Valid Arguments as True Conditionals

Abstract

This paper explores an idea of Stoic descent that is largely neglected nowadays, the idea that an argument is valid when the conditional formed by the conjunction of its premises as antecedent and its conclusion as consequent is true. As will be argued, once some basic features of our naïve understanding of validity are properly spelled out, and a suitable account of conditionals is adopted, the equivalence between valid arguments and true conditionals makes perfect sense. The account of validity outlined here, which displays one coherent way to articulate the Stoic intuition, accords with standard formal treatments of deductive validity and encompasses an independently grounded characterization of inductive validity.

Naïve Truth and the Evidential Conditional

“…Similar considerations hold for (e). 21 Clause 10 reproduces in similar way the falsity conditions of ψ χ as given in Definition 2.2.…”

Williamson’s Abductive Case for the Material Conditional Account

“…19 The intuitive understanding here is that anyone justified in believing A becomes justified to believe C as soon as she becomes justified to believe A ⇒ C (e.g., on the basis of testimony), supposing her being informed that if A, C, does not undermine whatever justifies her belief in A. 20 There is already robust empirical support for the thought that inferential connections (including nondeductive ones) play a central role in how people 18 See also Krzyżanowska [39], Douven [15,16], Vidal and Baratgin [91], Douven et al [19,22], Iacona [33], Rostworowski et al [68], Sikorski [74]. 19 For work on the logic of the inferential conditional, see Crupi and Iacona [11,12], Raidl et al [66], and Iacona [33].…”

“…20 There is already robust empirical support for the thought that inferential connections (including nondeductive ones) play a central role in how people 18 See also Krzyżanowska [39], Douven [15,16], Vidal and Baratgin [91], Douven et al [19,22], Iacona [33], Rostworowski et al [68], Sikorski [74]. 19 For work on the logic of the inferential conditional, see Crupi and Iacona [11,12], Raidl et al [66], and Iacona [33]. 20 Related proposals are to be found in Rott [69,70], Oaksford and Chater [57][58][59][60][61], van Rooij and Schulz [85], and Berto and Özgün [7].…”

Connexivity in the Logic of Reasons

“…More generally, Rott's account makes ¬p → q incompatible with p → q, so it validates P14. 13 As the foregoing remarks suggest, Aristotle's Second Thesis provides an interesting measure of adequacy for an interpretation of in terms of support. This emerges with clarity if one compares P14 with P11.…”