Evans envisaged a language containing both Russellian and descriptive names. A language with descriptive names, which can contribute to truth conditions even if they have no bearer, needs a free logicaltruth theory. But a metalanguage with this logic threatens to emasculate Russellian names. The paper details this problem and shows, on Evans's behalf, how it might be resolved.
This paper responds to criticism of the Kripkean account of logicaltruth 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. (shrink)
I consider the well-known criticism of Quine's characterization of first-order logicaltruth 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 logicaltruth over one in terms of substitutions. I conclude by highlighting the need for justifying the belief that the definition of first-order logicaltruth in terms of models is superior to its definition in terms of substitutions. (shrink)
This paper analyzes the logical truths as (very roughly) those truths that would still have been true under a certain range of counterfactual perturbations.What’s nice is that the relevant range is characterized without relying (overtly, at least) upon the notion of logicaltruth. This approach suggests a conception of necessity that explains what the different varieties of necessity (logical, physical, etc.) have in common, in virtue of which they are all varieties of necessity. However, this approach (...) places the counterfactual conditionals in an unfamiliar foundational role. (shrink)
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 logicaltruth, is fallacious. Next (section 2) I argue for an alternative explication of logicaltruth 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. (shrink)
This paper examines the question of the extensional correctness of Tarskian definitions of logicaltruth and logical consequence. I identify a few different informal properties which are necessary for a sentence to be an informal logicaltruth 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. (shrink)
It is shown that the logicaltruth of instances of the T-schema is incompatible with the formal nature of logicaltruth. In particular, since the formality of logicaltruth entails that the set of logical truths is closed under substitution, the logicaltruth of T-schema instances entails that all sentences are logical truths.
Donald Davidson has claimed that for every logicaltruth 5 of a language L, a theory of meaning for L will entail that S is a logicaltruth of L. Jim Edwards has argued (2002) that this claim is false if we take 'entails' to mean 'has as a logical consequence. In this paper, I first show that, pace Edwards, Davidson's claim is correct even under this strong reading. I then discuss the argument given by (...) Edwards and offer a diagnosis of where he went wrong. (shrink)
This English translation of the author's original work has been thoroughly revised, expanded and updated. The book covers logical systems known as type-free or self-referential . These traditionally arise from any discussion on logical and semantical paradoxes. This particular volume, however, is not concerned with paradoxes but with the investigation of type-free sytems to show that: (i) there are rich theories of self-application, involving both operations and truth which can serve as foundations for property theory and formal (...) semantics; (ii) these theories provide a new outlook on classical topics, such as inductive definitions and predicative mathematics; (iii) they are particularly promising with regard to applications. Research arising from paradoxes has moved progressively closer to the mainstream of mathematical logic and has become much more prominent in the last twenty years. A number of significant developments, techniques and results have been discovered. Academics, students and researchers will find that the book contains a thorough overview of all relevant research in this field. (shrink)
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 logicaltruth 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. (shrink)
The Identity of Indiscernibles seems like a good enough way to define identity. Roughly it simply says that if x and y have all and only the same properties, these will be the same object. However the principle has come under attack using a series of thought experiments employing the idea of radical symmetry. I follow the history of the debate including its theological origins to assess the contemporary arguments against the Identity of Indiscernibles. I argue that the principle is (...) viable as a logicaltruth, and so can be put to work in our idea of objects. (shrink)
W. V. O. Quine's well-known attack upon the analytic-synthetic distinction is held to affect only one of the two species of analytic statements he distinguishes. In particular it is not directed at and does not affect the so-called logical truths. In this paper the scope of Quine's attack is extended so as to embrace the logical truths as well. It is shown that the unclarifiability of the notion of 'synonymy' deprives us not only of "analytic statements that are (...) obtainable from logical truths by the replacement of synonyms with synonyms" but of "logical truths" themselves. (shrink)
Identity, existence, predication, necessity, and truth are vital concepts at the center of philosophy. Yet Colin McGinn believes that orthodox views of these topics are misguided in important ways. Philosophers and logicians have often distorted the nature of these concepts in an attempt to define them according to preconceived ideas. Logical Properties aims to respect the ordinary ways we talk and think when we employ these concepts, while at the same time showing that they are far more interesting (...) and peculiar than some have assumed; these notions correspond to real properties--logical properties--that challenge naturalistic metaphysical views. Written with a minimum of formal terminology, this book deals with logico-linguistic issues as well as ontological ones. The focus is on trying to get to the essence of the concept concerned, not merely finding some established notation for providing formal interpretations. (shrink)
The aim of this paper is to show what sorts of logics are required by externalist and internalist accounts of the meanings of natural kind nouns. These logics give us a new perspective from which to evaluate the respective positions in the externalist-internalist debate about the meanings of such nouns. The two main claims of the paper are the following: first, that adequate logics for internalism and externalism about natural kind nouns are second-order logics; second, that an internalist second-order logic (...) is a free logic—a second order logic free of existential commitments for natural kind nouns, while an externalist second-order logic is not free of existential commitments for natural kind nouns—it is existentially committed. (shrink)
