Against classical dialetheism

Dialetheism is the view that there are true contradictions. Classical dialetheism holds further the view that the law of excluded middle is indeed a logical law. Most famous dialetheists, such as G. Priest and J. Beall, are classical dialetheists; they take classical dialetheism to be the only plausible solution to the semantic paradoxes. The main contention of the paper is, however, that their views should be rejected. Based on inspecting Priest’s and Beall’s dialetheist theories from a special perspective, this paper contends that classical dialetheism has no natural and plausible way to assign truth values to various truth-ineliminable sentences, i.e., sentences whose truth-conditions essentially involve the property of being true. Several examples of such truth-ineliminable sentences are given in the paper, and two classical dialetheist strategies for assigning them truth values are inspected. This paper argues that none of these strategies is successful.     

The use theory of meaning and semantic stipulation

According to Horwich’s use theory of meaning, the meaning of a word W is engendered by the underived acceptance of certain sentences containing W. Horwich applies this theory to provide an account of semantic stipulation: Semantic stipulation proceeds by deciding to accept sentences containing an as yet meaningless word W. Thereby one brings it about that W gets an underived acceptance property. Since a word’s meaning is constituted by its (basic) underived acceptance property, this decision endows the word with a meaning. The use-theoretic account of semantic stipulation contrasts with the standard view that semantic stipulation proceeds by assigning the meaning (reference) to W that makes a certain set of sentences express true propositions. In this paper I will argue that the use-theoretic account does not work. I take Frege to have already made the crucial point: "a definition does not assert anything but lays down something ["etwas festsetzt"]” (Frege 1899, 36). A semantic stipulation for W cannot be the decision to accept a sentence containing W or be explained in terms of such an acceptance. Semantic stipulation constitutes a problem for Horwich's use theory of meaning, especially his basic notion of acceptance.

Theories of Truth without Standard Models and Yablo’s Sequences

The aim of this paper is to show that it’s not a good idea to have a theory of truth that is consistent but ω-inconsistent. In order to bring out this point, it is useful to consider a particular case: Yablo’s Paradox. In theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. Firstly, I exhibit some conceptual problems that follow from so introducing it. Secondly, I show that in second order theories with standard semantics the same procedure yields a theory that doesn’t have models. So, while having an ω- inconsistent theory is a bad thing, having an unsatisfiable theory of truth is actually worse. This casts doubts on whether the predicate in question is, after all, a truthpredicate for that language. Finally, I present some alternatives to prove an inconsistency adding plausible principles to certain theories of truth.     

Thomason’s Paradox for Belief,and Two Consequence Relations

Thomason (1979/2010)’s argument against competence psychologism in semantics envisages a representation of a subject’s competence as follows: he understands his own language in the sense that he can identify the semantic content of each of its sentences, which requires that the relation between expression and content be recursive. Then if the scientist constructs a theory that is meant to represent the body of the subject’s beliefs, construed as assent to the content of the pertinent sentences, and that theory satisfies certain ‘natural assumptions’, then it implies that the subject is inconsistent if the beliefs include arithmetic. I challenge the result by insisting that the motivation for Thomason’s principle (ii), via Moore’s Paradox, leads to a more complex representation, in which stating the facts and expressing one’s beliefs are treated differently. Certain logical connections among expressions of assent, and between expression and statement, are a matter of consequence on pain of pragmatic incoherence, not consequence on pain of classical logical inconsistency. But while this salvages the possibility that a modification of the above sort of representation could be adequate, Thomason’s devastating conclusion returns if the scientist identifies himself as the subject of that representation, even when paying heed to the requirement of pragmatic coherence of the sort highlighted by Moore’s Paradox.     

Ist die linguistische Theorie des logischen Apriori obsolet?

