When logicians work with multiple-conclusion systems, they use a metalinguistic comma ‘,’ to aggregate premises and/or conclusions. In this note, I present an analogy between this comma and Prior’s infamous connective tonk. The analogy reveals that these expressions have much in common. I argue that, indeed, the comma can be seen as a structural incarnation of tonk. The upshot is that, whatever story one has to tell about tonk, there are good reasons to tell a similar story about the comma (...) in typical multiple-conclusion systems, and vice versa. (shrink)

Prior’s Tonk is a famously horrible connective. It is defined by its inference rules. My aim in this article is to compare Tonk with some hitherto unnoticed nasty connectives, which are defined in semantic terms. I first use many-valued truth-tables for classical sentential logic to define a nasty connective, Knot. I then argue that we should refuse to add Knot to our language. And I show that this reverses the standard dialectic surrounding Tonk, and yields a novel solution to the (...) problem of many-valued truth-tables for classical sentential logic. I close by outlining the technicalities surrounding nasty connectives on many-valued truth-tables. (shrink)

This paper consider Prior's connective Tonk from a particular bilateralist perspective. I show that there is a natural perspective from which we can see Tonk and its ilk as perfectly well-defined pieces of vocabulary; there is no need for restrictions to bar things like Tonk.

Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk, for which, unlike for tonk, there are reduction steps for the removal of maximal formulas arising from introducing and eliminating formulas with those connectives as main operators. Adding either of them to bilateral classical logic results in an incoherent system. One way around this problem is (...) to count formulas as maximal that are the conclusion of reductio and major premise of an elimination rule and to require their removability from deductions. The main part of the paper consists in a proof of a normalisation theorem for bilateral logic. The closing sections address philosophical concerns whether the proof provides a satisfactory solution to the problem at hand and confronts bilateralists with the dilemma that a bilateral notion of stability sits uneasily with the core bilateral thesis. (shrink)

Many philosophers still believe that metaphysically analytic sentences exist, where a sentence is understood to be metaphysically analytic if and only if it is true solely in virtue of its meaning. I provide two arguments against this claim and hence conclude that metaphysically analytic sentences do not exist. Still, some philosophers, however, hold out hope that epistemically analytic sentences exist, where a sentence is epistemically analytic if and only if an agent's understanding the sentence suffices for the agent to be (...) justified in believing that this sentence is true. One such philosopher is Paul Boghossian, whose so-called analytic theory of the a priori is intended to show how epistemically analytic sentences can explain our a priori knowledge of the truths about logic. His theory, however, relies on the dubious Argument by Implicit Definition. I provide an objection to this argument and hence conclude that Boghossian's analytic theory of the a priori fails to vindicate the notion of epistemic analyticity. Still, I concede that just because Boghossian's attempt to do so fails, it does not follow that the notion of epistemic analyticity cannot, in another way, be vindicated. (shrink)