Strictness and connexivity

Abstract

conditional' abbreviates 'indicative conditional'. This is not intended to suggest that counterfactuals differ in some important respect. On the contrary, most of what will be said about conditionals can be extended, mutatis mutandis, to counterfactuals. But for the sake of simplicity we will not deal with such extension.According to connexiviststhe advocates of connexive logic -AT, AT ′ , BT, BT ′ are highly plausible, so a good theory of conditionals should validate them. The intuitive character of AT, AT ′ , BT, BT ′ is thus regarded as a main motivation, if not the main motivation, for adopting connexive logic. 1 Some connexivists have suggested that the truth conditions of p>q are to be given in terms of a relation between p and q, some sort of incompatibility that is not reducible to the impossibility that p and q are true. For example, Nelson has defined such a relation, and Angell has incorporated it into a logical system. A theory of conditionals along these lines validates AT, AT ′ , BT, BT ′ (Nelson 1930; Angell 1962).Nelson's definition is not the only option. In fact it is not even obvious that we need some non-standard notion of incompatibility in order to validate AT, AT ′ , BT, BT ′ . It is reasonable to expect that a definition based on entirely different notions can lead to the same result. So, we will simply call 'connexivist' any theory of conditionals that validates AT, AT ′ , BT, BT ′ , and we will not deal with the differences between the various connexivist theories. 2 This paper is about the intuitive basis of connexive logic, so the question it addresses is whether AT, AT ′ , BT, BT ′ should be treated as theorems in virtue of their intuitive content. The answer it suggests is that there is no reason to think they should: although the core idea behind AT, AT ′ , BT, BT ′ is essentially sound, it is far from obvious that AT, AT ′ , BT, BT ′ hold unrestrictedly.Note that here the qualification 'in virtue of their intuitive content' is crucial, for there may be independent reasons for treating AT, AT ′ , BT, BT ′ as theorems. A system of connexive logic, just as any formal apparatus, may be motivated in many different ways, and this paper focuses only on one of them. Aristotle's thesisAs we have seen, connexivists think that AT and AT ′ as highly plausible, so that a good theory of conditionals should validate them. What will be suggested

Connexivity and the Pragmatics of Conditionals

“…It goes back to Leibniz (see Lenzen 2019), further back to the twelfth century philosophers Afzal ad-Din Kashani in the east (see El-Rouayheb 2009) and Alberic of Paris in the west (see Estrada-González and Ramírez-Cámara 2020), and maybe, if we follow Wolfgang Lenzen's speculation, back to Aristotle himself (see Lenzen 2020). Much more recently, Andrea Iacona has suggested a similar idea and coupled it with a defense of strict implication, see Iacona (2019), and also the manuscript Crupi and Iacona (2019). 10 Let us also agree to bracket dialetheism (the view that some contradictions are true) and the closely related idea of truth value gluts (statements that are, in some sense, both true and false).…”

Connexivity in the Logic of Reasons

“…(3) If the coin lands heads, Fido can bark (4) If the coin lands tails, Fido can bark On each of the three accounts considered, (3) and ( 4) turn out to be both acceptable, given that very likely Fido can bark regardless of the outcome of the coin toss. 12 Independently of whether this result is desirable within an account of conditionals, it is certainly not desirable as part of an analysis of 'p is a reason for q', for the cases of the kind described are intuitively cases in which p does not support q. It would be implausible to say that the coin 9 Adams [1].…”

Rewriting the History of Connexive Logic

“…He starts with quoting the famous passage from De hypotheticis syllogismis: 'Si est A, cum sit B, est C; [...] atqui cum sit B, non est C; non est igitur A.' 13 Next McCall "transliterates" the underlying idea into the inference: If p, then if q then r, if q then not-r, therefore, not-p and he justifies this transformation as follows:…”

“…The terms 'humble connexivity' and 'hardcore connexivity' have been coined in[16,25], respectively. For a recent defence of "humble" connexivism cf [13][8] it is argued that any "Evidential Conditional" should only be "humbly" connexive 2.…”