We develop a bottom-up approach to truth-value semantics for classical logic of partial terms based on equality and apply it to prove the conservativity of the addition of partial description and selection functions, independently of any strictness assumption.

This chapter contains sections titled: Recent Relativism Standard Semantics and Ordinary Truth Relativist Semantics and Ordinary Truth Issues of Commensurability References.

The general fact of the impossibility of a bivalent, truth-functional semantics for the propositional structures determined by quantum mechanics should be more subtly demarcated according to whether the structures are taken to be orthomodular latticesP L or partial-Boolean algebrasP A; according to whether the semantic mappings are required to be truth-functional or truth-functional ; and according to whether two-or-higher dimensional Hilbert spaceP structures or three-or-higher dimensional Hilbert spaceP structures are being considered. If the (...) quantumP structures are taken to be orthomodular latticesP L, then bivalent mappings which preserve the operations and relations of aP L must be truth-functional . Then as suggested by von Neumann and Jauch-Piron and as proven in this paper, the mere presence of incompatible elements in aP L is sufficient to rule out any semantical or hidden-variable proposal which imposes this strong condition, for anytwo-or-higher dimensional Hilbert spaceP L structure. Thus from the orthomodular lattice perspective, the peculiarly non-classical feature of quantum mechanics and the peculiarly non-Boolean feature of the quantum propositional structures is the existence of incompatible magnitudes and propositions. However, the weaker truth-functionality condition can instead be imposed upon the semantic or hidden-variable mappings on theP L structures, although such mappings ignore the lattice meets and joins of incompatibles and preserve only the partial-Boolean algebra structural features of theP L structures. Or alternatively, the quantum propositional structures can be taken to be partial-Boolean algebrasP A, where bivalent mappings which preserve the operations and relations of aP A need only be truth-functional (c). In either case, the Gleason, Kochen-Specker proofs show that any semantical or hidden variable proposal which imposes this truth-functionality (c) condition is impossible for anythree-or-higher dimensional Hilbert spaceP A orP L structures. But such semantical or hidden-variable proposals are possible for any two dimensional Hilbert spaceP A orP L structures, in spite of the presence of incompatibles in these structures, in spite of the fact that Heisenberg's Uncertainty Principle applies to the incompatible elements in these structures, and in spite of the fact that these structures are non-Boolean in the Piron sense. (shrink)

How does metaphysical grounding interact with the truth-functions? I argue that the answer varies according to whether one has a worldly conception or a conceptual conception of grounding. I then put forward a logic of worldly grounding and give it an adequate semantic characterisation.

Our aim in the present paper is to investigate, from the standpoint of truth-theoretic semantics, English tense, temporal designators and quantifiers, and other expressions we use to relate ourselves and other things to the temporal order. Truth-theoretic semantics provides a particularly illuminating standpoint from which to discuss issues about the semantics of tense, and their relation to thoughts at, and about, times. Tense, and temporal modifiers, contribute systematically to conditions under which sentences we utter are (...) true or false. A Tarski-style truth-theoretic semantics, by requiring explicitly represented truth conditions, helps to sharpen questions about the function of tense, and to deepen our insight into the contribution the tenses and temporal modifiers make to what we say by using them. (shrink)

Many-valued logics are standardly defined by logical matrices. They are truth-functional. In this paper non truth-functional many-valued semantics are presented, in a philosophical and mathematical perspective.

Two of the main intuitions that underlie the phenomenon of vagueness are the truth-functional and the penumbral intuitions. After presenting and contrasting them, I will put forward Tappenden's gappy approach to vagueness (which takes into account the truth-functional intuition). I will contrast Tappenden'sview with another of the theories of vagueness that see it as a semantic phenomenon: Supervaluationism (which takes into account the penumbral intuition). Then I will analyze some objections to Tappenden's approach and some objections (...) to Supervaluationism. Finally, I will present my own worries about Tappenden's account. (shrink)

Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that thisextended notion of fibring preserves completeness (...) under certain reasonableconditions. This completeness transfer result, the second main contributionof the paper, generalizes the one established in Zanardo et al. (2001) butis obtained using new techniques that explore the properties of a suitablemeta-logic (conditional equational logic) where the (possibly)non-truth-functional valuations are specified. The modal paraconsistentlogic of da Costa and Carnielli (1988) is studied in the context of this novel notionof fibring and its completeness is so established. (shrink)

