Logics and Falsifications: A New Perspective on Constructivist Semantics

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From Frege's 'Evening Star' vs. Synonymous terms are seemingly substitutable for each other in a sentence without affecting its meaning. But what about intercepting or non-uniform substitution, as in 'Greeks are Hellenes'?

blacksmithsurgical.com/t3-assets/memoir/the-house-by-the-church-yard.php Frege had stressed that such sentences have "cognitive value. For him one reason is evident: 'Greeks are Greeks' and 'Greeks are Hellenes' are not used alike, with the latter used to explain the meaning of its terms, more like ' 'Greeks' means Hellenes'. Wertheimer points out that Putnam in an early paper had provided the first lines of argument for interception nonsynonymy: Logical form has semantic content, and interceptions lack the truth securing syntax of logical sentences, e.

Wertheimer views the criticisms of that paper as misdirected toward intensional conundra whereas Putnam was emphasizing logical syntax per se. For Wertheimer, the final irony here is that Putnam himself in a paper renounced interception nonsynonymy. With such a to and fro at the intersection of many issues Wertheimer regards interception nonsynonymy is an important, empirically evident phenomenon that must be understood.

Wertheimer proceeds to approach interception nonsynonymy from different perspectives and continues to play off of Putnam's two papers. Wertheimer then confronts an important defense of interception synonymy , that intercepting substitution does preserve meaning, made by Alonzo Church. Church, also in , suggested that a good way to test whether a sentence is about some linguistic expression, or rather about something that the expression is used to mean , is to translate the sentence into a foreign language.

Introduction

The authors critically investigate how contemporary paraconsistent logics can be used to better understand human reasoning in science and mathematics. Sandu uses IF-logic to argue for the logical consistency of a program for defining truth; in the next paper his collaborator argues from the vantage point that takes IF-logic as "our true basic logic. Concepts map objects to truth values, according to Frege. Buy it Again. Here, he criticised psychologism , naturalism , inductivism , and logical positivism , and put forth his theory of potential falsifiability as the criterion demarcating science from non-science. New ideas have a striking similarity to genetic mutations.

However, Wertheimer argues that Church's arguments with his test are at base circular and proceeds to disentangle various elements in an extended exegesis. Incidentally, Quine, with his well-known thesis of the "indeterminacy of translation," would also not subscribe to Church's test. Wertheimer then proceeds to questions of truth and modality, pointing out further inadequacies with Church's test; while logical truths are true by syntax, interceptions alter syntax and modality.

George Wilson takes as his starting point Putnam's "The Meaning of 'Meaning' " and within its realist context entertains temporal ambiguity of extensional reference for a general term. Focusing on a specific example, Putnam would endorse a : The extension of 'gold' as the term is used now is the same as the extension of 'gold' as the term was used in To elaborate, the extension of 'gold' is the collection of objects of which 'is gold' is true of; 'is gold' as used now is taken to be true of an object exactly when it is composed of the element with atomic number 79; and is before the advent of molecular chemistry.

Wilson however argues for the viability of b : It is not the case that the use of 'gold' in determined that 'is gold' was true of an object exactly when it is gold i. Wilson presents an argument of the type advanced by Gary Ebbs: Platinum, with atomic number 78, was chemically indistinguishable from gold in ; later, it can be maintained that any earlier ascription of 'gold' to platinum was mistaken or, acceding to previous usage, that platinum could be acknowledged as a kind of gold.

How are a and b to be reconciled? Wilson argues with another heuristic example about emerging standards that a and b are fully and intelligibly compatible, and that it is the implication , if a then not b , which is false.

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A standard was settled upon for 'gold' some time after , and "we apply it to our own uses of the word and, retroactively, to the legitimate precursors of those present uses. Varying extension also plays a role in the next paper, but for a reason other than ambiguity. Terry Horgan confronts the Sorites Paradox, regarding it as having profound implications for metaphysics, logic, and semantics, and describes a general approach to the issues it raises.

A paradox is an apparently unacceptable conclusion drawn from apparently acceptable premises by apparently acceptable reasoning; paradoxes have long played pivotal roles in philosophy because of the issues that they have elicited about meaning and truth. The Sorites Paradox addresses the vagueness of predicates that admit numerical calibration.

