Nathan Salmon, in his paper Trans-World Identification and Stipulation (1996) purports to give a proof for the claim that facts concerning trans-world identity cannot be conceptually reduced to general facts. He calls this claim ‘Extreme Haecceitism.’ I argue that his proof is fallacious. However, I also contend that the analysis and ultimate rejection of his proof clarifies the fundamental issues that are at stake in the debate between the reductionist and haecceitist solutions to the problem of trans-world identity. These issues (...) hinge on the ability of modal logic and possible worlds semantics to draw a hard and fast distinction between the logic and the metaphysics of modal logic. I shall claim that the considerations in this paper call into question the viability of such a distinction. (shrink)

I here argue for a particular formulation of truth-deflationism, namely, the propositionally quantified formula, (Q) “For all p, <p> is true iff p”. The main argument consists of an enumeration of the other (five) possible formulations and criticisms thereof. Notably, Horwich’s Minimal Theory is found objectionable in that it cannot be accepted by finite beings. Other formulations err in not providing non-questionbegging, sufficiently direct derivations of the T-schema instances. I end by defending (Q) against various objections. In particular, I argue (...) that certain circularity charges rest on mistaken assumptions about logic that lead to Carroll’s regress. I show how the propositional quantifier can be seen as on a par with first-order quantifiers and so equally acceptable to use. While the proposed parallelism between these quantifiers is controversial in general, deflationists have special reasons to affirm it. I further argue that the main three types of approach the truth-paradoxes are open to an adherent of (Q), and that the derivation of general facts about truth can be explained on its basis. (shrink)

This paper proposes an alternative view of the connection between knowledge and truth. Truth is traditionally seen as a semantic notion, i.e. a relation between what we say about the world and the world itself. Epistemologists and philosophers of science are therefore apt to resort to correspondence theories of truth in order to deal with the question whether our theories and beliefs are true. Correspondence theories try to define truth, but, in order to do so, they must choose a truth (...) bearer, i.e. something capable of being true, for instance, propositions, sentences or statements. According to the analysis here proposed, none of these truth bearers can be defined without reference to the others. The pragmatic, alternative view here presented, in its turn, is unaffected by this kind of conceptual difficulty. According to this view, one must focus on the use of truth terms – such as ‘true’, ‘false’, ‘correct’, ‘appropriate’, etc. – and the methodological role such terms play in the investigative practices and research programs to be found both in the sciences and in other, everyday investigative activities, such as forensic and journalistic investigations. (shrink)

I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the following (...) results: nothing can be called a negation properly if it does not satisfy Contraposition and Double Negation Introduction; the pair consisting of two split or Galois negations encodes a distinction without a difference; some paraconsistent negations also fail to count as real negations, but others may; intuitionistic negation qualifies as real negation, and classical Boolean negation does as well, to the extent that constructivist and paraconsistent doubts on it do not turn on the basic concept of compatibility but rather on the interpretation of worlds. (shrink)

Michael Kremer defines fixed-point logics of truth based on Saul Kripke’s fixed point semantics for languages expressing their own truth concepts. Kremer axiomatizes the strong Kleene fixed-point logic of truth and the weak Kleene fixed-point logic of truth, but leaves the axiomatizability question open for the supervaluation fixed-point logic of truth and its variants. We show that the principal supervaluation fixed point logic of truth, when thought of as consequence relation, is highly complex: it is not even analytic. We also (...) consider variants, engendered by a stronger notion of ‘fixed point’, and by variant supervaluation schemes. A ‘logic’ is often thought of, not as a consequence relation, but as a set of sentences – the sentences true on each interpretation. We axiomatize the supervaluation fixed-point logics so conceived. (shrink)

The starting point of this paper is the idea that linguistic representation is the result of a global process: a process of interaction of a community of cognitive-linguistic agents, with one another and with the environment. I maintain that the study of truth, meaning and related notions should be addressed without losing perspective of this process, and I oppose the ‘static’ or ‘analytic’ approach, which is fundamentally based on our own knowledge of the conventional meaning of words and sentences, and (...) the ability of using them that we have as competent speakers. I argue that the analytic perspective is responsible for five recurring difficulties in truthmaker theory: (1) the lack of attention to the difference of explanatory role between the distinct notions proposed as primary truthbearer; (2) the adscription of purely extra-linguistic truthmakers to ‘synthetic truths’, ignoring the contribution of the linguistic factor; (3) the adscription of purely linguistic truthmakers to ‘logical’ and ‘analytic truths’, ignoring the contribution of the worldly factor; (4) the difficulties in the search for minimal truthmakers; (5) the problems in the treatment of ‘negative facts’ and of other ‘logically complex facts’. I do not provide an account of how to solve these difficulties, but I do show how the ‘process model’ helps to clear up confusion regarding them. (shrink)

