De Finettian Logics of Indicative Conditionals Part I: Trivalent Semantics and Validity

Abstract

This paper explores trivalent truth conditions for indicative conditionals, examining the "defective" truth table proposed by de Finetti (1936) and Reichenbach (1935, 1944). On their approach, a conditional takes the value of its consequent whenever its antecedent is true, and the value Indeterminate otherwise. Here we deal with the problem of selecting an adequate notion of validity for this conditional. We show that all standard validity schemes based on de Finetti's table come with some problems, and highlight two ways out of the predicament: one pairs de Finetti's conditional (DF) with validity as the preservation of non-false values (TT-validity), but at the expense of Modus Ponens; the other modifies de Finetti's table to restore Modus Ponens. In Part I of this paper, we present both alternatives, with specific attention to a variant of de Finetti's table (CC) proposed by Cooper (

An Easy Road to Multi-contra-classicality

“…Third: as it has already been advanced since Footnote 16, mccLP is the same logic as the one named DF/TT in Egré et al. ( 2021 ), in the sense that they validate exactly the same set of valid arguments. The authors did not notice all its contra-classical potential, though—besides connexivity, they just discussed the validity of .…”

“…DF/TT in Egré et al. ( 2021 ) has been extensively studied as a logic suitable for suppositional reasoning, that is, as a logic where conditionals are read as expressing conditional degrees of belief. Thus, mccLP at least opens the door for studying suppositional reasoning from the point of view of inconsistent degrees of belief.…”

“…See Egré et al. ( 2021 ) for both historical and logical discussion, and Estrada-González and Ramírez Cámara ( 2020 ) for further discussion of the apparently odd properties of that connective, which resembles a lot the discussion below about the conditionality of the O conditional.…”

“… 8 Boethius’ (or Wansing’s) Theses strengthened into biconditional form is labelled ‘full commutation of the conditional with negation’ in Egré et al. ( 2021 ). …”

Revisiting Reichenbach’s logic

“…In fact, Egré et al. ( 2021 ) have shown that quasi-implication belongs to a family of intended conditionals > such that, with T-consequence will fail at least one of the following: Detachment, Self-identity, Non-symmetry ( ) or Non-entailment of conjunction ( ). Nonetheless, they have also shown that quasi-implication plus TT-consequence , that is…”