The starting point of this paper concerns the apparent difference between what we might call absolute truth and truth in a model, following Donald Davidson. The notion of absolute truth is the one familiar from Tarski’s T-schema: ‘Snow is white’ is true if and only if snow is white. Instead of being a property of sentences as absolute truth appears to be, truth in a model, that is relative truth, is evaluated in terms of (...) the relation between sentences and models. I wish to examine the apparent dual nature of logical truth (without dwelling on Davidson), and suggest that we are dealing with a distinction between a metaphysical and a linguistic interpretation of truth. I take my cue from John Etchemendy, who suggests that absolute truth could be considered as being equivalent to truth in the ‘right model’, i.e., the model that corresponds with the world. However, the notion of ‘model’ is not entirely appropriate here as it is closely associated with relative truth. Instead, I propose that the metaphysical interpretation of truth may be illustrated in modal terms, by metaphysical modality in particular. One of the tasks that I will undertake in this paper is to develop this modal interpretation, partly building on my previous work on the metaphysical interpretation of the law of non-contradiction (Tahko 2009). After an explication of the metaphysical interpretation of logical truth, a brief study of how this interpretation connects with some recent important themes in philosophical logic follows. In particular, I discuss logical pluralism and propose an understanding of pluralism from the point of view of the metaphysical interpretation. (shrink)

Classical logic counts sentences such as ‘Alice is identical with Alice’ as logically true. A standard objection to classical logic is that Alice’s self-identity, for instance, is not a matter of logic because the identity of particular objects is not a matter of logic. For this reason, many philosophers argue that classical logic is not the right logic, and that it should be abandoned in favour of free logic — logic free of existential commitments with respect to singular terms. In (...) most standard free logics, sentences such as ‘Alice is identical with Alice’ are not logically true. This paper argues that this objection from existential commitments is some- what superficial and that there is a deeper reason why ‘Alice is identical with Alice’ should not be considered a logical truth. Indeed, a key fundamental thought about the nature of logic is that a logical truth is true in virtue of its logical form. The fundamental problem I raise is that a sentence such as ‘Alice is identical with Alice’ appears to not even be true in virtue of its logical form. Thus this paper argues that given that such a sentence is not true in virtue of its logical form, it should not be counted as logically true. It moreover argues, on the same grounds, that even the sentences which free logicians regard as logically true shouldn’t be regarded as logically true. So in this sense free logic is no repair to classical logic. (shrink)

Translated from: W.V.O.Quine, W. H. O. (1986): Philosophy of Logic. Second Edition. Harvard University Press. Cambridge, Massachusetts and London, England, 47-61.

The concern of deductive logic is generally viewed as the systematic recognition of logical principles, i.e., of logical truths. This paper presents and analyzes different instantiations of the three main interpretations of logical principles, viz. as ontological principles, as empirical hypotheses, and as true propositions in virtue of meanings. I argue in this paper that logical principles are true propositions in virtue of the meanings of the logical terms within a certain linguistic framework. Since these (...) principles also regulate and control the process of deduction in inquiry, i.e., they are prescriptive for the use of language and thought in inquiry, I argue that logic may, and should, be seen as an instrument or as a way of proceeding (modus procedendi) in inquiry. (shrink)

In this paper, I ask whether we should see different logical systems as appropriate for different domains (or perhaps in different contexts) and whether this would amount to a form of logical pluralism. One, though not the only, route to this type of position, is via pluralism about truth. Given that truth is central to validity, the commitment the typical truth pluralist has to different notions of truth for different domains may suggest differences regarding (...) validity in those different domains. Indeed, as we’ll see, the differences between the proposed multiple notions of truth are often of a type that is clearly significant in relation to logical features, such as whether or not a constructive notion of truth is at issue. I criticise domain-based logical pluralism. Having done so I introduce a context-based framework that operates with a context-relative notion of validity. I show that this context-based framework can be employed by the domain-specific logical pluralist, but that framework also allows for logical pluralism that does not involve several domains. Different contexts may demand rules of classical logic, where others only justify intuitionistic rules, even when the same domain (e.g. mathematics) is at issue. (shrink)

