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.     

Epistemic norms: truth conducive enough

Synthese - Epistemology needs to account for the success of science. In True Enough (2017), Catherine Elgin argues that a veritist epistemology is inadequate to this task. She advocates shifting...     

Vacuous truth

Special thanks go to Paul Humphreys for his criticisms and helpful comments. Also Richard Gale, Gerald Massey, Nicholas Rescher, David Blumenfeld, James Humber, Richard Ketchum, and Wolfgang Dietel made helpful comments on an earlier version. Each found something in need of repair. Finally, I would like to thank the Hambidge Center and the Center for the Philosophy of Science at the University of Pittsburgh for providing in 1988 the setting and the resources that made this paper possible.     

Approximate truth

Conclusion The technical results presented here on continuity and approximate implication are obviously incomplete. In particular, a syntactic characterization of approximate implication is highly desirable. Nevertheless, I believe the results above do show that the theory has considerable promise for application to the areas mentioned at the top of the paper.Formulation and defense of realist interpretations of science, for example, require approximate truth because we hardly ever have evidence that a particular scientific theory corresponds perfectly with a portion of the real world. Realists need to assert, then, that evidence for a theory is evidence for its approximate truth, not its truth (see [3] and [18]). Approximate truth is, however, a vague notion, and specification of quantity terms and of a sense of approximation are needed to make precise applications of it. Suitability of both vocabulary and sense of approximation depend on the subject matter, and their selection is a partly empirical matter that raises complex issues. In light of the number of common inferences which are not continuous, realists also need to be concerned about indiscriminate use of deductive logic to derive consequences from approximately true theories. These issues will be considered further in a future paper.Approximate truth also has potential application in areas of artificial intelligence that require inference from inaccurate data. In the qualitative physical theories of de Kleer and Brown [6], for example, qualitative values are derived by partitioning the real numbers into regions. Inferences leading from inside to outside a region must be identified and avoided, and approximate implication and continuity may prove useful in doing this. More generally, growing use of predicate logic as a programming language invites application of the theory of approximate truth as a symbolic substitute for numerical evaluation of computation errors. This too will be the subject of a future paper.Thanks to R. Boyd, A. Garfinkel, H. Hertz, P. Solomon, P. Suppes, S. Weissman, and anonymous referees for advice and criticism.     

The truth and nothing but the truth,yet never the whole truth: Frege,Russell and the analysis of unities

It is widely assumed that Russell's problems with the unity of the proposition were recurring and insoluble within the framework of the logical theory of his Principles of Mathematics. By contrast, Frege's functional analysis of thoughts (grounded in a type-theoretic distinction between concepts and objects) is commonly assumed to provide a solution to the problem or, at least, a means of avoiding the difficulty altogether. The Fregean solution is unavailable to Russell because of his commitment to the thesis that there is only one ultimate ontological category. This, combined with Russell's reification of propositions, ensures that he must hold concepts and objects to be of the same logical and ontological type. In this paper I argue that, while Frege's treatment of the unity of the proposition has immediate advantages over Russell's, a deeper consideration of the philosophical underpinnings and metaphysical consequences of the two approaches reveals that Frege's supposed solution is, in fact, far from satisfactory. Russell's repudiation of the Fregean position in the Principles is, I contend, convincing and Russell's own position, despite its problems, conforms to a greater extent than Frege's with common sense and, furthermore, with certain ideas which are central to our understanding of the origins of the analytical tradition.     

Quine's truth

W. V. Quine has made statements about truth which are not obviously compatible, and his statements have been interpreted in more than one way. For example, Donald Davidson claims that Quine has an epistemic theory of truth, but Quine himself often says that truth is just disquotational. This paper argues that Quine should recognize two different notions of truth. One of these is disquotational, the other is empiricist. There is nothing wrong with recognizing two different notions of truth. Both may be perfectly legitimate, even though, to some extent, they may be applicable in different contexts. Roughly speaking, a sentence is true in the empiricist sense if it belongs to a theory which entails all observation sentences which would be assented to by the speakers of the language in question (and no observation sentences which would be dissented from by these speakers). Various objections to this idea are discussed and rejected.     

Reversing the truth effect: learning the interpretation of processing fluency in judgments of truth

Repeated statements receive higher truth ratings than new statements. Given that repetition leads to greater experienced processing fluency, the author proposes that fluency is used in truth judgments according to its ecological validity. Thus, the truth effect occurs because people learn that fluency and truth tend to be positively correlated. Three experiments tested this notion. Experiment 1 replicated the truth effect by directly manipulating processing fluency; Experiment 2 reversed the effect by manipulating the correlation between fluency and truth in a learning phase. Experiment 3 generalized this reversal by showing a transfer of a negative correlation between perceptual fluency (due to color contrast) and truth to truth judgments when fluency is due to prior exposure (i.e., repetition).