The purpose of this paper is to present a thought experiment and argument that spells trouble for “radical” deflationism concerning meaning and truth such as that advocated by the staunch nominalist Hartry Field. The thought experiment does not sit well with any view that limits a truth predicate to sentences understood by a given speaker or to sentences in (or translatable into) a given language, unless that language is universal. The scenario in question concerns sentences that are not (...) understood but are known to be logical consequences of known and understood sentences. Ultimately, the issue turns on the notion of logical consequence that is available to various versions of deflationism. (shrink)
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. (shrink)
If logicaltruth is necessitated by sheer syntax, mathematics is categorially unlike logic even if all mathematics derives from definitions and logical principles. This contrast gets obscured by the plausibility of the Synonym Substitution Principle implicit in conceptions of analyticity: synonym substitution cannot alter sentence sense. The Principle obviously fails with intercepting: nonuniform term substitution in logical sentences. 'Televisions are televisions' and 'TVs are televisions' neither sound alike nor are used interchangeably. Interception synonymy gets assumed because (...)logical sentences and their synomic interceptions have identical factual content, which seems to exhaust semantic content. However, intercepting alters syntax by eliminating term recurrence, the sole strictly syntactic means of ensuring necessary term coextension, and thereby syntactically securing necessary truth. Interceptional necessity is lexical, a notational artifact. The denial of interception nonsynonymy and the disregard of term recurrence in logic link with many misconceptions about propositions, logical form, conventions, and metalanguages. Mathematics is distinct from logic: its truth is not syntactic; it is transmitted by synonym substitution; term recurrence has no essential role. The '=' of mathematics is an objectual relation between numbers; the '=' of logic marks a syntactic relation of coreferring terms. (shrink)
This paper aims to explain how the Tractatus attempts to unify logic by deriving the truth-functionality of logical necessity from the thesis that a proposition shows its sense. I first interpret the Tractarian notion of showing as the displaying of what is intrinsic to an expression (or a symbol). Then I argue that, according to the Tractatus, 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. (shrink)
The syntax of Frege's scientific language iscommonly taken to be characterized by two oddities:the representation of the intended illocutionary roleof sentences by a special sign, the judgement-stroke,and the treatment of sentences as a species ofsingular terms. In this paper, an alternative view isdefended. The main theses are: (i) the syntax ofFrege's scientific language aims at an explication ofthe logical form of judgements; (ii) thejudgement-stroke is, therefore, a truth-operator, nota pragmatic operator; (iii) in Frege's first system,` ' expresses that (...) the circumstance is a fact, and in his second system that thetruth-value - is the True; (iv) in bothsystems, the judgement-stroke is construed as a signsui generis, not as a genuine predicate; (v) itscounterpart in natural language is the syntactic ``formof assertoric sentences'', not the (redundant)truth-predicate; (vi) neither in Frege's first nor inhis second system sentences are treated as singular terms. (shrink)
In this paper I examine a cluster of concepts relevant to the methodology of truth theories: ‘informative definition’, ‘recursive method’, ‘semantic structure’, ‘logical form’, ‘compositionality’, etc. The interrelations between these concepts, I will try to show, are more intricate and multi-dimensional than commonly assumed.
I argue that conventional implicatures embed in logical compounds, and are non-truth-conditional contributors to sentence meaning. This, I argue has significant implications for how we understand truth, truth-conditional content, and truth-bearers.
1. In ‘A problem for expressivism’ Frank Jackson and Philip Pettit argue ‘that expressivists do not have a persuasive story to tell about how ethical sentences can express attitudes without reporting them and, in particular, without being true or false’ (1998: 240). Brieﬂy: expressivists say that ethical sentences serve to express non-cognitive attitudes, but that these sentences do not report non-cognitive attitudes. The view that ethical sentences do report non-cognitive attitudes is not Expressivism (and not non-cognitivism), but rather a version (...) of cognitivism. According to (what we’ll call) Subjectivism, a typical ethical sentence like ‘Abortion is wrong’ reports the speaker’s non-cognitive attitude toward abortion; it says, in effect, that abortion is the object of some attitude of the speaker’s. Expressivists, by contrast, say that the sentence expresses a non-cognitive attitude toward abortion, but does not say that the speaker has it. Ayer put it this way: I can say that I am bored by uttering the sentence ‘I am bored’, but I can express boredom, without saying that I am bored, by yawning (Ayer 1952: 109). (shrink)
I discuss Quine's claim that anyone denying what we now take to be a logicaltruth would be using logical words in a novel way. I trace this to a confusions between outright denial and failure to assert, and assertion of a negation. (This abstract is written from memory decades after the article.).
This major contribution to the study of F.H. Bradley, the most influential member of the nineteenth century school of British Idealist philosophers, offers a sustained interpretation of his Principles of Logic. After explaining how it is possible for inferences to be valid and yet have conclusions containing new information, James Allard describes how this solution provides a basis for Bradley's metaphysical view that reality is one interconnected experience. In the process he uncovers a new problem as to the nature of (...)truth. (shrink)
Truth, etc. is a wide-ranging study of ancient logic based upon the John Locke lectures given by the eminent philosopher Jonathan Barnes in Oxford. The book presupposes no knowledge of logic and no skill in ancient languages: all ancient texts are cited in English translation; and logical symbols and logical jargon are avoided so far as possible. Anyone interested in ancient philosophy, or in logic and its history, will find much to learn and enjoy here.
