An old and well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to deal with this objection consists in proving so-called recapture results. Roughly, these results show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy faces some potential problems. First, typical recapture results are formulated in a purely logical language, and do not generalize nicely to languages containing (...) the kind of vocabulary that usually motivates non-classical theories—for example, a language containing a naïve truth predicate. Second, proofs of recapture results typically employ classical principles that are not valid in the targeted non-classical system; hence, non-classical theorists do not seem entitled to those results. In this paper, we analyze these problems and provide solutions on behalf of non-classical theorists. To address the first problem, we provide a novel kind of recapture result, which generalizes nicely to a truth-theoretic language. As for the second problem, we argue that it relies on an ambiguity and that, once the ambiguity is removed, there are no reasons to think that non-classical logicians are not entitled to their recapture results. (shrink)

Connexive logics are based on two ideas: that no statement entails or is entailed by its own negation (this is Aristotle’s thesis) and that no statement entails both something and the negation of this very thing (this is Boethius' thesis). Usually, connexive logics are contra-classical. In this note, I introduce a reading of the connexive theses that makes them compatible with classical logic. According to this reading, the theses in question do not talk about validity alone; rather, they talk in (...) part about (a property related to) the soundness of arguments. (shrink)

When logicians work with multiple-conclusion systems, they use a metalinguistic comma ‘,’ to aggregate premises and/or conclusions. In this note, I present an analogy between this comma and Prior’s infamous connective tonk. The analogy reveals that these expressions have much in common. I argue that, indeed, the comma can be seen as a structural incarnation of tonk. The upshot is that, whatever story one has to tell about tonk, there are good reasons to tell a similar story about the comma (...) in typical multiple-conclusion systems, and vice versa. (shrink)

A metainference is usually understood as a pair consisting of a collection of inferences, called premises, and a single inference, called conclusion. In the last few years, much attention has been paid to the study of metainferences—and, in particular, to the question of what are the valid metainferences of a given logic. So far, however, this study has been done in quite a poor language. Our usual sequent calculi have no way to represent, e.g. negations, disjunctions or conjunctions of inferences. (...) In this paper we tackle this expressive issue. We assume some background sentential language as given and define what we call an inferential language, that is, a language whose atomic formulas are inferences. We provide a model-theoretic characterization of validity for this language—relative to some given characterization of validity for the background sentential language—and provide a proof-theoretic analysis of validity. We argue that our novel language has fruitful philosophical applications. Lastly, we generalize some of our definitions and results to arbitrary metainferential levels. (shrink)

The infinitary function of the truth predicate consists in its ability to express infinite conjunctions and disjunctions. A transparency principle for truth states the equivalence between a sentence and its truth predication; it requires an introduction principle—which allows the inference from “snow is white” to “the sentence ‘snow is white’ is true”—and an elimination principle—which allows the inference from “the sentence ‘snow is white’ is true” to “snow is white”. It is commonly assumed that a theory of truth needs to (...) satisfy a transparency principle to fulfil the infinitary function. Picollo and Schindler (Erkenntnis 83:899–928, 2017) argue against this idea. They prove that, given certain assumptions, an elimination principle is sufficient for the purpose. Then, they pose a challenge: to show why we should incorporate introduction principles to our theory of truth. In this essay I take on the challenge. I show that, given the authors’ assumptions, an introduction principle is also sufficient to perform the infinitary function. (shrink)

En este capítulo ofrecemos una introducción sistemática e histórica a la lógica, disciplina que contribuyó en gran medida a la producción del conocimiento en general y a la formación del pensamiento científico en particular. La primera sección contiene la introducción sistemática: primero, presentamos las distintas disciplinas que forman parte de la lógica en el sentido amplio del término; luego, identificamos a la lógica en sentido canónico o estricto como el estudio la validez; por último, explicamos en qué sentido la validez (...) es una propiedad formal. La segunda sección contiene la introducción histórica; nos detenemos, en particular, a estudiar dos hitos: el nacimiento de la lógica como disciplina con Aristóteles, y la intervención de Gottlob Frege, a quien se debe, en gran parte, el surgimiento de la lógica tal como la conocemos. Finalmente, damos un breve comentario del estado actual de la disciplina. (shrink)