Modality,invariance, and logical truth

Conclusion Let us sum up. We began with the question, What is the interest of a model-theoretic definition of validity? Model theoretic validity consists in truth under all reinterpretations of non-logical constants. In this paper, we have described for each necessity concept a corresponding modal invariance property. Exemplification of that property by the logical constants of a language leads to an explanation of the necessity, in the corresponding sense, of its valid sentences. I have fixed upon the epistemic modalities in characterizing the logical constants: to be a logical constant in the language of a population is to be invariant over a modality describing complete possible epistemic states of that population (or an idealized analogue thereof). The grounds for this characterization are these: (1) It leads, I believe, to an extensionally reasonable demarcation of the logical constants, including clear cases and excluding clear non-cases. It gives a principled criterion for deciding unclear cases. (2) It provides an analysis of the topic-neutrality of logic. (3) It leads to an explanation of the epistemic necessity of the logical truths in terms of the topic-neutrality of the logical constants.All the same, it is reasonable to ask, even if the suggested demarcation of logic is extensionally correct, whether it can reasonably be expected to be fundamental. The epistemic invariance of an expression is a rather striking property, one which we should want to explain. What is missing, then, is an explanation of the distinguishing epistemic properties of the constants in terms of more fundamental properties involving their understanding and use. It would be these that properly define the nature, not just the extent, of logic.     

Time, tense, truth

A theory of time is a theory of the nature of temporal reality, and temporal reality determines the truth-value of temporal sentences. Therefore it is reasonable to ask how a theory of time can account for the way the truth of temporal sentences is determined. This poses certain challenges for both the A theory and the B theory of time. In this paper, I outline an account of temporal sentences. The key feature of the account is that the primary bearers of truth-values are not utterances, but sentences evaluated with respect to a time. I argue that unlike other views, the present proposal can meet the challenges faced both by the A and the B theory.     

Propositions,representation, and truth

Synthese - Theories of propositions as sets of truth-supporting circumstances are committed to the thesis that sentences or other representations true in all and only the same circumstances express...     

Relativism,truth, and incoherence

Conclusion There are many contemporary sources and defenders of epistemological relativism which have not been considered thus far. I have, for example, barely touched on the voluminous literature regarding frameworks, conceptual schemes, and Wittgensteinian forms of life. Davidson's challenge to the scheme/content distinction and thereby to conceptual relativism, Rorty's acceptance of the Davidsonian argument and his use of it to defend a relativistic position, Winchian and other sociological and anthropological arguments for relativism, recent work in the sociology of science, and Goodman's novel articulation of a relativism of worlds and of worldmaking, to mention just some of the contemporary loci of debate, all need to be addressed. So also do the plethora of relativistic arguments spawned by Kuhn and related literature in recent philosophy of science. Therefore, it cannot be said that there is no more to be said on behalf of epistemological relativism. Moreover, the positive task of delineating a defensible version of absolutism remains to be accomplished.Nevertheless, the defenses of relativism considered above do seem to have been successfully undercut. More specifically, the arguments for the incoherence of relativism are as compelling as ever, and have manifestly not been laid to rest by contemporary relativists. The basic Socratic insight that relativism is self-refuting, and so incoherent, remains a fundamental difficulty for those who would resuscitate and defend the ancient Protagorean doctrine or a modern variant of it.     

Autism, hypersystemizing, and truth

Evidence is reviewed suggesting that, in the general population, empathizing and systemizing show strong sex differences. The function of systemizing is to predict lawful events, including lawful change, or patterns in data. Also reviewed is the evidence that individuals on the autistic spectrum have degrees of empathizing difficulties alongside hypersystemizing. The hypersystemizing theory of autism spectrum conditions (ASC) proposes that people with ASC have an unusually strong drive to systemize. This can explain their preference for systems that change in highly lawful or predictable ways; why they become disabled when faced with systems characterized by less lawful change; and their "need for sameness" or "resistance to change". If "truth" is defined as lawful patterns in data then, according to the hypersystemizing theory, people with ASC are strongly driven to discover the "truth".     

Paradox,truth and logic part I: Paradox and truth

Conclusion The discussion of the semantics of inconsistent truth theories now comes to a pause. The preceding is of course but a sketch; many interesting questions remain to be answered. The second part of this essay, however, will not seek to answer them. Rather, I will turn to the discussion of the proof theory of truth theory: the local and global logic of truth.Under the first heading, I show how to replace the inductive construction of models with an appropriate infinitary proof theory, and relate this on the one hand to the so-called dependence approach to inductive truth theories (Davis, 1979; Yablo, 1982) and on the other to van Fraassen's fact semantics for relevance logic.Under the second heading, I offer formals systems which capture the inferences valid in all approximate models. Not surprisingly, these turn out to be relevant logics.With formalism in hand, I discuss finally the extent to which the gap and/or glut approach can in fact be said to solve the paradoxes; that is, to allow us to say that the very language we are speaking is of the sort described in our theory.     

Reference, paradoxes and truth

We introduce a variant of pointer structures with denotational semantics and show its equivalence to systems of boolean equations: both have the same solutions. Taking paradoxes to be statements represented by systems of equations (or pointer structures) having no solutions, we thus obtain two alternative means of deciding paradoxical character of statements, one of which is the standard theory of solving boolean equations. To analyze more adequately statements involving semantic predicates, we extend propositional logic with the assertion operator and give its complete axiomatization. This logic is a sub-logic of statements in which the semantic predicates become internalized (for instance, counterparts of Tarski’s definitions and T-schemata become tautologies). Examples of analysis of self-referential paradoxes are given and the approach is compared to the alternative ones.