Reply to McGee and McLaughlin

41st International Wittgenstein Symposium "Philosophy of Logic and Mathematics", Kirchberg am Wechsel, Austria, August 5-11, 2018

In this paper I argue that bivalent systems in logic and beyond are often too inexact and that bivalence about truth-values and other value spectra will consequently and generally need to be replaced with multivalence. I begin arguing for that conclusion by showing how, contrary to an at least potential misconception and framed in set theoretical terms, the somewhat reconceived law of excluded middle does not entail bivalence but is entirely compatible with multivalence too. From these logico-semantic considerations I then move on to some ontologico-empirical considerations in favor of multivalence and against bivalence that can be traced back to Lukasiewicz or to the Vienna Circle's logical empiricism. I conclude by pointing out that the paradigm shift from bivalence to multivalence has already occurred in the logic-related and so-called new psychology of reasoning and by going through some options of how the traditional values of "true" and "false" and the spectrum of truth-values can be adapted to a framework of 'quantified multivalence.'

Analiza i Egzystencja, 2013

The main question of our article is: What is the logical form of statements containing expressions such as “… is true” and “it is true that …”? We claim that these expressions are generally not used in order to assign a certain property to sentences. We indicate that a predicative interpretation of these expressions was rejected by Frege and adherents to the prosentential conception of truth. We treat these expressions as operators. The main advantage of our operational reading is the fact that it adequately represents how the words “true” and “truth” function in everyday speech. Our approach confirms the intuition that so-called T-equivalences are not contingent truths, and explains why they seem to be—in some sense—necessary sentences. Moreover, our operational reading of truth

Australasian Journal of Philosophy, 2003

Annals of Pure and Applied Logic, 2004

In this paper we consider truth as a vague predicate and inquire into the relation between truth and deÿnite truth. We use some tools from modal logic to clarify this distinction, as done in McGee (Truth, Vagueness, and Paradox, Hackett Publishing Company, Paris, 1991). Finally, we consider the question whether some of the results given by McGee can be transferred to the case in which the underlying logic is stronger than ÿrst-order logic. The result will be seen to be negative.

Tarski’s semantic conception of truth was first stated by Aristotle: ‘To say of what is that it is not, or of what is that it is not, is false, while to say of what is that it is, or of what is not that it is not, is true’ (Metaphysics, 1011b 26-28). Tarski takes his T-biconditional from this. However, whereas Aristotle defines ‘true’ before ‘false’ Tarski defines only ‘true’. I reformulate the definitions of ‘false’ and ‘true’ of various contemporary theories of truth. In the reformulations ‘false’ is defined first. I hope to uncover some structural features that are common to all theories of truth and conjecture how these can be weaved into a fabric from which we can ultimately tailor a unified theory of truth. My main aim is to arrive historically, with my reversal, at the Tarskian biconditional F: “‘p’ is false if and only if not-p,” which will replace Tarski’s biconditional T: “‘p’ is true if and only if p.” Now, ‘true’ will be defined as: “‘p’ is true if and only if not-not-p.” But by double negation this is equivalent to Tarski’s original convention T. So what is the big deal? If truth is simply a logical concept then the truth functional equivalence of double negation with affirmation is sufficient to establish the identity of Tarski’s biconditional T with my reformulated Tarskian biconditional T. However, if truth is a concept involving some extra-logical, linguistic, ontological, metaphysical, epistemological, or psychological dimensions, then there is a significant difference between the definition of ‘true’ that involves an affirmation and the one that involves a double negation. Furthermore, some intuitionist systems of logic reject double negation as a rule. Hence, defining ‘true’ in terms of ‘false’ will not even be logically equivalent to defining ‘false’ in terms of ‘true’. I will demonstrate that with this reversal of definitions we will get a better rendition of the liar’s paradox, which usually begins with a statement like ‘This sentence is not true.’ I will begin with falsehood and then the paradox is unveiled. The result is that whereas Tarski’s actual version of the liar’s antinomy appeals to the rule of double negation, my version does not. Nonetheless Tarski’s original proof can also be revised to avoid use of the rule of double negation. I also consider the possibility of the indefinability of truth, as proposed by Donald Davidson, and defend robust as well as deflationary theories in their search for truth and reject indefinability. In doing so, I take on an exercise in philosophical methodology of Plato and its influence on contemporary analytic philosophy.

Philosophy of Logic and Mathematics: Contributions of the 41st International Wittgenstein Symposium, 2018

In this paper I argue that bivalent systems in logic and beyond are often too inexact and that bivalence about truth-values and other value spectra will consequently and generally need to be replaced with multivalence. I begin arguing for that conclusion by showing how, contrary to an at least potential misconception and framed in set theoretical terms, the somewhat reconceived law of excluded middle does not entail bivalence but is entirely compatible with multivalence too. From these logico-semantic considerations I then move on to some ontologico-empirical considerations in favor of multivalence and against bivalence that can be traced back to Lukasiewicz or to the Vienna Circle’s logical empiricism. I conclude by pointing out that the paradigm shift from bivalence to multivalence has already occurred in the logic-related and so-called new psychology of reasoning and by going through some options of how the traditional values of “true” and “false” and the spectrum of truth-values can be adapted to a framework of ‘quantified multivalence.’

Genericity, 2012

In we presented a modal conditional analysis of the semantic interpretation of characterizing generics (in the terminology of . Since that time there have been a number of advances to our understanding of this area: Cohen (1999aCohen ( ,b, 2005)), Leslie (2007, 2008), Nickel (2010), . However, some of these advances have been seen as overthrowing the modal conditional analysis, and we think this is not correct. The present paper is a defense of the modal conditional analysis when it is augmented with information about prosody.

2008

Michael Tye responds to the problem of higher-order vagueness for his trivalent semantics by maintaining that truth-value predicates are "vaguely vague": it's indeterminate, on his view, whether they have borderline cases and therefore indeterminate whether every sentence is true, false, or indefinite. Rosanna Keefe objects (1) that Tye's argument for this claim tacitly assumes that every sentence is true, false, or indefinite, and (2) that the conclusion is any case not viable. I arguecontra (1) -that Tye's argument needn't make that assumption. A version of her objection is in fact better directed against other arguments Tye advances, though Tye can absorb this criticism without abandoning his position's core. On the other hand, Keefe's second objection does hit the mark: embracing 'vaguely vague' truth-value predicates undermines Tye's ability to support validity claims needed to defend his position. To see this, however, we must develop Keefe's remarks further than she does.

Nous, 1999