Let T be any logical truth. Does the subject know that T (any random subject)? It is not rational for any subject to believe that they don’t, whoever they are. Similarly, it is not rational for them to believe that their evidence doesn’t support T, and it is not even rational for them to believe that they don’t believe that T. It is not rational for anyone anywhere at any time to believe that they don’t know that T. (...) Such are the conclusions arrived at in this paper. (shrink)

Starting from certain metalogical results, I argue that first-order logical truths of classical logic are a priori and necessary. Afterwards, I formulate two arguments for the idea that first-order logical truths are also analytic, namely, I first argue that there is a conceptual connection between aprioricity, necessity, and analyticity, such that aprioricity together with necessity entails analyticity; then, I argue that the structure of natural deduction systems for FOL displays the analyticity of its truths. Consequently, each philosophical approach (...) to these truths should account for this evidence, i.e., that first-order logical truths are a priori, necessary, and analytic, and it is my contention that the semantic account is a better candidate. (shrink)

The present thesis focuses on counterfactuals. Specifically, we will address new questions and open problems that arise for the standard semantic accounts of counterfactual conditionals. The first four chapters deal with the Lewisian semantic account of counterfactuals. On a technical level, we contribute by providing an equivalent algebraic semantics for Lewis' variably strict conditional logics, which is notably absent in the literature. We introduce a new kind of algebra and differentiate between local and global versions of each of Lewis' variably (...) strict conditional logics. We study the algebraic properties of Lewis' logics and the structure theory of our newly introduced algebras. Additionally, we employ a new algebraic construction, based on the framework of Boolean algebras of conditionals, to provide an alternative semantics for Lewisian counterfactual conditionals. This semantic account allows us to establish new truth conditions for Lewisian counterfactuals, implying that Lewisian counterfactuals are definable conditionals, and each counterfactual can be characterized as a modality of a corresponding probabilistic conditional. We further extend these results by demonstrating that each Lewisian counterfactual can also be characterized as a modality of the corresponding Stalnaker conditional. The resulting formal semantic framework is much more expressive than the standard one and, in addition to providing new truth conditions for counterfactuals, it also allows us to define a new class of conditional logics falling into the broader framework of weak logics. On the philosophical side, we argue that our results shed new light on the understanding of Lewisian counterfactuals and prompt a conceptual shift in this field: Lewisian counterfactual dependence can be understood as a modality of probabilistic conditional dependence or Stalnakerian conditional dependence. In other words, whether a counterfactual connection occurs between A and B depends on whether it is "necessary" for a Stalnakerian/probabilistic dependence to occur between A and B. We also propose some ways to interpret the kind of necessity involved in this interpretation. The remaining two chapters deal with the probability of counterfactuals. We provide an answer to the question of how we can characterize the probability that a Lewisian counterfactual is true, which is an open problem in the literature. We show that the probability of a Lewisian counterfactual can be characterized in terms of belief functions from Dempster-Shafer theory of evidence, which are a super-additive generalization of standard probability. We define an updating procedure for belief functions based on the imaging procedure and show that the probability of a counterfactual A > B amounts to the belief function of B imaged on A. This characterization strongly relies on the logical results we proved in the previous chapters. Moreover, we also solve an open problem concerning the procedure to assign a probability to complex counterfactuals in the framework of causal modelling semantics. A limitation of causal modelling semantics is that it cannot account for the probability of counterfactuals with disjunctive antecedents. Drawing on the same previous works, we define a new procedure to assign a probability to counterfactuals with disjunctive antecedents in the framework of causal modelling semantics. We also argue that our procedure is satisfactory in that it yields meaningful results and adheres to some conceptually intuitive constraints one may want to impose when computing the probability of counterfactuals. (shrink)

This paper proposes substitutional definitions of logical truth and consequence in terms of relative interpretations that are extensionally equivalent to the model-theoretic definitions for any relational first-order language. Our philosophical motivation to consider substitutional definitions is based on the hope to simplify the meta-theory of logical consequence. We discuss to what extent our definitions can contribute to that.

