Andrea Iacona

This paper investigates the logic of compatibility as a ground for the logic of conditionals. We identify a family of principles expressing key properties of compatibility, which can be coherently ordered. Assuming that conditionals are definable in terms of incompatibility — the negation of compatibility — each of the principles identified yields corresponding principles governing conditionals. Clarifying these derivability relations provides a new perspective on several existing accounts of conditionals.

This chapter is based on the idea that there is an important sense in which the things we say may involve a degree of specificity that goes beyond what we have in mind when we say them. In that sense, the things we say are interpretations of the sentences we use that are sufficiently specific for the purpose of ascribing truth or falsity to those sentences. This chapter explains how the relation between logic and natural language can be elucidated on the basis of this idea, and shows how some fundamental issues concerning vagueness can be handled accordingly.

There are essentially three ways to treat conditionals with impossible antecedents in a formal framework that employs classical truth values: one can hold that such conditionals are all true, that they are all false, or that some are true while others are false. These three options will be examined under the background hypothesis that a conditional is true when its antecedent is incompatible with the negation of its consequent. It will be argued that the third option can be coherently developed by defining a suitable notion of compatibility.

This paper outlines a truth-conditional view of logical form, that is, a view according to which logical form is essentially a matter of truth-conditions. Section 1 provides some preliminary clarifications. Section 2 shows that the main motivation for the view is the fact that fundamental logical relations such as entailment or contradiction can formally be explained only if truth-conditions are formally represented. Sections 3 and 4 articulate the view and dwell on its affinity with a conception of logical form that has been defended in the past. Sections 5-7 draw attention to its impact on three major issues that concern, respectively, the extension of the domain of formal explanation, the semantics of tensed discourse, and the analysis of quantification.Este artículo esboza una concepción veritativo-condicional de la forma lógica, es decir, una concepción de acuerdo con la cual la forma lógica es esencialmente una cuestión de condiciones de verdad. La sección 1 proporciona algunas clarificaciones preliminares. La sección 2 muestra que la principal motivación para esta concepción es el hecho de que hay relaciones lógicas fundamentales, como la implicación o la contradicción, que sólo pueden explicarse formalmente si las condiciones de verdad se representan formalmente. Las secciones 3 y 4 articulan dicha concepción y profundizan en su afinidad con una concepción de la forma lógica que ha sido defendida en el pasado. Las secciones 5 a 7 destacan su impacto sobre tres asuntos principales que conciernen, respectivamente, a la extensión del dominio de las explicaciones formales, la semántica del discurso temporalizado, y el análisis de la cuantificación.

One question that arises in connection with Ockhamism, and that perhaps has not yet received the attention it deserves, is how a coherent formal account of truth ascriptions can be provided by using a suitable truth predicate in the object language. We address this question and show its implications for some semantic issues that have been discussed in the literature on future contingents. Arguably, understanding how truth ascriptions work at the formal level helps to gain a deeper insight into Ockhamism itself.

So far, the method of supervaluations has been mainly employed to define a non-gradable property of sentences, supertruth, in order to provide an analysis of truth. But it is also possible, and arguably at least as plausible, to define a gradable property of sentences along the same lines. This paper presents a supervaluationist semantics that is quantitative rather than qualitative. As will be shown, there are at least two distinct interpretations of the semantics — one alethic, the other epistemic — which can coherently be adopted to address key issues such as vagueness and future contingents.

According to alethic pluralism, there is more than one way of being true: truth is not unique, in that there is a plurality of truth properties, each of which pertains to a specific domain of discourse. This paper shows how such a plurality can be represented in a coherent formal framework by means of a Kripke-style construction that yields intuitively correct extensions for distinct truth predicates. The theory of truth we develop can handle at least three crucial problems that have been raised in connection with alethic pluralism: mixed compounds, mixed inferences, and semantic paradoxes.

This paper investigates the relationships between two claims about conditionals that are often discussed separately. One is the claim that conditionals express inferences, in the sense that a conditional holds when its consequent can be inferred from its antecedent. The other is the claim that conditionals intuitively obey the characteristic principles of connexive logic. Following a line of thought that goes back to Chrysippus, we suggest that these two claims may coherently be understood as distinct manifestations of a single and more basic idea, namely, that a conditional holds when its antecedent is incompatible with the negation of its consequent. The account of conditionals we propose is based precisely on this idea.

According to the view of conditionals named 'inferentialism', a conditional holds when its consequent can be inferred from its antecedent. This paper identifies some major challenges that inferentialism has to face, and uses them to assess three accounts of conditionals: one is the classical strict account, the other two have recently been proposed by Douven and Rott. As will be shown, none of the three proposals meets all challenges in a fully satisfactory way. We argue through novel formal results that a variation of the evidential account of conditionals suggested by Crupi and Iacona is the most promising candidate to develop inferentialism in a coherent formal framework.

According to a view called ‘nihilism’, sentences containing vague expressions cannot strictly speaking be true or false, because they lack definite truth conditions. While most theorists of vagueness tend to regard nihilism as a hopeless view, a few isolated attempts have been made to defend it. This paper aims to develop such attempts in a new direction by showing how nihilism, once properly spelled out, can meet three crucial explanatory challenges that, respectively, concern truth, assertibility, and communication.

This paper discusses some key connexive principles construed as principles about reasons, that is, as principles that express logical properties of sentences of the form ‘p is a reason for q’. Its main goal is to show how the theory of reasons outlined by Crupi and Iacona, which is based on their evidential account of conditionals, yields a formal treatment of such sentences that validates a restricted version of the principles discussed, overcoming some limitations that affect most extant accounts of conditionals.

According to the analysis of concessive conditionals suggested by Crupi and Iacona, a concessive conditional $$p{{\,\mathrm{\hookrightarrow }\,}}q$$ p ↪ q is adequately formalized as a conjunction of conditionals. This paper presents a sound and complete axiomatic system for concessive conditionals so understood. The soundness and completeness proofs that will be provided rely on a method that has been employed by Raidl, Iacona, and Crupi to prove the soundness and completeness of an analogous system for evidential conditionals.

This paper develops the idea that valid arguments are equivalent to true conditionals by combining Kripke’s theory of truth with the evidential account of conditionals offered by Crupi and Iacona. As will be shown, in a first-order language that contains a naïve truth predicate and a suitable conditional, one can define a validity predicate in accordance with the thesis that the inference from a conjunction of premises to a conclusion is valid when the corresponding conditional is true. The validity predicate so defined significantly increases our expressive resources and provides a coherent formal treatment of paradoxical arguments.

This paper raises some questions about the formalization of sentences containing ‘if’ or similar expressions. In particular, it focuses on three kinds of sentences that resemble conditionals in some respects but exhibit distinctive logical features that deserve separate consideration: whether-or-not sentences, biscuit conditionals, and concessive conditionals. As will be suggested, the examples discussed show in different ways that an adequate formalization of a sentence must take into account the content expressed by the sentence. This upshot is arguably what one should expect on the view that logical form is determined by truth conditions.

This paper investigates Ockhamism from a metaphysical point of view. Its main point is that the claim that future contingents are true or false is less demanding than usually expected, as it does not require particularly contentious assumptions about the future. First it will be argued that Ockhamism is consistent with a wide range of metaphysical views. Then it will be shown that each of these views leaves room for the claim that the future is open, at least on some plausible interpretations of that claim.