The present article purports to show that the protocol sentence debate, pursued by some leading members of the Vienna Circle in the mid-1930s, was essentially a controversy over the explanation and the real significance of the concept of truth. It is further shown that the fundamental issue underlying the discussions about the concept of truth was the relationship between form and content, as well as between logic/language and the world. R. Carnap was the philosopher who most explicitly and (...) systematically attempted to come to grips with this problem. It is shown that the form-content distinction pervades the three most important phases of Carnap's philosophical development: the structuralist (in Der logische Aufbau der Welt), the syntactical and the semantical. His final semantical stance is essentially determined by the concept of linguistic frameworks. The article purports to demonstrate that this concept cannot be dispensed with in philosophy, but that Carnap failed to work out its ontological implications. Finally, the concept of an internal ontology is briefly delineated. (shrink)
(i) It is propositions, not sentences, that are true or false. It is true ‘Dogs bark’ does not make sense. It is true that dogs bark does. (ii) and (iii) Davidson wrong about ‘that’. (iv) The difference between ‘implies’ and ‘if ... then ...’. (v), (vi), (vii) and (viii) Russell, not Quine, right about the subject matter of logic. (ix) The objectual and substitutional interpretations of quantifiers compatible. (x), (xi), (xii), (xiii), (xiv), (xv) and (xvi) Implications for well-known theories of (...)truth; truth correspondence. (xvii), (xviii) and (xix) and (xx) Implications for the principle of bivalence, the law of excluded middle, and the principle of non-contradiction. (xxi) Recapitulation. (xxii) ‘That’ and entailment. (xxiii) Propositions not entities, subsistent or otherwise. Footnotes1 This article was stimulated by some remarks by J. J. C. Smart in criticism of a piece of work (God, Freedom and Immortality, Ashgate, 1999) that he was kind enough to read for me. I am greatly indebted to my friend David Rees for correcting the manuscript, and making some valuable suggestions concerning its content. (shrink)
Finland is internationally known as one of the leading centers of twentieth century analytic philosophy. This volume offers for the first time an overall survey of the Finnish analytic school. The rise of this trend is illustrated by original articles of Edward Westermarck, Eino Kaila, Georg Henrik von Wright, and Jaakko Hintikka. Contributions of Finnish philosophers are then systematically discussed in the fields of logic, philosophy of language, philosophy of science, history of philosophy, ethics and social philosophy. Metaphilosophical reflections on (...) the nature of philosophy are highlighted by the Finnish dialogue between analytic philosophy, phenomenology, pragmatism, and critical theory. (shrink)
Benjamin Schnieder has argued that several traditional definitions of truth-functionality fail to capture a central intuition informal characterizations of the notion often capture. The intuition is that the truth-value of a sentence that employs a truth-functional operator depends upon the truth-values of the sentences upon which the operator operates. Schnieder proposes an alternative definition of truth-functionality that is designed to accommodate this intuition. We argue that one traditional definition of ‘truth-functionality’ is immune from the (...) counterexamples that Schnieder proposes and is preferable to Schnieder’s alternative. (shrink)
First, we describe a psychological experiment in which the participants were asked to determine whether sentences of first-order logic were true or false in finite graphs. Second, we define two proof systems for reasoning about truth and falsity in first-order logic. These proof systems feature explicit models of cognitive resources such as declarative memory, procedural memory, working memory, and sensory memory. Third, we describe a computer program that is used to find the smallest proofs in the aforementioned proof systems (...) when capacity limits are put on the cognitive resources. Finally, we investigate the correlation between a number of mathematical complexity measures defined on graphs and sentences and some psychological complexity measures that were recorded in the experiment. (shrink)
A formula is a contingent logicaltruth when it is true in every model M but, for some model M , false at some world of M . We argue that there are such truths, given the logic of actuality. Our argument turns on defending Tarski’s definition of truth and logicaltruth, extended so as to apply to modal languages with an actuality operator. We argue that this extension is the philosophically proper account of validity. (...) We counter recent arguments to the contrary presented in Hanson’s ‘Actuality, Necessity, and LogicalTruth’ (Philos Stud 130:437–459, 2006 ). (shrink)
Anti-realism is a doctrine about logic, language, and meaning that is based on the work of Wittgenstein and Frege. In this book, Professor Tennant clarifies and develops Dummett's arguments for anti-realism and ultimately advocates a radical reform of our logical practices.
The paper deals with the question whether logicaltruth carry information. On the one hand it seems that we gain new information by drawing inferences or arriving at some theorems. On the other hand the formal accounts of information and information content which are most widely known today say that logicaltruth carry no information at all. The latter is shown by considering these accounts. Then several ways to deal with the dilemma are distinguished, especially syntactic (...) and ontological solutions. A version of a syntactical solution is favoured. (shrink)