What is the fundamental insight behind truth-functionality ? When is a logic interpretable by way of a truth-functional semantics? To address such questions in a satisfactory way, a formal definition of truth-functionality from the point of view of abstract logics is clearly called for. As a matter of fact, such a definition has been available at least since the 70s, though to this day it still remains not very widely well-known. A clear distinction can be (...) drawn between logics characterizable through: (1) genuinely finite-valued truth-tabular semantics; (2) no finite-valued but only an infinite-valued truthtabular semantics; (3) no truth-tabular semantics at all. Any of those logics, however, can in principle be characterized through non-truth-functional valuation semantics, at least as soon as their associated consequence relations respect the usual tarskian postulates. So, paradoxical as that might seem at first, it turns out that truth-functional logics may be adequately characterized by non-truth-functional semantics . Now, what feature of a given logic would guarantee it to dwell in class (1) or in class (2), irrespective of its circumstantial semantic characterization? (shrink)

The aim of the present paper is to introduce a system, where the epistemic state of an agent is represented truth-functionally. In order to obtain this system, we propose a four-valued logic, that we call the logic of rational agent, where the fact of knowing something is formalized at the level of valuations, without the explicit use of epistemic knowledge operator. On the basis of this semantics, a sound and complete system with two distinct truth-functional negations (...) is provided. These negations allow us to express the statements about knowing or not knowing something at the syntactic level. Moreover, such a system is applied to the analysis of knowability paradox. In particular, we show that the paradox is not derivable in terms of the logic of rational agent. (shrink)

The expressive truth functions of two-valued logic have all been identified. This paper begins the task of identifying the expressive truth functions of n-valued logic by characterizing the unary ones. These functions have distinctive algebraic, semantic, and closure-theoretic properties.

This book explores linguistic and philosophical issues presented by sentences expressing personal taste, such as Roller coasters are fun, or Licorice is tasty. Standard semantic theories explain the meanings of sentences by specifying the conditions under which they are true; here, Peter Lasersohn asks how we can account for sentences that are concerned with matters of opinion rather than matters of fact. He argues that a truth-theoretic semantic theory is appropriate even for sentences like these, but that for such (...) sentences, truth and falsity must be assigned relative to perspectives, rather than absolutely. The book provides a detailed and explicit formal grammar, working out the implications of this conception of truth both for simple sentences and for reports of mental attitude. The semantic analysis is paired with a pragmatic theory explaining what it means to assert a sentence which is true or false only relativistically, and with a speculative account of the functional motivation for a relativized notion of truth. (shrink)

Łukasiewicz presented two different analyses of modal notions by means of many-valued logics: the linearly ordered systems Ł3,..., Open image in new window,..., \; the 4-valued logic Ł he defined in the last years of his career. Unfortunately, all these systems contain “Łukasiewicz type paradoxes”. On the other hand, Brady’s 4-valued logic BN4 is the basic 4-valued bilattice logic. The aim of this paper is to show that BN4 can be strengthened with modal operators following Łukasiewicz’s strategy for defining (...) class='Hi'>truth-functional modal logics. The systems we define lack “Łukasiewicz type paradoxes”. Following Brady, we endow them with Belnap–Dunn type bivalent semantics. (shrink)

It is argued that truth value of a sentence containing free variables in a context of use, just as the reference of the free variables concerned, depends on the assumptions and posits given by the context. However, context may under-determine the reference of a free variable and the truth value of sentences in which it occurs. It is argued that in such cases a free variable has indeterminate reference and a sentence in which it occurs may have indeterminate (...) truth value. On letting, say, x be such that \, the sentence ‘Either \ or \’ is true but the sentence ‘\’ has an indeterminate truth value: it is determinate that the variable x refers to either 2 or \, but it is indeterminate which of the two it refers to, as a result ‘\’ has a truth value but its truth value is indeterminate. The semantic indeterminacy is analysed in a ‘radically’ supervaluational semantic framework closely analogous to the treatment of vagueness in McGee and McLaughlin and Smith, which saves bivalence, the T-schema and the truth-functional analysis of the boolean connectives. It is shown that on such an analysis the modality ‘determinately’ is quite clearly not an epistemic modality, avoiding a potential objection raised by Williamson against such ‘radically’ supervaluational treatments of vagueness, and that determinate truth is the semantic value preserved in classically valid arguments. The analysis is contrasted with the epistemicist proposal of Breckenridge and Magidor which implies that ‘\’ has a determinate but unknowable truth value. (shrink)

Nondeterministic programs occurring in recently developed programming languages define nondeterminate partial functions. Formulas (Boolean expressions) of such nondeterministic languages are interpreted by a nonempty subset of {T (true), F (false), U (undefined)}. As a semantic basis for the propositional part of a corresponding nondeterministic three-valued logic we study the notion of a truth-function over {T, F, U} which is computable by a nondeterministic evaluation procedure. The main result is that these truth-functions are precisely the functions satisfying four basic (...) properties, called -isotonic, –-isotonic, hereditarily guarded, and hereditarily guard-using, and that a function satisfies these properties iff it is explicitly definable (in a certain normal form) from if..then..else..fi, binary choice, and constants. (shrink)

