Actuality, Necessity, and Logical Truth

The traditional view that all logical truths are metaphysically necessary has come under attack in recent years. The contrary claim is prominent in David Kaplan’s work on demonstratives, and Edward Zalta has argued that logical truths that are not necessary appear in modal languages supplemented only with some device for making reference to the actual world (and thus independently of whether demonstratives like ‘I’, ‘here’, and ‘now’ are present). If this latter claim can be sustained, it strikes close to the heart of the traditional view. I begin this paper by discussing and refuting Zalta’s argument in the context of a language for propositional modal logic with an actuality connective (section 1). This involves showing that his argument in favor of real world validity his preferred explication of logical truth, is fallacious. Next (section 2) I argue for an alternative explication of logical truth called general validity. Since the rule of necessitation preserves general validity, the argument of section 2 provides a reason for affirming the traditional view. Finally (section 3) I show that the intuitive idea behind the discredited notion of real world validity finds legitimate expression in an object language connective for deep necessity. Earlier versions of this paper were read at the universities of Graz, Maribor, and Salzburg, and at a workshop on the philosophy of logic at the National Autonomous University of Mexico (UNAM) in Mexico City. My thanks to those present at these events for many helpful suggestions. Thanks are also due to an anonymous referee for Philosophical Studies.     

Logical Truth and Tarskian Logical Truth

This paper examines the question of the extensional correctness of Tarskian definitions of logical truth and logical consequence. I identify a few different informal properties which are necessary for a sentence to be an informal logical truth and look at whether they are necessary properties of Tarskian logical truths. I examine arguments by John Etchemendy and Vann McGee to the effect that some of those properties are not necessary properties of some Tarskian logical truths, and find them unconvincing. I stress the point that since the hypothesis that Tarski's definitions are extensionally correct is deeply entrenched, the burden of proof is still on the shoulders of Tarski's critics, who have not lifted the burden. This revised version was published online in June 2006 with corrections to the Cover Date.     

Counterfactual Logic and the Necessity of Mathematics

Journal of Philosophical Logic - This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious...     

Quine and Logical Truth

It is a consequence of Quine’s confirmation holism that the logical laws are in principle revisable. Some have worried this is at odds with another dictum in Quine, viz., that any translation which construes speakers as systematically illogical is ipso facto inadequate. In this paper, I try to formulate exactly what the problem is here, and offer a solution to it by (1) disambiguating the term ‘logic,’ and (2) appealing to a Quinean understanding of ‘necessity.’ The result is that the different theses in Quine’s philosophy of logic are to be situated within different contexts of inquiry.

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论前期维特根斯坦的逻辑真理观

维特根斯坦在其早期代表作《逻辑哲学论》中深入探讨了逻辑真理的理解问题.然而当今学界流行的看法是,维特根斯坦有着最狭隘的逻辑真理观逻辑真理即重言式.本文试图澄明维氏使用重言式概念的原初含义,并从其以逻辑为基础的世界观、真值函项理论及优范式理论等角度分别加以阐述,说明维氏所理解的逻辑真理乃穷尽可能的必然,而对逻辑真理的这种理解同样可推广到谓词逻辑,并指出用穷尽可能来定义逻辑必然并不会导致恶性循环.     

Temporal Necessity and Logical Fatalism

I begin by briefly mentioning two different logical fatalistic argument types: one from temporal necessity, and one from antecedent truth value. It is commonly thought that the latter of these involves a simple modal fallacy and is easily refuted, and that the former poses the real threat to an open future. I question the conventional wisdom regarding these argument types, and present an analysis of temporal necessity that suggests the anti-fatalist might be better off shifting her argumentative strategy. Specifically, two points of interest emerge from my analysis: first, temporal necessity turns out to be an inappropriate and ineffective tool for the fatalist to make use of; and, second, the dismissal of the argument from antecedent truth value turns out to be an over-hasty one.     

A Non-Inferentialist, Anti-Realistic Conception of Logical Truth and Falsity

Anti-realistic conceptions of truth and falsity are usually epistemic or inferentialist. Truth is regarded as knowability, or provability, or warranted assertability, and the falsity of a statement or formula is identified with the truth of its negation. In this paper, a non-inferentialist but nevertheless anti-realistic conception of logical truth and falsity is developed. According to this conception, a formula (or a declarative sentence) A is logically true if and only if no matter what is told about what is told about the truth or falsity of atomic sentences, A always receives the top-element of a certain partial order on non-ontic semantic values as its value. The ordering in question is a told-true order. Analogously, a formula A is logically false just in case no matter what is told about what is told about the truth or falsity of atomic sentences, A always receives the top-element of a certain told-false order as its value. Here, truth and falsity are pari passu, and it is the treatment of truth and falsity as independent of each other that leads to an informational interpretation of these notions in terms of a certain kind of higher-level information.     

Showing,Analysis and the Truth-Functionality of Logical Necessity in Wittgenstein's Tractatus

This paper aims to explain how the Tractatus attempts to unifylogic by deriving the truth-functionality of logical necessityfrom the thesis that a proposition shows its sense. I first interpret the Tractarian notion of showing as the displaying ofwhat is intrinsic to an expression (or a symbol). Then I argue that, according to theTractatus, the thesis that a proposition shows its sense implies the determinacy of sense, the possibility of the complete elimination of non-primitive symbols, the analyticity thesis and the strong analyticity thesis. The picture theory emerges as what provides the only acceptable account of an elementary proposition, subject to the constraint that a proposition must show its sense. The picture theory and the analyticity thesis then entail the contingency thesis (that an elementary proposition is contingent) and the independence thesis (that elementary propositions are mutually logically independent) which, together with the strong analyticity thesis, imply that all logical propositions are tautologies.     