Both the traditional Aristotelian and modern symbolic approaches to logic have seen logic in terms of discrete symbol processing. Yet there are several kinds of argument whose validity depends on some topological notion of continuous variation, which is not well captured by discrete symbols. Examples include extrapolation and slippery slope arguments, sorites, fuzzy logic, and those involving closeness of possible worlds. It is argued that the natural first attempts to analyze these notions and explain their relation to reasoning fail, so (...) that ignorance of their nature is profound. (shrink)

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

Development of decision-support and intelligent agent systems necessitates mathematical descriptions of uncertainty and fuzziness in order to model vagueness. This paper seeks to present an outline of Peirce’s triadic logic as a practical new way to model vagueness in the context of artificial intelligence. Charles Sanders Peirce was an American scientist–philosopher and a great logician whose triadic logic is a culmination of the study of semiotics and the mathematical study of anti-Cantorean model of continuity and infinitesimals. After presenting Peircean semiotics (...) within AI perspective, a mathematical formulation of a Peircean triadic set is given in relationship with classical and fuzzy sets. Using basic logical operators, all possible respective implication operators, bi-equivalence operators, valid rules of inference, and associative, distributive and commutative logical properties are derived and verified through the truth function approach. In order to suggest practical directions, aggregation operators for Peirce’s triadic logic have been formulated. A mathematical formulation of a medical diagnostic problem and ER diagram of a library management system using Peirce’s triadic relation show potential for further applications of the proposed triadic set and triadic logic. Alongside, a classical AI game—The Wumpus World—is implemented to show practical efficacy in comparison with binary implementation. Besides giving some preliminary formulations for trichotomous set theory and definition of finite automaton, development of hybrid architectures for intelligent agents and evolutionary computations are discussed as potential practical avenues for Peirce’s triadic logic. (shrink)

It is characteristic of realists to separate ontology from epistemology and of idealists to mix the two things up. By ‘idealists’ here I am mainly referring to the British neo-Hegelians but the charge of mixing up ontology and epistemology can be made against at least one ‘subjective idealist’, namely Bishop Berkeley, as his wellknown dictum ‘esse ispercipi’ testifies. The objective idealists rejected the correspondence theory of truth and on the whole accepted a coherence theory. The qualification is needed here because (...) H. H. Joachim, in The Nature of Truth, found the coherence theory unable to deal with the problem of error. (shrink)

Philosophy of religion, in both its analytic and Continental streams, has been undergoing a renewal for some time now, and I seek to explore this transformation in the fortunes of the discipline by looking at how truth – and religious truth in particular – is conceptualised in both strands of philosophy. I begin with an overview of the way in which truth has been commonly understood across nearly all groups within the analytic tradition, and I will underscore the difficulties and (...) shortcomings of the analytic approach by comparing it with a Continental, and specifically Heideggerian, approach. I then proceed to a conception of truth that is even further removed from the analytic tradition, one that is prominent in the theology of Christianity and which identifies truth with Christ. The point of this detour through divergent understandings of truth is to show how philosophy of religion, whether analytic or Continental, remains entrenched in forms of thinking that will need to be overcome if it is to have a credible future. (shrink)

The causal theory of properties is standardly combined with a realist's ontology of universals or tropes. In this paper, I consider an uncharted alternative – a nominalist causal theory of properties. I discuss advantages and disadvantages of the resulting theory of properties, and explore the Rylean understanding of causal powers that emerges.

In response to the liar’s paradox, Kripke developed the fixed-point semantics for languages expressing their own truth concepts. Kripke’s work suggests a number of related fixed-point theories of truth for such languages. Gupta and Belnap develop their revision theory of truth in contrast to the fixed-point theories. The current paper considers three natural ways to compare the various resulting theories of truth, and establishes the resulting relationships among these theories. The point is to get a sense of the lay of (...) the land amid a variety of options. Our results will also provide technical fodder for the methodological remarks of the companion paper to this one. (shrink)