A semantics of vagueness should reject the principle that every statement has a truth-value yet retain the classical tautologies. A many-value, non-truth-functional semantics and a semantics of super-valuations each have this result. According to the super-valuation approach, 'if a man with n hairs on his head is bald, then a man with n plus one hairs on his head is also bald' is false because it comes out false no matter how the vague predicate (...) 'is bald' is appropriately made precise. But why should a sentence in which components actually remain imprecise be regarded as actually false just because it would be false if its components were precise? On one of the alternative treatments of quantification allowed by the many-value approach, the sentence in question is assigned an intermediate value closer to 'false' than to 'true'. Despite the elegance of the super-valuation approach, there are reasons to prefer the many-value approach. (shrink)

This article deals with supervaluationism and the failure of truth-functionality. It draws some distinctions that may contribute to a better understanding of this semantic framework.

In this paper, I examine the concept of truth in classical Chinese philosophy, beginning with a critical examination of Chad Hansen’s claim that it has no such concept. By using certain passages that emphasize analogous concepts in the philosophy of language of the Later Mohist Canons, I argue that while there is no word in classical Chinese that functions as truth generally does in Western philosophy for grammatical reasons, the Later Mohists were certainly working with a notion of (...) semantic adequacy in which a language-to-world relationship is made an object of investigation, challenging Hansen’s position that classical Chinese functions within a primarily pragmatic linguistic framework in which a language-to-user relationship determines the meaning of words. (shrink)

Over the last two decades, semantic theory has been marked by a continuing shift from a static view of meaning to a dynamic one. The increasing interest in extending semantic analysis from isolated sentences to larger units of discourse has fostered the intensive study of anaphora and coreference, and this has engendered a shift from viewing meaning as truth conditions to viewing it as the potential to change the "informational context".

Many areas of philosophy employ a distinction between factual and non-factual (descriptive/non-descriptive, cognitive/non-cognitive, etc) uses of language. This book examines the various ways in which this distinction is normally drawn, argues that all are unsatisfactory, and suggests that the search for a sharp distinction is misconceived. The book develops an alternative approach, based on a novel theory of the function and origins of the concept of truth. The central hypothesis is that the main role of the normative notion of (...) truth is to encourage speakers to argue, with long-run behavioural advantages. This offers a fresh perspective on many debates about realism in contemporary philosophy. (shrink)

§1. The mission of axiomatic set theory. What is set theory needed for in the foundations of mathematics? Why cannot we transact whatever foundational business we have to transact in terms of our ordinary logic without resorting to set theory? There are many possible answers, but most of them are likely to be variations of the same theme. The core area of ordinary logic is by a fairly common consent the received first-order logic. Why cannot it take care of itself? (...) What is it that it cannot do? A large part of every answer is probably that first-order logic cannot handle its own model theory and other metatheory. For instance, a first-order language does not allow the codification of the most important semantical concept, viz. the notion of truth, for that language in that language itself, as shown already in Tarski. In view of such negative results it is generally thought that one of the most important missions of set theory is to provide the wherewithal for a model theory of logic. For instance Gregory H. Moore asserts in his encyclopedia article “Logic and set theory” thatSet theory influenced logic, both through its semantics, by expanding the possible models of various theories and by the formal definition of a model; and through its syntax, by allowing for logical languages in which formulas can be infinite in length or in which the number of symbols is uncountable. (shrink)

A central topic in the logic of science concerns the proper semantic analysis of theoretical sentences, that is sentences containing theoretical terms. In this paper, we present a novel choice-semantical account of theoretical truth based on the epsilon-term definition of theoretical terms. Specifically, we develop two ways of specifying the truth conditions of theoretical statements in a choice functional semantics, each giving rise to a corresponding logic of such statements. In order to investigate the inferential strength (...) of these logical systems, we provide a translation of each truth definition into a modal definition of theoretical truth. Based on this, we show that the stronger notion of choice-semantical truth captures more adequately our informal semantic understanding of scientific statements. (shrink)

This paper examines two explanations Sellars gives, at successive stages of his career, of how semantic vocabulary lets us relate linguistic expressions to extra-linguistic reality. Despite their differences, both explanations reveal a distinctive pragmatist approach. According to Sellars, we do not use semantic vocabulary to describe language-world relations. Rather, our taking language to relate to the world is implicit in the moves licensed by our semantic assertions. I argue that Sellars's discussions of the function of semantic vocabulary point to an (...) overlooked position regarding the relation between the concepts of meaning and truth. According to him, the function of meaning ascriptions cannot be explained independently of the function of truth ascriptions. That is because the function of meaning ascriptions essentially involves licensing claims about the world when combined with truth ascriptions. If he is right, this poses a challenge to deflationary accounts of the function of truth talk. (shrink)