In Appearance and Explanation, McCain and Moretti propose a novel internalist account of epistemic justification called phenomenal explanationism, which combines phenomenal conservatism and explanationism. I argue that the current version of phenomenal explanationism faces a dilemma: either it omits the awareness requirement but implies an implausible form of logical-mathematical omniscience, or it preserves the requirement but leads to a vicious regress. I suggest how phenomenal explanationism might be revised to avoid this dilemma.

Monists say that the nature of truth is invariant, whichever sentence you consider; pluralists say that the nature of truth varies between different sets of sentences. The orthodoxy is that logic and logical form favour monism: there must be a single property that is preserved in any valid inference; and any truth-functional complex must be true in the same way as its components. The orthodoxy, I argue, is mistaken. Logic and logical form impose only structural (...) constraints on a metaphysics of truth. Monistic theories are not guaranteed to satisfy these constraints, and there is a pluralistic theory that does so. (shrink)

Developing a suggestion of Wittgenstein, I provide an account of truth tables as formulas of a formal language. I define the syntax and semantics of TPL (the language of Tabular Propositional Logic), and develop its proof theory. Single formulas of TPL, and finite groups of formulas with the same top row and TF matrix (depiction of possible valuations), are able to serve as their own proofs with respect to metalogical properties of interest. The situation is different, however, for groups (...) of formulas whose top rows differ. For them I provide (i) a tree-style system of ‘row tree proofs’, which is shown to be sound and complete, and (ii) an alternative, re-writing strategy. (shrink)

Husserl’s theory of fulfilment conceives of empty acts, such as symbolic thought, and fulfilling acts, such as sensory perceptions, in a strict parallel. This parallelism is the basis for Husserl’s semantics, epistemology, and conception of truth. It also entails that any true proposition can be known in principle, which Church and Fitch have shown to explode into the claim that every proposition is _actually_ known. I assess this logical challenge and discuss a recent response by James Kinkaid. While (...) Kinkaid’s proposal saves one direction of the parallel for semantics, it gives up the parallelism for truth. I spell out a different response which meshes naturally with Husserl’s account of meaning. If the parallelism is restricted to a class of basic propositions, the truth of non-basic propositions can be defined inductively, without leading to the paradox. I then discuss objections that have been raised against a similar proposal by Dummett. The result is that exegetically plausible and popular interpretations of Husserl’s correlationism are indeed challenged by Church and Fitch. But when taking into account the ‘logical adumbration’ of propositional blindspots, truth and possible fulfilment can be connected without paradox. (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)

Though my ultimate concern is with issues in epistemology and metaphysics, let me phrase the central question I will pursue in terms evocative of philosophy of religion: What are the implications of our logic-in particular, of Cantor and G6del-for the possibility of omniscience?

This paper offers an analysis of a hitherto neglected text on insoluble propositions dating from the late XiVth century and puts it into perspective within the context of the contemporary debate concerning semantic paradoxes. The author of the text is the italian logician Peter of Mantua (d. 1399/1400). The treatise is relevant both from a theoretical and from a historical standpoint. By appealing to a distinction between two senses in which propositions are said to be true, it offers an unusual (...) solution to the paradox, but in a traditional spirit that contrasts a number of trends prevailing in the XiVth century. It also counts as a remarkable piece of evidence for the reconstruction of the reception of English logic in italy, as it is inspired by the views of John Wyclif. Three approaches addressing the Liar paradox (Albert of Saxony, William Heytesbury and a version of strong restrictionism) are first criticised by Peter of Mantua, before he presents his own alternative solution. The latter seems to have a prima facie intuitive justification, but is in fact acceptable only on a very restricted understanding, since its generalisation is subject to the so-called revenge problem. (shrink)

Logical reasoning is not only a component of religious faith (cf., for instance, the "Golden rule"), but, in addition, the religious faith itself can be conceived as a logical pragmatic function applied to sentences and their meanings. Pragmatic role of religious faith is shown on the examples of the analogy of seed and spoken word (e.g., Mt 13:3-23) and on the degrees of faith described in the episode about Nicodemus (John 3). Pragmatics adds (different grades of) perseverance to (...) the correctness of reasoning and to the truth-preservation of the consequence relation. Correspondingly, religious faith is described by formally defined model and satisfaction relation, which are applied to and examined on the text of John 3. (shrink)

Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology (...) suffered by at least some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems. (shrink)

Semantic externalism in the style of McDowell and Evans faces a puzzle formulated by Pryor: to explain that a sentence such as 'Jack exists' is only a posteriori knowable, despite being logically entailed by the seemingly logical truth 'Jack is self-identical', and hence being itself a logical truth and therefore a priori knowable. Free logics can dissolve the puzzle. Moreover, Pryor has argued that the existentially hedged 'If Jack exists, then Jack is self-identical', when properly formalised, (...) is a logical truth in a system of neutral free logic and therefore a priori knowable, while it does not entail that Jack exists. The latter holds also for negative free logic. In response, Yeakel has argued that on any system of neutral free logic existence hedges will either entail some unwanted existence claims or they will not entail some wanted existence claims. The dilemma also holds for any non-positive free logic. It will be shown that the extension of one of the systems of neutral free logic with a truth operator escapes Yeakel's dilemma, whereas no other non-positive free logic when extended with the truth operator does the same (or it breaks quantifier exchangeability). (shrink)

In this paper I investigate how differences in approach to truth and logic (in particular, a deflationist vs. a substantivist approach to these fields) affect philosophers’ views concerning pluralism and normativity in these fields. My perspective on truth and logic is largely epistemic, focusing on the role of truth in knowledge (rather than on the use of the words “true” and “truth” in natural language), and my reference group includes Carnap (1934), Harman (1986), Horwich (1990), Wright (...) (1992), Beall and Restall (2006), Field (2009), Lynch (2009), and Sher (2016a).1 Whenever possible, I focus on positive rather than negative views on the issues involved, although in some cases this is not possible. (shrink)

A. J. Ayer’s Language, Truth, and Logic had been responsible for introducing the Vienna Circle’s ideas, developed within a Germanophone framework, to an Anglophone readership. Inevitably, this migration from one context to another resulted in the alteration of some of the concepts being transmitted. Such alterations have served to facilitate a number of false impressions of Logical Empiricism from which recent scholarship still tries to recover. In this paper, I will attempt to point to the ways in which (...) LTL has helped to foster the various mistaken stereotypes about Logical Empiricism which were combined into the received view. I will begin by examining Ayer’s all too brief presentation of an Anglocentric lineage for his ideas. This lineage, as we shall see, simply omits the major 19th century Germanophone influences on the rise of analytic philosophy. The Germanophone ideas he presents are selectively introduced into an Anglophone context, and directed towards various concerns that arose within that context. I will focus on the differences between Carnap’s version of the overcoming of metaphysics, and Ayer’s reconfiguration into what he calls the elimination of metaphysics. Having discussed the above, I will very briefly outline the consequences that Ayer’s radicalisation of the Vienna Circle’s doctrines had on the subsequent Anglophone reception of Logical Empiricism. (shrink)

Postmodernists claim that there is no truth. However, the statement 'there is no truth ' is self -contradictory. This essay shows the following: One cannot state the idea 'there is no truth ' universally without creating a paradox. In contrast, the statement 'there is truth ' does not produce such a paradox. Therefore, it is more logical that truth exists.

This paper shows how to conservatively extend classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth—involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system allows for (...) Cut—elimination, but the other does not.). (shrink)

Note: The author holds the copyright, and there was no agreement, express or implied, not to use a facsimile PDF. -/- Using erotetic logic, the paper defines the "the whole truth" in a manner consistent with U.S. Supreme Court precedent. It cannot mean "the whole story," as witnesses in an adversary system are permitted /only/ to answer the questions put to them, nor are they permitted to speculate, add irrelevant material, etc. Nor can it mean not to add an (...) admixture of falsity, as that is already included in "nothing but the truth," and, strictly speaking, in "the truth," as any such as admixture renders the whole thing false (given bivalence is presupposed) by &-introduction. (shrink)

A review of John Woods, Truth in Fiction: Rethinking its Logic. Cham: Springer, 2018.

