall x: Lorain County Remix by Cathal Woods and J. Robert Loftis.) This booklet is licensed under a Creative Commons Attribution 4.0 license.

forall x: Calgary is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truth-functional propositional logic TFL and truth-table semantics, the syntax of first-order (predicate) logic FOL with identity (first-order interpretations), symbolizing English in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as modal logic, soundness, and functional completeness. Exercises with solutions are available. It is provided in PDF (for screen reading, printing, and a special version for dyslexics), HTML, and in LaTeX source code.

In a recent article, Hofweber presents a new, and surprising, argument for idealism. His argument is surprising because it starts with an apparently innocent premiss from the philosophy of language: that ‘that’-clauses do not refer. I do not think that Hofweber's argument works, and my first aim in this paper is to explain why. However, I agree with Hofweber that what we say about ‘that’-clauses has important metaphysical consequences. My second aim is to argue that, far from leading us into idealism, denying that ‘that’-clauses refer is the first step toward a kind of direct realism about belief.

This book articulates and defends Fregean realism, a theory of properties based on Frege's insight that properties are not objects, but rather the satisfaction conditions of predicates. Robert Trueman argues that this approach is the key not only to dissolving a host of longstanding metaphysical puzzles, such as Bradley's Regress and the Problem of Universals, but also to understanding the relationship between states of affairs, propositions, and the truth conditions of sentences. Fregean realism, Trueman suggests, ultimately leads to a version of the identity theory of truth, the theory that true propositions are identical to obtaining states of affairs. In other words, the identity theory collapses the gap between mind and world. This book will be of interest to anyone working in logic, metaphysics, the philosophy of language or the philosophy of mind.

forall x: Dortmund is an adaptation and German translation of forall x: Calgary. As such, it is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity, the syntax of truth-functional (propositional) logic and truth-table semantics, the syntax of first-order (predicate) logic with identity and first-order interpretations, formalizing German in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as the syntax and (Kripke-)semantics of modal logic. The book is provided in PDF and in LaTeX source code. A booklet with solutions for the exercises in the book is available.