This article is about the conception of truth and signification in Augustine's early philosophical writings. In the first, semantic-linguistic part, the gradual shift of Augustine's position towards the Academics is treated closely. It reveals that Augustine develops a notion of sign which, by integrating elements of Stoic epistemology, is suited to function as a transmitter of true knowledge through linguistic expressions. In the second part, both the ontological structure of signified (sensible) things and Augustine's solution to the apparent tautologies (...) of mathematical truths are examined. Again his notion of sign turns out to be the keystone; this time, however, the natural in contrast to the conventional sign of linguistic expressions. In their complementarity, both parts show how Augustine intensely struggles with and (partially) overcomes the skepticism of the sensible world through his conception of sign and signification. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Did Hobbes Have a Semantic Theory of Truth? WILLEM R. DEJONG 1. INTRODUCTION THE qUESTIONRAISEDin the title of this article may strike the reader as a bit anachronistic. A phrase like 'semantic theory of truth' evokes associations with rather recent developments in logic, especially the work of Alfred Tarski. Nevertheless, it is generally agreed that Hobbes made important observations of a semantical nature. Moreover, in an interesting (...) article still frequently referred to, R. M. Martin has argued that Hobbes "has in mind a clear-cut semantical concept of truth."' Examining Hobbes's semantical ideas somewhat more closely than Martin did, T6rnebohm has given a more precise characterization of Hobbes's view on truth and falsity; he speaks of Hobbes's comprehension theory of truth. ~One of the main purposes of this article is to investigate whether such a theory is correctly attributed to Hobbes. For Tarski 'true' and 'false' are predicates of (declarative) sentences) But this is not enough to speak of a semantic theory of truth: The leading idea behind Tarski's fundamental work in the field of semantics is (a restricted version of) the principle of compositionality. This principle, also known as Frege's principle, says that the semantic value of a (complex) expression is a function of the semantic values of the syntactic (and categorematic) parts it is ' R. M. Martin, "On the Semantics of Hobbes," Philosophyand PhenomenologicalResearch 14 095314): 2o5-11, esp. ~o7, 211. Cf. I. C. Hungerland and G. R. Vick, "Hobbes's Theory of Language, Speech and Reasoning," in ThomasHobbes:Computatwsire Logica--Logic, translated and commentary by A. Martinich, ed. and introduced by I. C. Hungerland and G. R. Vick (New York: 1981), 15--167, esp. 17, 121-22. 9 H. T6rnebohm, "A Study in Hobbes' Theory of Denotation and Truth," Theor~a26 (196o): 53-7o; see p. 66. 3 A. Tarski, "The Semantic Conception of Truth and the Foundations of Semantics," Philosophy and PhenomenologicalResearch4 (1944): 341-375; see p. 342. [63] 64 JOURNAL OF THE HISTORY OF PHILOSOPHY 28:1 JANUARY 199o composed of. Moreover, in the case of linguistic expressions which are (deciarative ) sentences this semantic value should be its truth-value. 4 As we shall see, Hobbes's theory of propositions is basically a theory of subject-predicate propositions. It is therefore reasonable to qualify his theory of truth as a semantic one only if it satisfies Frege's principle to a certain extent. Ideally, this means that the truth-value of subject-predicate propositions should be conceived as a function of the semantic interpretations of its subject and predicate. In the next three sections I will concentrate principally on the logicosyntactical aspects of language. I will then discuss successively the general structure of propositions, the various sorts of names, and the syntax of Hobbes's theory of propositions. Section 5 is devoted to Hobbes's theory of truth as interpreted by Martin and T0rnebohm. The outcome of this examination makes it necessary to break away from Martin's restricted conception of semantics. Martin, like Tarski, takes semantics as "semantics in the narrower sense," i.e., as the discipline Quine refers to as the theory of reference. 5 However, sometimes this term is used in a broader sense; the field of semantics is taken then to include the theory of meaning too. Although the wording differs frequently, the distinction between meaning and reference is almost a constant in the history of thinking about language. On the side of meaning one finds terms like connotation, intension, conception, signification and analyticity, while terms like naming, denoting, extension (and sometimes again signification) are ]inked to the notion of reference. In the Computatio sive Logica, the first part of De Corpore, containing Hobbes's most mature work on the philosophy of language, this opposition is displayed by way of a distinction between, on the one side, nominare, denotare and appellare and, on the other side, significare. Hobbes's view of the significative, as opposed to the denotative, role of linguistic expressions is treated in sections 6, 7, and 8. There it will be shown that Hobbes's radical nominalism is decisive for his doctrine of signification; moreover, this nominalism raises serious problems for the relation... (shrink)