In this paper I argue against Michael Morris’ claim, that the Tractatus view involves holding that the possibility of truth-functional combination is prior to the possibility for sentential constituents to combine with one another. I provide an alternative interpretation in which I deny the presence of any distinction in the Tractatus between these two possibilities. I then turn to Adrian Moore’s ‘disjunctivist’ account of sentencehood, itself inspired by the Tractatus view. I argue that Moore’s account need not involve a (...) commitment to the kind of priority Morris describes, and that it need not involve a commitment to transcendental idealism. (shrink)

Gila Sher approaches knowledge from the perspective of the basic human epistemic situation—the situation of limited yet resourceful beings, living in a complex world and aspiring to know it in its full complexity. What principles should guide them? Two fundamental principles of knowledge are epistemic friction and freedom. Knowledge must be substantially constrained by the world (friction), but without active participation of the knower in accessing the world (freedom) theoretical knowledge is impossible. This requires a grounding of all knowledge, empirical (...) and abstract, in both mind and world, but the fall of traditional foundationalism has led many to doubt the viability of this ‘classical’ project. Sher challenges this skepticism, charting a new foundational methodology, foundational holism, that differs from others in being holistic, world-oriented, and universal (i.e., applicable to all fields of knowledge). Using this methodology, Epistemic Friction develops an integrated theory of knowledge, truth, and logic. This includes (i) a dynamic model of knowledge, incorporating some of Quine’s revolutionary ideas while rejecting his narrow empiricism, (ii) a substantivist, non-traditional correspondence theory of truth, and (iii) an outline of a joint grounding of logic in mind and world. The model of knowledge subjects all disciplines to demanding norms of both veridicality and conceptualization. The correspondence theory is robust and universal yet not simplistic or naive, admitting diverse forms of correspondence. Logic’s grounding in the world brings it in line with other disciplines while preserving, and explaining, its strong formality, necessity, generality, and normativity. (shrink)

In this treatise, I analyse the concepts of truth and impossibility, and then use a proof by cases method to show that truth is impossible. Since logic is the determination of how true ideas are, and truth is impossible, I proceed to establish a more optimal and comprehensive system called "anti-logic" that replaces logic. Anti-logic is everything logic is not (for instance, if logic is a finite system, then anti-logic is infinite). Developing this notion of anti-logic further, (...) I apply it to ethics, sociology, theology and much more, which allows for an effective guide to the world and to life. (shrink)

Gila Sher interviewed by Chen Bo: -/- I. Academic Background and Earlier Research: 1. Sher’s early years. 2. Intellectual influence: Kant, Quine, and Tarski. 3. Origin and main Ideas of The Bounds of Logic. 4. Branching quantifiers and IF logic. 5. Preparation for the next step. -/- II. Foundational Holism and a Post-Quinean Model of Knowledge: 1. General characterization of foundational holism. 2. Circularity, infinite regress, and philosophical arguments. 3. Comparing foundational holism and foundherentism. 4. A post-Quinean model of knowledge. (...) 5. Intellect and figuring out. 6. Comparing foundational holism with Quine’s holism. 7. Evaluation of Quine’s Philosophy -/- III. Substantive Theory of Truth and Relevant Issues: 1. Outline of Sher’s substantive theory of truth. 2. Criticism of deflationism and treatment of the Liar. 3. Comparing Sher’s substantive theory of truth with Tarski’s theory of truth. -/- IV. A New Philosophy of Logic and Comparison with Other Theories: 1. Foundational account of logic. 2. Standard of logicality, set theory and logic. 3. Psychologism, Hanna’s and Maddy’s conceptions of logic. 4. Quine’s theses about the revisability of logic. -/- V. Epilogue. (shrink)

Prior to Kripke’s seminal work on the semantics of modal logic, McKinsey offered an alternative interpretation of the necessity operator, inspired by the Bolzano–Tarski notion of logical truth. According to this interpretation, ‘it is necessary that A’ is true just in case every sentence with the same logical form as A is true. In our paper, we investigate this interpretation of the modal operator, resolving some technical questions, and relating it to the logical interpretation of modality (...) and some views in modal metaphysics. In particular, we present an hitherto unpublished solution to problems 41 and 42 from Friedman’s 102 problems, which uses a different method of proof from the solution presented in the paper of Tadeusz Prucnal. (shrink)