This thesis comprises three main chapters—each comprising one relatively standalone paper. The unifying theme is fragmentalism about truth, which is the view that the predicate “true” either expresses distinct concepts or expresses distinct properties. -/- In Chapter 1, I provide a formal development of alethic pluralism. Pluralism is the view that there are distinct truth properties associated with distinct domains of subject matter, where a truth property satisfies certain truth-characterizing principles. On behalf of pluralists, I propose an account of logic (...) and semantics that shows how they can answer central conceptual and logical challenges for their view. -/- In Chapter 2, I motivate and develop a modal account of propositions on the basis of an iterative conception of propositions, where the modality is logico-mathematical. The modal account of propositions takes the conception to motivate an inherently potential hierarchy of propositions. I show that the account helps provide satisfying solutions to the intensional paradoxes of Russell-Myhill, Kaplan, and Prior. -/- In Chapter 3, I propose that “true” is polysemous. I suggest that “true” is initially polysemous between correspondence truth and disquotational truth, and further polysemous between the meanings corresponding to the subconcepts of the concept truth generated by the indefinite extensibility of that concept. I show that the proposal provides satisfying solutions to the semantic paradoxes. (shrink)

In 1880, when Oliver Wendell Holmes (later to be a Justice of the U.S. Supreme Court) criticized the logical theology of law articulated by Christopher Columbus Langdell (the first Dean of Harvard Law School), neither Holmes nor Langdell was aware of the revolution in logic that had begun, the year before, with Frege's Begriffsschrift. But there is an important element of truth in Holmes's insistence that a legal system cannot be adequately understood as a system of axioms and corollaries; and (...) this element of truth is not obviated by the more powerful logical techniques that are now available. (shrink)

In a recent paper, “The Concept of Logical Consequence,” W. H. Hanson criticizes a formal-structural characterization of logical consequence in Tarski and Sher. Hanson accepts many principles of the formal-structural view. Relating to Sher 1991 and 1996a, he says.

This paper discusses George Boole’s two distinct approaches to the explanatory relationship between logical and psychological theory. It is argued that, whereas in his first book he attributes a substantive role to psychology in the foundation of logical theory, in his second work he abandons that position in favour of a linguistically conceived foundation. The early Boole espoused a type of psychologism and later came to adopt a type of anti-psychologism. To appreciate this invites a far-reaching reassessment of his philosophy (...) of logic. (shrink)

Three misrepresentations of informal and formal logic by two feminist writers are discussed. Andrea Nye's criticism that the semantics for formal logic abstracts from context is a misrepresentation of formal logic because Nye ignores the development of intensional logics. Second, Nye's criticism that informaIlogicians ignore the origins of arguments is a misrepresentation of fallacy theory. Prominent writers in the field specifiy numerous cases where the origins of an argument are relevant to its evaluation. Third, Valerie Plumwood's criticism that negation in (...) classical logic rests on an exclusivistic dualism that encourages the exclusion of women is shown to be false. (shrink)

This paper addresses questions of universality related to ontological engineering, namely aims at substantiating (negative) answers to the following three basic questions: (i) Is there a ‘universal ontology’?, (ii) Is there a ‘universal formal ontology language’?, and (iii) Is there a universally applicable ‘mode of reasoning’ for formal ontologies? To support our answers in a principled way, we present a general framework for the design of formal ontologies resting on two main principles: firstly, we endorse Rudolf Carnap’s principle of logical (...) tolerance by giving central stage to the concept of logical heterogeneity, i.e. the use of a plurality of logical languages within one ontology design. Secondly, to structure and combine heterogeneous ontologies in a semantically well-founded way, we base our work on abstract model theory in the form of institutional semantics, as forcefully put forward by Joseph Goguen and Rod Burstall. In particular, we employ the structuring mechanisms of the heterogeneous algebraic specification language HetCasl for defining a general concept of heterogeneous, distributed, highly modular and structured ontologies, called hyperontologies. Moreover, we distinguish, on a structural and semantic level, several different kinds of combining and aligning heterogeneous ontologies, namely integration, connection, and refinement. We show how the notion of heterogeneous refinement can be used to provide both a general notion of sub-ontology as well as a notion of heterogeneous equivalence of ontologies, and finally sketch how different modes of reasoning over ontologies are related to these different structuring aspects. (shrink)

To save antirealism from Fitch's Paradox, Tennant has proposed to restrict the scope of the antirealist principle that all truths are knowable to truths that can be consistently assumed to be known. Although the proposal solves the paradox, it has been accused of doing so in an ad hoc manner. This paper argues that, first, for all Tennant has shown, the accusation is just; second, a restriction of the antirealist principle apparently weaker than Tennat's yields a non-ad hoc solution to (...) Fitch's Paradox; and third, the alternative is only apparently weaker than, and even provably equivalent to, Tennant's. It is thereby shown that the latter is not ad hoc after all. (shrink)