José L. Zalabardo defends a pragmatist account of what grounds the meaning of central semantic discourses--ascriptions of truth, of propositional attitudes, and of meanings. He argues that it is the procedures that regulate acceptance and rejection that give the sentences of these discourses their meanings, and explores the application of the pragmatist template to ethical discourse. The pragmatist approach is presented as an alternative to representationalist accounts of the meaning grounds of declarative sentences, according to which a sentence has (...) the meaning it has as a result of links with the bits of the world that it purports to represent. Zalabardo develops a version of the open-question argument to support the claim that the meaning grounds of the discourses he focuses on cannot receive representationalist accounts. It is generally assumed that a declarative sentence cannot perform the function of representing the world unless it has a representationalist meaning ground. Zalabardo rejects this assumption, arguing that sentences with pragmatist meaning grounds can represent the world in exactly the same sense that sentences with representationalist meaning grounds do. This requires that there are states of affairs that the target sentences represent as obtaining, and Zalabardo develops an account of the nature of the states of affairs that can play this role for sentences with pragmatist meaning grounds. Pragmatist Semantics concludes by developing the suggestion that the meaning grounds of all our representational discourses might be ultimately pragmatist. (shrink)

This dissertation explores several accounts of the intuitions speakers have concerning the truth values of utterances of sentences containing vague nouns and adjectives. While some semanticists have attempted to account for these intuitions with multi-valued logics and supervaluation theories of truth, I focus on how utterances of vague sentences affect hearers' beliefs. ;Following a critique of the major semantical accounts of vagueness, I propose a formal theory of how beliefs are revised following utterances of sentences of the form (...) X is A, X is A and B, and X is A and not A, where A and B are vague scalar adjectives. Formally, a hearer's beliefs are represented as a set of weighted sentences, and the information conveyed by a speaker's utterance is represented as a set of weighted conditionals. When a speaker utters a sentence, a function on these sets yields the hearer's revised beliefs. I derive from this theory a criterion for proper assertability: a sentence is properly assertable in a given context if the maximum information loss that could obtain between competent discourse participants is less than some threshold. I argue that this criterion often predicts the truth-value judgements competent speakers make which violate the basic rules of logic. I extend these theories to utterances of sentences containing vague non-scalar nouns. ;In the second half of the dissertation, I propose two semantic accounts of vagueness. One incorporates the assertability criterion into its definition of truth. The other is independent of it. The former accounts for a large set of intuitions concerning the truth values of utterances of vague sentences. The latter accounts for only a subset of those intuitions, leaving the rest to be explained independently by the theory of proper assertability. ;I conclude with brief discussions of the Sorites Paradox and the experimental data obtained by Tversky and Kahneman which purport to demonstrate people's poor intuitions concerning the probabilities of conjunctions. (shrink)

Free Semantics is based on normalized natural deduction for the weak relevant logic DW and its near neighbours. This is motivated by the fact that in the determination of validity in truth-functional semantics, natural deduction is normally used. Due to normalization, the logic is decidable and hence the semantics can also be used to construct counter-models for invalid formulae. The logic DW is motivated as an entailment logic just weaker than the logic MC of meaning (...) containment. DW is the logic focussed upon, but the results extend to MC. The semantics is called 'free semantics' since it is disjunctively and existentially free in that no disjunctive or existential witnesses are produced, unlike in truth-functional semantics. Such 'witnesses' are only assumed in generality and are not necessarily actual. The paper sets up the free semantics in a truth-functional style and gives a natural deduction interpetation of the meta-logical connectives. We then set out a familiar tableau-style system, but based on natural deduction proof rather than truth-functional semantics. A proof of soundness and completeness is given for a reductio system, which is a transform of the tableau system. The reductio system has positive and negative rules in place of the elimination and introduction rules of Brady's normalized natural deduction system for DW. The elimination-introduction turning points become closures of threads of proof, which are at the points of contradiction for the reductio system. (shrink)

I compare the semantic approach to the logic of worldly grounding put forward in my “Grounding and Truth-Functions” (2010) with the approach developed by Fine in “Guide to Ground” (2012a) and “The Pure Logic of Ground” (2012b). I argue that both are defective in some respects, and offer an alternative approach in the same spirit but based on a new semantic framework, which combines the best aspects of the frameworks within which the previous approaches were developed.