By separating the general concept of truth into syntactic truth and semantic truth, this article proposes a new theory of truth to explain several paradoxes like the Liar paradox, Card paradox, Curry’s paradox, etc. By revealing the relationship between syntactic /semantic truth and being-nothing-becoming which are the core concepts of dialectical logic, it is able to formalize dialectical logic. It also provides a logical basis for complexity theory by transferring all reasoning into a directed (...) (cyclic/acyclic) graph which explains both paradoxical and paradox-free reasoning. The different structure between cyclic graphs and acyclic graphs is the key to understanding paradoxes. By explaining the immanent between logic, paradox, and cellular automata, it also illustrates dialectical logic as ontology. (shrink)

This study concerns logical systems considered as theories. By searching for the problems which the traditionally given systems may reasonably be intended to solve, we clarify the rationales for the adequacy criteria commonly applied to logical systems. From this point of view there appear to be three basic types of logical systems: those concerned with logical truth; those concerned with logical truth and with logical consequence; and those concerned with deduction per se (...) as well as with logical truth and logical consequence. Adequacy criteria for systems of the first two types include: effectiveness, soundness, completeness, Post completeness, "strong soundness" and strong completeness. Consideration of a logical system as a theory of deduction leads us to attempt to formulate two adequacy criteria for systems of proofs. The first deals with the concept of rigor or "gaplessness" in proofs. The second is a completeness condition for a system of proofs. An historical note at the end of the paper suggests a remarkable parallel between the above hierarchy of systems and the actual historical development of this area of logic. (shrink)

Philosophers are divided on whether the proof- or truth-theoretic approach to logic is more fruitful. The paper demonstrates the considerable explanatory power of a truth-based approach to logic by showing that and how it can provide (i) an explanatory characterization —both semantic and proof-theoretical—of logical inference, (ii) an explanatory criterion for logical constants and operators, (iii) an explanatory account of logic’s role (function) in knowledge, as well as explanations of (iv) the characteristic features of logic —formality, (...) strong modal force, generality, topic neutrality, basicness, and (quasi-)apriority, (v) the veridicality of logic and its applicability to science, (v) the normativity of logic, (vi) error, revision, and expansion in/of logic, and (vii) the relation between logic and mathematics. The high explanatory power of the truth-theoretic approach does not rule out an equal or even higher explanatory power of the proof-theoretic approach. But to the extent that the truth-theoretic approach is shown to be highly explanatory, it sets a standard for other approaches to logic, including the proof-theoretic approach. (shrink)

Every countable language which conforms to classical logic is shown to have an extension which has a consistent definitional theory of truth. That extension has a consistent semantical theory of truth, if every sentence of the object language is valuated by its meaning either as true or as false. These theories contain both a truth predicate and a non-truth predicate. Theories are equivalent when sentences of the object lqanguage are valuated by their meanings.

View more Abstract If logical truth 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)

Tarski "proved" that there cannot possibly be any correct formalization of the notion of truth entirely on the basis of an insufficiently expressive formal system that was incapable of recognizing and rejecting semantically incorrect expressions of language. -/- The only thing required to eliminate incompleteness, undecidability and inconsistency from formal systems is transforming the formal proofs of symbolic logic to use the sound deductive inference model.

The aim of this paper is to provide a proof-theoretic characterization of relevant logics including fusion and fission connectives, as well as Ackermann’s truth constant. We achieve this by employing the well-established methodology of labelled sequent calculi. After having introduced several systems, we will conduct a detailed proof-theoretic analysis, show a cut-admissibility theorem, and establish soundness and completeness. The paper ends with a discussion that contextualizes our current work within the broader landscape of the proof theory of relevant logics.