In a rendition of Horgan's, let B n abbreviate 'A man with n hairs on his head is bald'. He rejects the "epistemic" position according to which there actually is such a transition point but it "is unknowable to finite minds like ours," so to him some kind of repudiation of standard two-valued logic is necessary for an adequate analysis. Horgan next argues that there are two broad metaphysical approaches to vagueness depending on whether one affirms or denies ontological vagueness , vagueness in the mind-independent, discourse-independent world.

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The first approach posits genuine objects and properties that are vague, and the second approach takes vagueness to be a matter of language and of thought content. Horgan favors the latter approach and the treatment of truth as indirect correspondence between vague language and non-vague reality.

One such treatment is "supervaluationism," according to which there could be many permissible interpretations that make precise the references for the vocabulary, and to be true is formulated as holding in all permissible interpretations. Horgan himself advocates another treatment, initially called by him "language-game" semantics, which construes truth as "semantically correct assertibility" under contextually operative semantic standards. He takes as an essential attribute of vagueness "boundarylessness," which for a predicate like 'is bald' emphasizes that there is no determinate fact of the matter about the transition from true statements B n to false ones.

Horgan concludes that boundarylessness is logically incoherent, in a generic way that does not presuppose any particular logic of vagueness. But for Horgan, "the world cannot be logically incoherent, even in the weak way: it cannot have features that are the ontological analogues of mutually unsatisfiable semantic standards. Horgan's "transvaluationism" is his general approach to vagueness, and it makes two fundamental claims: First, vagueness is weakly logically incoherent but not strongly so; and second, vagueness is "viable, legitimate, and indeed essential in human language and thought.

One is reminded here of Wittgenstein's open attitude toward formal contradictions. In a "forced march" of "is it true? Timothy Williamson's paper, bridging the first swath of papers of this volume with the next, provides a new approach to the semantic paradoxes that, in contradistinction to indexicality analyses, posits changes in linguistic meaning to key terms. A semantic paradox is a paradox that turns on 'true'. The best known of the semantic paradoxes fall under the rubric of the Liar Paradox, one version being to decide whether the speaker of 'What I am now saying is false' is saying something true or false.

Williamson begins by asking: If paradoxes arise from shifts of context for terms like 'true', should this be attributed to their indexicality change of reference without change of linguistic meaning or to their ambiguity change of linguistic meaning? Stability of linguistic meaning would seem to be the basis of successful communication, and this would seem to favor the indexicality explanation according to which terms like 'true' function like 'I', a term we understand even if uttered by a stranger.

However, Williamson takes a critical view of the indexicality approach, particularly of Tyler Burge. In a modern version of approaches taken by Russell and Tarski, Burge resolved the Liar Paradox with a system of levels i and terms 'true i ' for each level that do not interact pathologically with each other. While having such a system brings out the indexicality, Williamson argues that a strengthened Liar Paradox using 'true at any level' infects Burge's approach. Williamson then takes David Kaplan's treatment of indexicality and develops a 'context' sensitive version of the Liar Paradox, one that suggests a non-indexicality analysis.

Williamson's proposal is that the semantic paradoxes turn on actual shifts of linguistic meaning for their key terms. He sketches a schematic approach for context-sensitive speech acts based on 'say' and connecting that with 'true' and 'false'.

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The conceptual roles of 'true' and 'false' are fixed relative to 'say', but in his dynamic view 'say' can undergo small changes of meaning. Williamson argues that his approach is not defeated by a strengthened Liar Paradox because future understanding cannot be anticipated in present meanings.

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He suggests that even the term 'meaning' is unstable, and concludes by presenting a rather Wittgensteinian picture: Instabilities of meaning preclude any exhaustive treatment of all the semantic paradoxes, and indeed, further reflection uncovers new paradoxes and new solutions. All of the previous papers dealt with truth, to the extent that they were engaged with the relationship between language and reality.

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However, they had remained largely neutral as to the nature of truth: What is it for a sentence or proposition to be true? Theories of truth tackle this and like questions, and one can say that to the extent that they expand beyond the logic of truth they become avowedly metaphysical.

Aristotle wrote in his Metaphysics , "To say of what is that it is not, or of what is not that it is, is false; and to say of what is that it is, or of what is not that it is not, is true. Tarski in the early s made the first significant advance in the logic of truth with his "semantical conception" of truth. He first articulated equivalences, of which an instance is: 'snow is white' is true if and only if snow is white. To elaborate, 'snow is white' is a sentence in the object language, the language under study, and the sentence is to be true exactly when snow is white, this entire assertion being made in the meta-language where the concept of truth is being articulated.