The main aim of the thesis is to give a semantic account of implicit content – the kind of content that plays a crucial role in implicit communication. Implicit communication is a species of communication in which a speaker communicates certain contents that go over and above the contents retrievable from the linguistic meaning of the words used. The focus of the thesis is a certain kind of implicit communication involving locations (when sentences such as “It is raining” are used (...) to communicate that it is raining at a certain location) and judges (when sentences such as “Avocado is tasty” are used to communicate that avocado is tasty for a certain person, called “the judge”). The way the topic of implicit content is approached is via the notion, widespread in contemporary philosophy of language, of “unarticulated constituents”. The thesis contains an investigation of this notion, with the specific aim of disentangling the many senses it has been used and of providing a general definition of the notion. A direct product of this investigation is a partitioning of the logical space; three positions are then selected, which correspond to the main contenders in the current debate involving unarticulated constituents: truth-conditional semantics, truth-conditional pragmatics and relativism. The biggest part of the thesis is dedicated to investigating certain arguments that have surfaced in the debate between these positions, with the ultimate goal of proposing a relativist account of implicit content. The particular version of relativism offered consists in the combination of the claim that locations and judges are part of the circumstances of evaluation, rather than the content of utterances, with “the variadic functions approach” to certain natural language expressions. Also, several arguments against a truth-conditional semantic approach to predicates of personal taste are provided. (shrink)

In many real-life applications of logic it is useful to interpret a particular sentence as true together with its negation. If we are talking about classical logic, this situation would force all other sentences to be equally interpreted as true. Paraconsistent logics are exactly those logics that escape this explosive effect of the presence of inconsistencies and allow for sensible reasoning still to take effect. To provide reasonably intuitive semantics for paraconsistent logics has traditionally proven to be a challenge. (...) Possible-translations semantics can meet that challenge by allowing for each interpretation to be composed of multiple scenarios. Using that idea, a logic with a complex semantic behavior can be understood as an appropriate combination of ingredient logics with simpler semantic behaviors into which the original logic is given a collection of translations preserving its soundness. Completeness is then achieved through the judicious choice of the admissible translating mappings. The present note provides interpretation by way of possible-translations semantics for a group of fundamental paraconsistent logics extending the positive fragment of classical propositional logic. The logics PI, Cmin, mbC, bC, mCi and Ci, among others, are all initially presented through their non-truth-functional bivaluation semantics and sequent versions and then split by way of possible-translations semantics based on 3-valued ingredients. (shrink)

This paper establishes a sound and complete semantics for the impure logic of ground. Fine (Review of Symbolic Logic, 5(1), 1–25, 2012a) sets out a system for the pure logic of ground, one in which the formulas between which ground-theoretic claims hold have no internal logical complexity; and it provides a sound and complete semantics for the system. Fine (2012b) [§§6-8] sets out a system for an impure logic of ground, one that extends the rules of the original (...) pure system with rules for the truth-functional connectives, the first-order quantifiers, and λ-abstraction. However, no semantics has yet been provided for this system. The present paper partly fills this lacuna by providing a sound and complete semantics for a system GG containing the truth-functional operators that is closely related to the truth-functional part of the system of Fine (2012b). (shrink)

The idea that science aspires to and routinely achieves truths about the world has been challenged in recent writings. Rather than beginning with a theory of scientific development, or of scientific explanation, we begin with a consideration of truth claims in ordinary discourse, particularly with Davidson's truth-functional semantics. Next we consider the way in which some framework features of ordinary language discourse are extended to and modified in scientific discourse. Two areas are treated in more detail: (...) quantum theory, and the peculiar problem of semantic entailment it involves; and quantum field theory. These supply a basis for criticizing some historicist and logicist treatments of the truth of scientific claims. (shrink)

The aim of this paper is to show that it is the explicativecharacter of Tarski's semantic definition of truth given in his study of 1933 that allows forconsideration of a philosophical background of this definition in the proper sense. Given the explicativecharacter of this definition it is argued that the philosophical tradition that should be taken intoaccount with regard to this philosophical background is the tradition of the Lvov-Warsaw Schoolin its connections with the School of Brentano. As an example (...) of the explanatory power ofconsidering this tradition as far as Tarski's philosophical choices are concerned I use here thenotion of sentence-inscription, i.e., the notion of that entity of which truth is predicated inthe definition in question. One of the consequences of these statements is that philosophicaldiscussions concerning the semantic definition of truth can be regarded from two points ofview. On the one hand, they may take the perspective of its explicational function, i.e., theperspective of its philosophical background. On the other hand, they might consider the philosophicalconsequences of the definition with respect to the goal of the explication, i.e., they may considerits philosophical content independently of its historical background. (shrink)