The paper presents a truth-maker semantics for Strict/Tolerant Logic (ST), which is the currently most popular logic among advocates of the non-transitive approach to paradoxes. Besides being interesting in itself, the truth-maker presentation of ST offers a new perspective on the recently discovered hierarchy of meta-inferences that, according to some, generalizes the idea behind ST. While fascinating from a mathematical perspective, there is no agreement on the philosophical significance of this hierarchy. I aim to show that there is (...) no clear philosophical significance of meta-inferences above the first level. (shrink)

This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions (“the revenge of the Liar”). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a classical (...) two-valued language. Formally speaking, the solution is a language with one meaning of symbols and two valuations of the truth values of sentences. The primary valuation is a classical valuation that is partial in the presence of the truth predicate. It enables us to determine the classical truth value of a sentence or leads to the failure of that determination. The language with the primary valuation is precisely the largest intrinsic fixed point of the strong Kleene three-valued semantics (LIFPSK3). The semantic shift that allows us to express the failure of the primary valuation is precisely the classical closure of LIFPSK3: it extends LIFPSK3 to a classical language in parts where LIFPSK3 is undetermined. Thus, this article provides an argumentation, which has not been present in contemporary debates so far, for the choice of LIFPSK3 and its classical closure as the right model for the truth predicate. In the end, an erroneous critique of Kripke-Feferman axiomatic theory of truth, which is present in contemporary literature, is pointed out. (shrink)

We present a theory of truth in fiction that improves on Lewis's [1978] ‘Analysis 2’ in two ways. First, we expand Lewis's possible worlds apparatus by adding non-normal or impossible worlds. Second, we model truth in fiction as belief revision via ideas from dynamic epistemic logic. We explain the major objections raised against Lewis's original view and show that our theory overcomes them.

Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical concepts -- logical constants, logical truths, and logical consequence -- are defined using the internal syntactic and semantic structure of language. For a first-order language, it has been shown that its logical constants are connectives and a certain type of quantifiers for which the (...) universal and existential quantifiers form a functionally complete set of quantifiers. Neither equality nor cardinal quantifiers belong to the logical constants of a first-order language. (shrink)

This article reviews John Wood’s Truth in Fiction: Rethinking its Logic.

ABSTRACT: A detailed presentation of Stoic logic, part one, including their theories of propositions (or assertibles, Greek: axiomata), demonstratives, temporal truth, simple propositions, non-simple propositions(conjunction, disjunction, conditional), quantified propositions, logical truths, modal logic, and general theory of arguments (including definition, validity, soundness, classification of invalid arguments).

ABSTRACT: This 1974 paper builds on our 1969 paper (Corcoran-Weaver [2]). Here we present three (modal, sentential) logics which may be thought of as partial systematizations of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of these three logics coincide with one another and with those of standard formalizations of Lewis's S5. These logics, when regarded as logistic systems (cf. Corcoran [1], p. 154), are seen to be (...) equivalent; but, when regarded as consequence systems (ibid., p. 157), one diverges from the others in a fashion which suggests that two standard measures of semantic complexity may not be as closely linked as previously thought. -/- This 1974 paper uses the linear notation for natural deduction presented in [2]: each two-dimensional deduction is represented by a unique one-dimensional string of characters. Thus obviating need for two-dimensional trees, tableaux, lists, and the like—thereby facilitating electronic communication of natural deductions. The 1969 paper presents a (modal, sentential) logic which may be thought of as a partial systematization of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of this logic coincides those of standard formalizations of Lewis’s S4. Among the paper's innovations is its treatment of modal logic in the setting of natural deduction systems--as opposed to axiomatic systems. The author’s apologize for the now obsolete terminology. For example, these papers speak of “a proof of a sentence from a set of premises” where today “a deduction of a sentence from a set of premises” would be preferable. 1. Corcoran, John. 1969. Three Logical Theories, Philosophy of Science 36, 153–77. J P R -/- 2. Corcoran, John and George Weaver. 1969. Logical Consequence in Modal Logic: Natural Deduction in S5 Notre Dame Journal of Formal Logic 10, 370–84. MR0249278 (40 #2524). 3. Weaver, George and John Corcoran. 1974. Logical Consequence in Modal Logic: Some Semantic Systems for S4, Notre Dame Journal of Formal Logic 15, 370–78. MR0351765 (50 #4253). (shrink)

