Abstract: A widespread assumption in contemporary philosophy of logic is that there is one true logic, that there is one and only one correct answer as to whether a given argument is deductively valid. In this paper we propose an alternative view, logical pluralism. According to logical pluralism there is not one true logic; there are many. There is not always a single answer to the question “is this argument valid?” 1 Logic, Logics and Consequence Anyone acquainted with contemporary Logic knows that there are many so-called logics. 1 But are these logics rightly so-called? Are any of the menagerie of non-classical logics, such as relevant logics, intuitionistic logic, paraconsistent logics or quantum logics, as deserving of the title ‘logic ’ as classical logic? On the other hand, is classical logic really as deserving of the title ‘logic ’ as relevant logic (or any of the other non-classical logics)? If so, why so? If not, why not? Logic has a chief subject matter: Logical Consequence. The chief aim of

this paper we provide a rigorous, and grammar independent, answer to this question. This enables us to characterize the syntactic invariants of a language determined by a grammar for that language. We use the formal notion of (syntactic) invariant to answer such pretheoretical questions as the following: In a grammar of English, is the property of being an NP (an S, a VP , : : : ) a "structural" one? That is, in our terms, is it syntactically invariant? One expects that the answer is: Yes. But is it true in any grammar that the property of having a given category C is a structural property? The question assumes that we have a definition of "structural property", and our intuitions as linguists are not pretheoretically decisive here. For example, one of the intuitions behind X

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English contains singular terms, quantifiers and predicates (e.g. ‘it’, ‘something ’ and ‘... is an elephant’). But it also contains plural terms, quantifiers and predicates (e.g. ‘they’, ‘some things ’ and ‘... are scattered on the floor’). 1 Philosophers have become increasingly interested in plurals over the past couple of decades. The purpose of this paper is to explain why plurals might be thought to have philosophical importance, and why they have led to philosophical debate. 1

this paper an argument is a two-part system composed of a set of propositions P (the premise-set) and a single proposition c (the conclusion). The expression `c is a [logical] consequence of P' is used with the same meaning as the expression `c is [logically] implied by P'. The expressions `is a logical consequence of ' and the converse `implies' are relational. Often, I shall be talking in the same sense of validity of an argument. Validity is a property of arguments; an argument with premise-set P and conclusion c is valid if and only if P implies c; i.e., c is a logical consequence of P. Notice that this notion of argument is strictly ontic; it does not involve any agent that thinks, determines or establishes that a given proposition is or is not a consequence of a given set of propositions

Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a priori and empirical, necessary and contingent, analytic and synthetic—indeed, it is often invoked to explain these. Nor, it turns out, can it be explained by appeal to schematic inference patterns, syntactic rules, or grammar. What does it mean, then, to say that logic is distinctively formal? Three things: logic is said to be formal (or “topic-neutral”) (1) in the sense that it provides constitutive norms for thought as such, (2) in the sense that it is indifferent to the particular identities of objects, and (3) in the sense that it abstracts entirely from the semantic content of thought. Though these three notions of formality are by no means equivalent, they are frequently run together. The reason, I argue, is that modern talk of the formality of logic has its source in Kant, and these three notions come together in the context of Kant’s transcendental philosophy. Outside of this context (e.g., in Frege), they can come apart. Attending to this

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This paper is not meant to be a "reply to my critics." Such a reply would be of very little interest to any one reader, inasmuch as the critics themselves disagree so sharply on fundamental points, and so the lines of criticism are often at odds with one another. Instead, the paper is meant to be a rethinking of my overall argument in light of what I have learned from the various critiques, in particular what I have learned about ways in which CLC was confusing, incomplete, or otherwise misleading. Where appropriate, I indicate in footnotes how points made in this paper relate to specific criticism that has appeared in print

In this paper we will try to reconstruct Tarski's views on the criterion of logicality and the nature of logical entities in his 1966 lecture ([31]), in terms of an explicit ontological scheme of functional types, sequential frames and categories, which results from a simple adaptation

Logic is often said to provide norms for thought or reasoning. Indeed, this idea is central to the way in which logic has traditionally been defined as a discipline, and without it, it is not clear how we would distinguish logic from the disciplines that crowd it on all sides: psychology, metaphysics, mathematics, and semantics. But it turns out to be surprisingly hard to say how facts about the validity of inferences relate to norms for reasoning, and some philosophers have concluded that the whole idea is confused. In this talk I will survey a space of possible “bridge principles ” connecting logical facts with norms for reasoning. After discussing some considerations relevant to choosing between these bridge principles, I will defend two of them. I will then consider the implications of various choices of bridge principle for the long-standing debates about the roles of relevance, necessity, and formality in our notion of logical consequence. The methodological aim of the talk is to provide an alternative to the usual brute appeals to our “intuitions ” about logical consequence in these fundamental debates.