ABSTRACTDo truth tables—the ordinary sort that we use in teaching and explaining basic propositional logic—require an assumption of consistency for their construction? In this essay we show that truth tables can be built in a consistency-independent paraconsistent setting, without any appeal to classical logic. This is evidence for a more general claim—that when we write down the orthodox semantic clauses for a logic, whatever logic we presuppose in the background will be the logic that appears in the foreground. Rather than (...) any one logic being privileged, then, on this count partisans across the logical spectrum are in relatively similar dialectical positions. (shrink)

It is commonly held that the ascription of truth to a sentence is intersubstitutable with that very sentence. However, the simplest subclassical logics available to proponents of this view, namely K3 and LP, are hopelessly weak for many purposes. In this article, I argue that this is much more of a problem for proponents of LP than for proponents of K3. The strategies for recapturing classicality offered by proponents of LP are far less promising than those available to proponents of (...) K3. This undermines the ability of proponents LP to engage in public reasoning in classical domains. (shrink)

One longstanding problem for glut theorists is the problem of ‘just true.’ On Beall's conservative version of glut theory advanced in Spandrels of Truth , he addresses the problem in two steps. The first is a rejection of the problem: he claims that the only general notion of ‘just true’ is just truth itself. On that view, the alleged problem of ‘just true’ is reduced to the problem of truth itself, which has a solution—glut theory. The second step is to (...) acknowledge that there is a notion of ‘just true’ which is more limited but nonetheless meets all reasonable criteria demanded by those who advance the longstanding just-true objection. Marcus Rossberg disagrees. According to Rossberg, a just-true operator ought to iterate and be non-arbitrary in ways that Beall's proposed just-true operator is not. My aim in this paper is to construct a new conditional in terms of which a new just-true operator may be defined, a necessity operator, and to show that it meets all of the target desiderata of the debate. I then use that new operator to address the arbitrariness worries raised by Rossberg. (shrink)

Minimalism is the view that our concept of truth is constituted by our disposition to accept instances of the truth schema ‘The proposition that p is true if and only if p’. The generalisation problem is the challenge to account for universal generalisations concerning logical truths such as ‘Every proposition of the form 〈if p, then p〉 is true’. This paper argues that such generalisations can be deduced using a single example of the logical truth in question and a single (...) corresponding instance of the truth schema, employing the logical method of reasoning with arbitrary instances of universal and existential generalisations. Suggesting an inferentialist construal of Minimalism, the paper introduces conditional and general acceptance dispositions, distinguishes inferential meaning constitution from implicit definition, highlights the inferential nature of acceptance of instances of the truth schema, sketches a suitable account of structured propositions, compares higher-order with first-order means of quantification, and argues that the conception of truth Minimalism attributes to ordinary speakers is essentially inferential. It finally applies the deductive strategy to generalisations concerning logical validity as well as more complex logical truths. (shrink)

I argue that there is nothing about the structure of inference to the best explanation (IBE) that prevents it from establishing a contradiction in general, though there are some potential limitations on when it can be used for this purpose. Studying the relationship between IBE and contradictions is worthwhile for three reasons. First, it enhances our understanding of IBE. We see that, in many cases, IBE does not require explanations to be consistent, though there are some cases where consistency may (...) be required. Second, the argument has implications for the debate over scientific realism. Many scientific theories appear to be inconsistent. The best argument for scientific realism, however, appeals to IBE. My argument thus shows that a certain kind of realist faces a threat from inconsistent theories. Third, the argument is important for dialetheism. Dialetheists maintain that some contradictions are true. Many of the arguments in favour of dialetheism appeal to explanatory considerations. What I say here provides support for defending dialethism using an IBE-based methodology. (shrink)