The schematic form of these equivalences, already seen in some of the earlier papers in this volume, is called T, and Tarski argued that definitions of truth must meet the material adequacy condition , that every instance of his schema T holds. Tarski next provided a definition of truth for the sentences of any language formalized in first-order logic, assuming his schema T for the basic atomic sentences and showing how the schema may be extended to all sentences of the language.

His definition brought out the inherent assumption of compositionality for the language, that the meaning or truth value of a complex sentence is functionally determined by the meaning or truth value of its constituent parts. Moreover, his definition accommodated infinitely many sentences, being a seminal example of what is now known as a recursive definition.

The crucial move that he made was first to define satisfaction , a relation between sequences of items in an interpretation model for open formulas formulas with unquantified variables , and then to define truth for sentences formulas without unquantified variables in terms of satisfaction. Carnap and Quine both lauded Tarski's work, the former regarding it as having legitimized the notion of truth by reducing it to unproblematic notions and the latter emphasizing how the truth predicate as embodied by schema T is "a device of disquotation" for passing from words quoted to words used.

Tarski's analysis of truth in terms of satisfaction serves as the basis of the mathematical field of model theory, the generalization of abstract algebra incorporating formal semantics in a set-theoretic environment. Having established his now famous mathematical result on the undefinability of truth in formal languages, Tarski believed that it is hopeless to define truth for natural languages. However, for most philosophers bent on tackling the concept of truth for us and our natural languages, Tarski's analysis only serves as a beginning-if that-depending on how one takes his schema T.

Tarski's work nevertheless established a framework of discussion for succeeding work on truth, as illustrated by the four papers here on theories of truth. Dan Goldstick explores two commitments of what he terms the 'Correspondence Theory of Truth'. Correspondence theories of truth analyze truth in terms of a bifurcation into propositions or sentences and reality or facts , and an interconnecting correlation.

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Such theories are longstanding in various versions, with Tarski's "semantical conception" arguably one. Goldstick begins by asking what more there is to the Correspondence Theory than Aristotle's dictum and Tarski's disquotational equivalence. Goldstick dismisses logical atomism, according to which the truth of "molecular" propositions are to be analyzed in terms of their "atomic" parts. Elsewhere, he had in fact argued that the sentence 'Water is heavier than ice, and water is water' expresses the same proposition as 'Water is heavier than ice'.

Goldstick then discusses the two commitments of the theory: the distinctness of the existence of a true belief from the existence of the fact believed including the denial that one in general logically entails the other , and an isomorphism between the two. This articulation of correspondence in terms of beliefs, distinctness, and structural similarity has much in common with Russell's pre-Tarskian articulation of correspondence in The Problems of Philosophy Goldstick then raises the following concern: Just as there must be an isomorphism between true beliefs and the facts of the matter, a parallel case can be made for an isomorphism between false beliefs and the facts of matter.

Recalling Wittgenstein's treatment of negation in his Tractatus 4. This leads him to conclude that beyond correspondence there must be more to the nature of truth, in the direction of the differentiation of facts, a direction he intends to pursue. Lorenz Puntel offers a new explanation of the concept of truth, one directed at answering the question that serves as his title: What does '.

He first declares that his explanation will be deliberately restricted to particular sentences expressing propositions at the basic level of 'snow is white', arguing that the basic case has not been adequately treated. Puntel also argues against well-known arguments, including Tarski's, that truth is inexpressible undefinable.

Puntel then stresses that his title question is but a special case of the more general question, what does this sort of "semantic vocabulary" express?

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He describes how, starting with language as primordially a system of symbols, "the function of semantic vocabulary is to make language fully determinate 'from within language itself'. Puntel then reviews R. Brandom's "prosentence" theory of truth.

According to the original prosentence theory of truth, just as the pronoun 'he' in 'Tom did as he was told' functions "anaphorically" by referring to the antecedent noun 'Tom', 'it is true' and 'that is true' function anaphorically by referring to antecedent sentences. For Brandom 'is true' is a prosentence-forming operator which when applied to a term like 'it' or 'that' for a sentence tokening yields a prosentence with that tokening as anaphoric antecedent.