Semantic relativism maintains that the truth-value of some propositions is sensitive to a judge parameter, facilitating cases whereby a proposition can be true relative to one judge, but false relative to another. Most prominently, semantic relativism has been applied to predicates of personal tastes (PPTs). Recently, Lasersohn [2007. “Expressives, Perspective and Presupposition.” Theoretical Linguistics 33 (2): 223–230; 2017. Subjectivity and Perspective in Truth-Theoretic Semantics. Oxford: Oxford University Press] has urged an extension of semantic relativism to terms traditionally (...) construed as expressives including derogatory epithets (e.g. ‘asshole’) and, more tentatively, expressions like ‘damn’. In this paper, we challenge Lasersohn’s extension of relativism. Section 1 gives a background on semantic theories for expressives and on semantic relativism. In Section 2, we focus on Lasersohn’s [2007. “Expressives, Perspective and Presupposition.” Theoretical Linguistics 33 (2): 223–230] account where he attempts to apply relativism to a wider range of expressives. We argue that because PPTs and expressives have fundamentally different semantic functions, the prospects for a relativistic account are slim. Several problems are presented. Our focus is on the perspective sensitivity of expressive content and the phenomenon of projection failure, as both reveal a fundamental disparity between expressives and PPTs. (shrink)

After some generalities about connections between functions and relations in Sections 1 and 2 recalls the possibility of taking the semantic values of ‐ary Boolean connectives as ‐ary relations among truth‐values rather than as ‐ary truth functions. Section 3, the bulk of the paper, looks at correlates of these truth‐value relations as applied to formulas, and explores in a preliminary way how their properties are related to the properties of “logical relations” among formulas such as equivalence, implication (...) (entailment) and contrariety (logical incompatibility), concentrating for illustrative purposes on binary logical relations such as those just listed. To avoid an excess of footnotes, some points have been deferred to an Appendix as “Longer Notes”. (shrink)

In 1977, R. B. Angell presented a logic for analytic containment, a notion of relevant implication stronger than Anderson and Belnap's entailment. In this paper I provide for the first time the logic of first degree analytic containment, as presented in [2] and [3], with a semantical characterization—leaving higher degree systems for future investigations. The semantical framework I introduce for this purpose involves a special sort of truth-predicates, which apply to pairs of collections of formulas instead of individual formulas, (...) and which behave in some respects like Gentzen's sequents. This semantics captures very general properties of the truth-functional connectives, and for that reason it may be used to model a vast range of logics. I briefly illustrate the point with classical consequence and Anderson and Belnap's tautological entailments. (shrink)

The standard truth-conditional semantics for substitutional quantification, due to Saul Kripke, does not specify what proposition is expressed by sentences containing the particular substitutional quantifier. In this paper, I propose an alternative semantics for substitutional quantification that does. The key to this semantics is identifying an appropriate propositional function to serve as the content of a bound occurrence of a formula containing a free substitutional variable. I apply this semantics to traditional philosophical reasons for interest (...) in substitutional quantification, namely, theories of truth and ontological commitment. (shrink)

Paul Horwich gives the definitive exposition of a prominent philosophical theory about truth, `minimalism'. His theory has attracted much attention since the first edition of Truth in 1990; he has now developed, refined, and updated his treatment of the subject, while preserving the distinctive format of the book. This revised edition appears simultaneously with a new companion volume, Meaning; the two books demystify central philosophical issues, and will be essential reading for all who work on the philosophy of (...) language. (shrink)

According to Semantic Minimalism, every use of "Chiara is tall" (fixing the girl and the time) semantically expresses the same proposition, the proposition that Chiara is (just plain) tall. Given standard assumptions, this proposition ought to have an intension (a function from possible worlds to truth values). However, speakers tend to reject questions that presuppose that it does. I suggest that semantic minimalists might address this problem by adopting a form of "nonindexical contextualism," according to which the proposition invariantly (...) expressed by "Chiara is tall" does not have a context-invariant intension. Nonindexical contextualism provides an elegant explanation of what is wrong with "context-shifting arguments" and can be seen as a synthesis of the (partial) insights of semantic minimalists and radical contextualists. (shrink)

Traditional approaches in deontic logic have focused on the so-called reportative reading of obligation sentences, by providing truth-functional semantics based on a primitive ideality order between possible worlds. Those approaches, however, do not take into account that, in natural language, obligation sentences primarily carry a prescriptive effect. The paper focuses precisely on that prescriptive character, and shows that the reportative reading can be derived from the prescriptive one. A dynamic, non truth-functional semantics for necessity (...) deontic modals is developed, in which the ideality relations among possible worlds can be updated. Finally, it is proven that the semantics solves several of the classic deontic paradoxes. (shrink)