Aristotle’s words in the Metaphysics: “to say of what is that it is, or of what is not that it is not, is true” are often understood as indicating a correspondence view of truth: a statement is true if it corresponds to something in the world that makes it true. Aristotle’s words can also be interpreted in a deflationary, i.e., metaphysically less loaded, way. According to the latter view, the concept of truth is contained in platitudes like: ‘It (...) is true that snow is white iff snow is white’, ‘It is true that neutrinos have mass iff neutrinos have mass’, etc. Our understanding of the concept of truth is exhausted by these and similar equivalences. This is all there is to truth. In his book Truth (Second edition 1998), Paul Horwich develops minimalism, a special variant of the deflationary view. According to Horwich’s minimalism, truth is an indefinable property of propositions characterized by what he calls the minimal theory, i.e., all (nonparadoxical) propositions of the form: It is true that p if and only if p. Although the idea of minimalism is simple and straightforward, the proper formulation of Horwich’s theory is no simple matter. In this paper, I shall discuss some of the difficulties of a logical nature that arise. First, I discuss problems that arise when we try to give a rigorous characterization of the theory without presupposing a prior understanding of the notion of truth. Next I turn to Horwich’s treatment of the Liar paradox and a paradox about the totality of all propositions that was first formulated by Russell (1903). My conclusion is that Horwich’s minimal theory cannot deal with these difficulties in an adequate way, and that it has to be revised in fundamental ways in order to do so. Once such revisions have been carried out the theory may, however, have lost some of its appealing simplicity. (shrink)

In explaining the notion of a fundamental property or relation, metaphysicians will often draw an analogy with languages. The fundamental properties and relations stand to reality as the primitive predicates and relations stand to a language: the smallest set of vocabulary God would need in order to write the “book of the world.” This paper attempts to make good on this metaphor. To that end, a modality is introduced that, put informally, stands to propositions as logical truth stands (...) to sentences. The resulting theory, formulated in higher-order logic, also vindicates the Humean idea that fundamental properties and relations are freely recombinable and a variant of the structural idea that propositions can be decomposed into their fundamental constituents via logical operations. Indeed, it is seen that, although these ideas are seemingly distinct, they are not independent, and fall out of a natural and general theory about the granularity of reality. (shrink)

Sorensen (1992) has provided two modal-logical schemas to reconstruct the logical structure of two types of destructive thought experiments: the Necessity Refuter and the Possibility Refuter. The schemas consist of five propositions which Sorensen claims but does not prove to be inconsistent.We show that the five propositions, as presented by Sorensen, are not inconsistent, but by adding a premise (and a logical truth), we prove that the resulting sextet of premises is inconsistent. Häggqvist (2009) has provided (...) a different modal-logical schema (Counterfactual Refuter), which is equivalent to four premises, again claimed to be inconsistent. We show that this schema also is not inconsistent, for similar reasons. Again, we add another premise to achieve inconsistency. The conclusion is that all three modal-logical reconstructions of the arguments that accompany thought experiments, two by Sorensen and one by Häggqvist, have now been made rigorously correct. This may inaugurate new avenues to respond to destructive thought experiments. (shrink)

Prior’s Tonk is a famously horrible connective. It is defined by its inference rules. My aim in this article is to compare Tonk with some hitherto unnoticed nasty connectives, which are defined in semantic terms. I first use many-valued truth-tables for classical sentential logic to define a nasty connective, Knot. I then argue that we should refuse to add Knot to our language. And I show that this reverses the standard dialectic surrounding Tonk, and yields a novel solution to (...) the problem of many-valued truth-tables for classical sentential logic. I close by outlining the technicalities surrounding nasty connectives on many-valued truth-tables. (shrink)

I argue for two claims: that the ordinary English truth predicate is a gradable adjective and that truth is a property that comes in degrees. The first is a semantic claim, motivated by the linguistic evidence and the similarity of the truth predicate’s behavior to other gradable terms. The second is a claim in natural language metaphysics, motivated by interpreting the best semantic analysis of gradable terms as applied to the truth predicate. In addition to providing (...) arguments for these two claims, I draw out consequences for debates about deflationism and truth-based analyses of notions such as assertion and logical consequence. (shrink)