Logic isn’t special. Its theories are continuous with science; its method continuous with scientific method. Logic isn’t a priori, nor are its truths analytic truths. Logical theories are revisable, and if they are revised, they are revised on the same grounds as scientific theories. These are the tenets of anti-exceptionalism about logic. The position is most famously defended by Quine, but has more recent advocates in Maddy, Priest, Russell, and Williamson. Although these authors agree on many methodological issues about logic, (...) they disagree about which logic anti-exceptionalism supports. Williamson uses an anti-exceptionalist argument to defend classical logic, while Priest claims that his anti-exceptionalism supports nonclassical logic. This paper argues that the disagreement is due to a difference in how the parties understand logical theories. Once we reject Williamson’s deflationary account of logical theories, the argument for classical logic is undercut. Instead an alternative account of logical theories is offered, on which logical pluralism is a plausible supplement to anti-exceptionalism. (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

The goals of this paper are two-fold: I wish to clarify the Aristotelian conception of the law of non-contradiction as a metaphysical rather than a semantic or logical principle, and to defend the truth of the principle in this sense. First I will explain what it in fact means that the law of non-contradiction is a metaphysical principle. The core idea is that the law of non-contradiction is a general principle derived from how things are in the world. For example, (...) there are certain constraints as to what kind of properties an object can have, and especially: some of these properties are mutually exclusive. Given this characterisation, I will advance to examine what kind of challenges the law of non-contradiction faces; the main opponent here is Graham Priest. I will consider these challenges and conclude that they do not threaten the truth of the law of non-contradiction understood as a metaphysical principle. (shrink)

In this paper I develop a framework for understanding ontic vagueness. The project of the paper is two-fold. I first outline a definitional account of ontic vagueness – one that I think is an improvement on previous attempts because it remains neutral on other, independent metaphysical issues. I then develop one potential manifestation of that basic definitional structure. This is a more robust (and much less neutral) account which gives a fully classical explication of ontic vagueness via modal concepts. The (...) overarching aim is to systematically investigate the puzzling question of what exactly it could be for the world itself to be vague. (shrink)

I argue for a property mereology and for mereological bundle theory. I then apply this theory to the one over many problem (universals) and puzzles concerning persistence and material constitution.

Understandably absorbed in technical details, discussion of the semantic paradoxes risks losing sight of broad methodological principles. This chapter sketches a general approach to the comparison of rival logics, and applies it to argue that revision of classical propositional logic has much higher costs than its proponents typically recognize.

Logical realism is the view that there is logical structure in the world. I argue that, if logical realism is true, then we are deeply ignorant of that logical structure: either we can’t know which of our logical concepts accurately capture it, or none of our logical concepts accurately capture it at all. I don’t suggest abandoning logical realism, but instead discuss how realists should adjust their methodology in the face of this ignorance.

Logical pluralism is the view that there is more than one correct logic. In this article, I explore what logical pluralism is, and what it entails, by: (i) distinguishing clearly between relativism about a particular domain and pluralism about that domain; (ii) distinguishing between a number of forms logical pluralism might take; (iii) attempting to distinguish between those versions of pluralism that are clearly true and those that are might be controversial; and (iv) surveying three prominent attempts to argue for (...) logical pluralism and evaluating them along the criteria provided by (ii) and (iii). (shrink)

In , Peter van Inwagen asked a good question. (Asking the right question is often the hardest part.) He asked: what do you have to do to some objects to get them to compose something—to bring into existence some further thing made up of those objects? Glue them together or what?1 Some said that you don’t have to do anything.2 No matter what you do to the objects, they’ll always compose something further, no matter how they are arranged. Thus we (...) learned of the fusion of the coins in our pockets and the Eiffel tower. (shrink)

Recent work on analyticity distinguishes two kinds, metaphysical and epistemic. This paper argues that the distinction allows for a new view in the philosophy of logic according to which the claims of logic are metaphysically analytic and have distinctive modal profiles, even though their epistemology is holist and in many ways rather Quinean. It is argued that such a view combines some of the more attractive aspects of the Carnapian and Quinean approaches to logic, whilst avoiding some famous problems.