In this paper we consider the class of truth-functional modal many-valued logics with the complete lattice of truth-values. The conjunction and disjunction logic operators correspond to the meet and join operators of the lattices, while the negation is independently introduced as a hierarchy of antitonic operators which invert bottom and top elements. The non-constructive logic implication will be defined for a subclass of modular lattices, while the constructive implication for distributive lattices (Heyting algebras) is based on relative (...) pseudo-complements as in intuitionistic logic. We show that the complete lattices are intrinsically modal, with banal identity modal operator. We define the autoreferential set-based representation for the class of modal algebras, and show that the autoreferential Kripke-style semantics for this class of modal algebras is based on the set of possible worlds equal to the complete lattice of algebraic truth-values. The philosophical assumption is based on the consideration that each possible world represents a level of credibility, so that only propositions with the right logic value (i.e., level of credibility) can be accepted by this world, then we connect it with paraconsistent properties and LFI logics. The bottom truth value in this complete lattice corresponds to the trivial world in which each formula is satisfied, that is, to the world with explosive inconsistency. The top truth value corresponds to the world with classical logics, while all intermediate possible worlds represent the different levels of paraconsistent logics. (shrink)

This book attempts to marry truth-conditional semantics with cognitive linguistics in the church of computational neuroscience. To this end, it examines the truth-conditional meanings of coordinators, quantifiers, and collective predicates as neurophysiological phenomena that are amenable to a neurocomputational analysis. Drawing inspiration from work on visual processing, and especially the simple/complex cell distinction in early vision (V1), we claim that a similar two-layer architecture is sufficient to learn the truth-conditional meanings of the logical coordinators and logical (...) quantifiers. As a prerequisite, much discussion is given over to what a neurologically plausible representation of the meanings of these items would look like. We eventually settle on a representation in terms of correlation, so that, for instance, the semantic input to the universal operators (e.g. and, all)is represented as maximally correlated, while the semantic input to the universal negative operators (e.g. nor, no)is represented as maximally anticorrelated. On the basis this representation, the hypothesis can be offered that the function of the logical operators is to extract an invariant feature from natural situations, that of degree of correlation between parts of the situation. This result sets up an elegant formal analogy to recent models of visual processing, which argue that the function of early vision is to reduce the redundancy inherent in natural images. Computational simulations are designed in which the logical operators are learned by associating their phonological form with some degree of correlation in the inputs, so that the overall function of the system is as a simple kind of pattern recognition. Several learning rules are assayed, especially those of the Hebbian sort, which are the ones with the most neurological support. Learning vector quantization (LVQ) is shown to be a perspicuous and efficient means of learning the patterns that are of interest. We draw a formal parallelism between the initial, competitive layer of LVQ and the simple cell layer in V1, and between the final, linear layer of LVQ and the complex cell layer in V1, in that the initial layers are both selective, while the final layers both generalize. It is also shown how the representations argued for can be used to draw the traditionally-recognized inferences arising from coordination and quantification, and why the inference of subalternacy breaks down for collective predicates. Finally, the analogies between early vision and the logical operators allow us to advance the claim of cognitive linguistics that language is not processed by proprietary algorithms, but rather by algorithms that are general to the entire brain. Thus in the debate between objectivist and experiential metaphysics, this book falls squarely into the camp of the latter. Yet it does so by means of a rigorous formal, mathematical, and neurological exposition – in contradiction of the experiential claim that formal analysis has no place in the understanding of cognition. To make our own counter-claim as explicit as possible, we present a sketch of the LVQ structure in terms of mereotopology, in which the initial layer of the network performs topological operations, while the final layer performs mereological operations. The book is meant to be self-contained, in the sense that it does not assume any prior knowledge of any of the many areas that are touched upon. It therefore contains mini-summaries of biological visual processing, especially the retinocortical and ventral /what?/ parvocellular pathways computational models of neural signaling, and in particular the reduction of the Hodgkin-Huxley equations to the connectionist and integrate-and-fire neurons Hebbian learning rules and the elaboration of learning vector quantization the linguistic pathway in the left hemisphere memory and the hippocampus truth-conditional vs. image-schematic semantics objectivist vs. experiential metaphysics and mereotopology. All of the simulations are implemented in MATLAB, and the code is available from the book’s website. • The discovery of several algorithmic similarities between visison and semantics. • The support of all of this by means of simulations, and the packaging of all of this in a coherent theoretical framework. (shrink)

This book presents modern logic as the formalization of reasoning that needs and deserves a semantic foundation. Chapters on propositional logic; parsing propositions; and meaning, truth and reference give the reader a basis for establishing criteria that can be used to judge formalizations of ordinary language arguments. Over 120 worked examples illustrate the scope and limitations of modern logic, as analyzed in chapters on identity, quantifiers, descriptive names, and functions. The chapter on second-order logic shows how different conceptions of (...) predicates and propositions do not lead to a common basis for quantification over predicates, as they do for quantification over things. Notable for its clarity of presentation and supplemented by many exercises, this volume will be invaluable for philosophers, linguists, mathematicians, and computer scientists who wish to better understand the tools they use in formal reasoning. (shrink)