Direct Reference and Logical Truth: a Reply to Lasonen-Aarnio

This simple defense of material implication helps clarify the debate between the orthodox logicians, who claim 'If p then q' and 'p |horseshoe| q' are not interderivable and the nonorthodox logicians, who claim that the two expressions are interderivable. The paper shows the orthodox logician must deny that ordinary language arguments of the form modus ponens and modus tollens are truth-functional in any consistent sense on three lines of the truth-table.

Synthese, 2022

Journal of Philosophical Logic, 2023

This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also named implicative conditionals, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent. p ⇒ q is thus defined as ¬ (p ∧ ¬q)∧ p∧ ¬q. We explore the logical properties of this conditional in a reflexive normal Kripke semantics, provide an axiomatic system and prove it to be sound and complete for our semantics. The implicative conditional validates transitivity and contraposition, which we take to be integral parts of reasoning and communication. But it only validates restricted versions of strengthening the antecedent, right weakening, simplification, and rational monotonicity. Apparent counterexamples to some of these properties are explained as due to contextual factors. Finally, the implicative conditional avoids the paradoxes of material and strict implication, and validates some connexive principles such as Aristotle's theses and weak Boethius' thesis, as well as some highly entrenched principles of conditionals, such as conjunction of consequents, disjunction of antecedents, modus ponens, cautious monotonicity and cut.

I argue that indicative conditionals are best viewed as having partial truth conditions: "If A, B" is true if A and B are both true, false if A is true and B is false, and lacks truth value if A is false. The truth conditions are shown to explain a variety of important phenomena regarding indicative conditionals, including Adams' Thesis about the assertability conditions of conditionals, and how indicative conditionals embed in more complex constructions. In particular, the truth conditions are shown to provide the semantic basis for characterising several distinct logics of indicative conditionals, of which the logic of assertion is the main focus of the paper.

Analysis, 2004

unisi.it

The paper aims at discussing the problem of existential import in the framework of logics of so-called consequential implication, which is a modal reinterpretation of connexive implication. In developing this line of inquiry it is argued that two ways are open: (a) to resort to the language of the first order extensions of consequential logic; (b) to translate modal operators into first order quantifiers, so to define a special operator of consequential implication in terms of quantificational language itself. The two approaches are explored in some of their logical and philosophical aspects. It is stressed that more than one operator satisfies the properties pertaining to consequential implication, so that more than one quantificational translation of consequential operators may be introduced, pointing out the legitimacy of different intuitions concerning the implicative relations among quantified propositions. §1. The discussion about existential import has been characterized since the beginning by a confusion over the exact nature of its object. The problem of existential import consists, in fact, in a couple of questions which are frequently conflated, namely (a) whether universal propositions such as, for instance, "All unicorns are Italian" implies what traditional logicians call the corresponding "particular" proposition "Some unicorns are Italian".

2007

In this paper I discuss some objections raised by Donnellan (1977) and by Soames (2005) against the examples of contingent a priori truths proposed by Kripke (1980) and by Kaplan (1989). According to Kaplan and Kripke, the mechanism of direct reference alone can guarantee that some contingent truths can be known without any relevant experience. Both Donnellan and Soames claim that the examples brought up by Kaplan and Kripke can only be considered as real pieces of knowledge if the knowledge involved is de re, i.e., if we know the object (i.e., the referent of the proper name or of the demonstrative expression) of which something is predicated. I shall argue that Soames and Donnellan’s considerations do not undermine the possibility envisaged by Kripke and

The Review of Symbolic Logic, 2022

In some recent works, Crupi and Iacona proposed an analysis of ‘if’ based on Chrysippus’ idea that a conditional holds whenever the negation of its consequent is incompatible with its antecedent. This paper presents a sound and complete system of conditional logic that accommodates their analysis. The soundness and completeness proofs that will be provided rely on a general method elaborated by Raidl, which applies to a wide range of systems of conditional logic.

Paraconsistency: Logic and Applications, 2012

Although propositional logic is about the analysis of all logical connectives, we must undoubtedly recognise a primus inter pares in this class: the conditional connective "if.. . then". Since the ancient times reams of paper have been depleted, and rivers of ink have been spilt, in order to discuss the logical properties of conditionals-even crows on the roofs once did so, according to an oft-quoted passage by Callimachus. Here I'll beg those birds to move over and let me join them in croaking about which conditionals are sound and which are not. Given the massive proportions of such a debate, it is to some extent surprising that there is comparably little agreement among the specialists on how to classify conditional sentences in natural languages like English. For the purpose of the present discussion, let us focus on what is in my opinion the most accurate taxonomy of conditionals sentences from a logical viewpoint. This taxonomy, or something closely resembling it, is to be found in several places in the literature (e.g. Routley et al. 1982; Mares 2004); conditionals are ranked in decreasing order according to the logical cogency of the connection between their antecedents and their consequents. • At the top of the ladder we find entailments, where the degree of logical cogency is maximal: necessarily, if the antecedent holds true, then so does the consequent. For example,

Erkenntnis, 1994