An approach to explaining the nature and source of logic and its laws with a rich historical tradition takes the laws of logic to be laws of thought. This view seems intuitively compelling, after all, logic seems to be intimately related with how we think. But how exactly should we understand it? And what arguments can we give in favour? I will propose one line of argument for the claim that the laws of logic are laws of thought. I will (...) motivate the claim that there is a certain phenomenon, namely, that there are logical principles which are immune to rational doubt. I will then give an argument to the best explanation; I will argue that the best explanation of this phenomenon is to take the laws of logic to be constitutive-normative laws of thought. The proposal, and some responses to potential objections, will have a notably Kantian flavour. (shrink)

Logical pluralism is the claim that different accounts of validity can be equally correct. Beall and Restall have recently defended this position. Validity is a matter of truth-preservation over cases, they say: the conclusion should be true in every case in which the premises are true. Each logic specifies a class of cases, but differs over which cases should be considered. I show that this account of logic is incoherent. Validity indeed is truth-preservation, provided this is properly understood. Once understood, (...) there is one true logic, relevance logic. The source of Beall and Restall’s error is a recent habit of using a classical metalanguage to analyse non-classical logics generally, including relevance logic. (shrink)

This chapter defends the account of metaphysical indeterminacy of Barnes and Williams against Eklund's objections.

The starting point of this paper concerns the apparent difference between what we might call absolute truth and truth in a model, following Donald Davidson. The notion of absolute truth is the one familiar from Tarski’s T-schema: ‘Snow is white’ is true if and only if snow is white. Instead of being a property of sentences as absolute truth appears to be, truth in a model, that is relative truth, is evaluated in terms of the relation between sentences and models. (...) I wish to examine the apparent dual nature of logical truth (without dwelling on Davidson), and suggest that we are dealing with a distinction between a metaphysical and a linguistic interpretation of truth. I take my cue from John Etchemendy, who suggests that absolute truth could be considered as being equivalent to truth in the ‘right model’, i.e., the model that corresponds with the world. However, the notion of ‘model’ is not entirely appropriate here as it is closely associated with relative truth. Instead, I propose that the metaphysical interpretation of truth may be illustrated in modal terms, by metaphysical modality in particular. One of the tasks that I will undertake in this paper is to develop this modal interpretation, partly building on my previous work on the metaphysical interpretation of the law of non-contradiction (Tahko 2009). After an explication of the metaphysical interpretation of logical truth, a brief study of how this interpretation connects with some recent important themes in philosophical logic follows. In particular, I discuss logical pluralism and propose an understanding of pluralism from the point of view of the metaphysical interpretation. (shrink)

This talk surveys a range of positions on the fundamental metaphysical and epistemological questions about elementary logic, for example, as a starting point: what is the subject matter of logic—what makes its truths true? how do we come to know the truths of logic? A taxonomy is approached by beginning from well-known schools of thought in the philosophy of mathematics—Logicism, Intuitionism, Formalism, Realism—and sketching roughly corresponding views in the philosophy of logic. Kant, Mill, Frege, Wittgenstein, Carnap, Ayer, Quine, and Putnam (...) are among the philosophers considered along the way. (shrink)

This paper argues against Logical Realism, in particular against the view that there are facts of matters of logic that obtain independently of us, our linguistic conventions and inferential practices. The paper challenges logical realists to provide a non-intuition based epistemology, one which would be compatible with the empiricist and naturalist convictions motivating much recent anti-realist philosophy of mathematics.

In this paper I argue that Beall and Restall's claim that there is one true logic of metaphysical modality is incompatible with the formulation of logical pluralism that they give. I investigate various ways of reconciling their pluralism with this claim, but conclude that none of the options can be made to work.