The linguistic theory of the logical A Priori: is it obsolete In holistic interpretations, the logical truths are considered as continuous with empirical science: they are revisable, a posteriori, though very near to the centre of our web of belief. In this paper, we consider the merits and demerits of this approach, and we propose that it is necessary to revaluate holistic philosophies of logic. Some arguments are put forward which point in favour of the logical empiricists’ theory of logical truth. We argue (following Hartry Field) that the concept of “correlation between logical facts and logical beliefs” (which is at the heart of the holistic theory) is inconsistent. Finally, we concentrate on the principle of contradiction and argue (following Manley Thompson) that this principle is fundamental for meaning, truth, and thinking. This thesis is derived from considerations on the nature of intentionality. This revised version was published online in August 2006 with corrections to the Cover Date.     

SUPERVALUATION FIXED-POINT LOGICS OF TRUTH

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.     

A defense of contingent logical truths

A formula is a contingent logical truth when it is true in every model M but, for some model M, false at some world of M. We argue that there are such truths, given the logic of actuality. Our argument turns on defending Tarski’s definition of truth and logical truth, extended so as to apply to modal languages with an actuality operator. We argue that this extension is the philosophically proper account of validity. We counter recent arguments to the contrary presented in Hanson’s ‘Actuality, Necessity, and Logical Truth’ (Philos Stud 130:437–459, 2006).     

On the Possibility of Inference to the Best Explanation

Various proposals have suggested that an adequate explanatory theory should reduce the number or the cardinality of the set of logically independent claims that need be accepted in order to entail a body of data. A (and perhaps the only) well-formed proposal of this kind is William Kneale’s: an explanatory theory should be finitely axiomatizable but it’s set of logical consequences in the data language should not be finitely axiomatizable. Craig and Vaught showed that Kneale theories (almost) always exist for any recursively enumerable but not finitely axiomatizable set of data sentences in a first order language with identity. Kneale’s criterion underdetermines explanation even given all possible data in the data language; gratuitous axioms may be “tacked on.” Define a Kneale theory, T, to be logically minimal if it is deducible from every Kneale theory (in the vocabulary of T) that entails the same statements in the data language as does T. If they exist, minimal Kneale theories are candidates for best explanations: they are “bold” in a sense close to Popper’s; some minimal Kneale theory is true if any Kneale theory is true; the minimal Kneale theory that is data equivalent to any given Kneale theory is unique; and no Kneale theory is more probable than some minimal Kneale theory. I show that under the Craig-Vaught conditions, no minimal Kneale theories exist.     

Context-Sensitivity in Jain Philosophy: A Dialogical Study of Siddharṣigaṇi’s <Emphasis Type="Italic">Commentary on the Handbook of Logic</Emphasis>

In classical India, Jain philosophers developed a theory of viewpoints (naya-vāda) according to which any statement is always performed within and dependent upon a given epistemic perspective or viewpoint. The Jainas furnished this epistemology with an (epistemic) theory of disputation that takes into account the viewpoint in which the main thesis has been stated. The main aim of our paper is to delve into the Jain notion of viewpoint-contextualisation and to develop the elements of a suitable logical system that should offer a reconstruction of the Jainas’ epistemic theory of disputation. A crucial step of our project is to approach the Jain theory of disputation with the help of a theory of meaning for logical constants based on argumentative practices called dialogical logic. Since in the dialogical framework the meaning of the logical constants is given by the norms or rules for their use in a debate, it provides a meaning theory closer to the Jain context-sensitive disputation theory than the main-stream formal model-theoretic semantics.     

TRUTH CONDITIONS OF TENSED SENTENCE TYPES

Quentin Smith has argued that the new tenseless theory of time is faced with insurmountable problems and should be abandoned in favour of the tensed theory of time. Smith;s main argument attacks the fundamental premise of the tenseless theory: that tenseless truth conditions for tokens of tensed sentences adequately capture the meaning of tensed sentences. His position is that tenseless truth conditions cannot explain the logical relations between tensed sentences, thus the tensed theory must be accepted. Against Smith, this paper adopts an alternative approach to the explanation of the entailment relations between sentences which contain indexicals. The approach drops the reliance upon tokens and instead relies on the evaluation of sentence types with respect to a context rather than upon actual or possible utterances of tokens of the types. This (new) version of the tenseless theory of time can adequately explain the relevant entailment relations between tensed sentences.