On the Substitutional Characterization of First-Order Logical Truth

I consider the well-known criticism of Quine's characterization of first-order logical truth that it expands the class of logical truths beyond what is sanctioned by the model-theoretic account. Briefly, I argue that at best the criticism is shallow and can be answered with slight alterations in Quine's account. At worse the criticism is defective because, in part, it is based on a misrepresentation of Quine. This serves not only to clarify Quine's position, but also to crystallize what is and what is not at issue in choosing the model-theoretic account of first-order logical truth over one in terms of substitutions. I conclude by highlighting the need for justifying the belief that the definition of first-order logical truth in terms of models is superior to its definition in terms of substitutions.     

Kant on the Logical Origin of Concepts

In his lectures on general logic Kant maintains that the generality of a representation (the form of a concept) arises from the logical acts of comparison, reflection and abstraction. These acts are commonly understood to be identical with the acts that generate reflected schemata. I argue that this is mistaken, and that the generality of concepts, as products of the understanding, should be distinguished from the classificatory generality of schemata, which are products of the imagination. A Kantian concept does not provide mere criteria for noting sameness and difference in things, but instead reflects the inner nature of things. Its form consists in the self‐consciousness of a capacity to judge (i.e. the Concept is the ‘I think’).     

On the Referential Indeterminacy of Logical and Mathematical Concepts

Hartry Field has recently examined the question whether our logical and mathematical concepts are referentially indeterminate. In his view, (1) certain logical notions, such as second-order quantification, are indeterminate, but (2) important mathematical notions, such as the notion of finiteness, are not (they are determinate). In this paper, I assess Fields analysis, and argue that claims (1) and (2) turn out to be inconsistent. After all, given that the notion of finiteness can only be adequately characterized in pure second-order logic, if Field is right in claiming that second-order quantification is indeterminate (see (1)), it follows that finiteness is also indeterminate (contrary to (2)). After arguing that Field is committed to these claims, I provide a diagnosis of why this inconsistency emerged, and I suggest an alternative, consistent picture of the relationship between logical and mathematical indeterminacy.     

A Defense of the Kripkean Account of Logical Truth in First-Order Modal Logic

This paper responds to criticism of the Kripkean account of logical truth in first-order modal logic. The criticism, largely ignored in the literature, claims that when the box and diamond are interpreted as the logical modality operators, the Kripkean account is extensionally incorrect because it fails to reflect the fact that all sentences stating truths about what is logically possible are themselves logically necessary. I defend the Kripkean account by arguing that some true sentences about logical possibility are not logically necessary.     

中医研究中的中西医概念对应存在的逻辑问题及分析

在中医现代化研究中,必然要涉及到中西医概念“对应理解”问题。现实情况中,中西医概念的“混淆理解”“概念不对等”等逻辑问题是普遍存在的,中医的概念能否找到最恰当对应的现代医学概念,这既影响到研究选题的合理性、可行性,又直接影响到研究结果的可靠性、可推广性。这些研究既包括中医基础理论研究,也包括中医临床研究和各种实验室研究,而要解决这样的问题,就需要研究人员补齐短板,了解形式逻辑中概念逻辑的基本规则和要求,汇通中西医学理论,加深对中医基础概念的内涵及外延的精准理解。

     

Boolos and the Metamathematics of Quine's Definitions of Logical Truth and Consequence

The paper is concerned with Quine's substitutional account of logical truth. The critique of Quine's definition tends to focus on miscellaneous odds and ends, such as problems with identity. However, in an appendix to his influential article On Second Order Logic, George Boolos offered an ingenious argument that seems to diminish Quine's account of logical truth on a deeper level. In the article he shows that Quine's substitutional account of logical truth cannot be generalized properly to the general concept of logical consequence. The purpose of this paper is threefold: first, to introduce the reader to the metamathematics of Quine's substitutional definition of logical truth; second, to make Boolos' result accessible to a broader audience by giving a detailed and self-contained presentation of his proof; and, finally, to discuss some of the possible implications and how a defender of the Quinean concepts might react to the challenge posed by Boolos' result.     

Alethic Pluralism,Logical Validity,and Natural Truth

Philosophia - Alethic pluralism holds that there are many ways of being true. The view has been accused of being unable to do justice to the traditional account of logical validity, understood as...     

Explaining 'The Hardness of the Logical Must': Wittgenstein on Grammar, Arbitrariness and Logical Necessity

This paper explains (in Part A) Wittegnstein's understanding of the 'grammar' of our (or any) language, tracing its origins in the Tractatus's concept of logical syntax, and then examining the senses in which Wittegnstein, in his later work, viewed grammar as being 'arbitrary'. Then, armed with this understanding, it moves on (in Part B) to the task of examining how, within the framework of a Wittegnsteinian view of language, we should understand the inescapable 'compellingness' of logical necessity – what Wittegnstein calls the "hardness of the logical must". Whereas it is often thought that Wittegnstein's views on the nature of the 'grammar' of our concpets leads him towards a vitiatingly conventionalist or anti-realist understanding of necessity, in which its logical 'superhardness' becomes problematic, this paper will argue that there is actually no such tension in Wittegnstein's thought. In fact, it will be argued, an understanding of the ways in which our conceptual grammar is arbitrary casts a great deal of light on how it is that our concepts can nevertheless support a logically superhard, and normatively commanding, notion of necessity. In support of this view, I distinguish Wittegnstein's views on necessity from the 'classical' conventionalism of the Vienna Circle, and from the radical conventionalism of Michael Dummett, and defend Wittegnstein's view from a powerful recent attack from Quassim Cassam.