Francesco Bellucci

In a brilliant article published in a past issue of the Transactions, Jorge A. Flórez examines Peirce’s theory of the origin of abduction in Aristotle. In the article Flórez makes two substantial points. In the first place, he argues that Peirce’s theory of the origin of abduction in the 25th chapter of the second book of the Prior Analytics is mistaken, because in that chapter Aristotle discusses first-figure syllogisms with a dialectic or contingent minor premise, and not, as Peirce thought, second-figure syllogisms. The second substantial point that Flórez makes is that something having the form of a Peircean abduction is rather to be found in the 13th chapter of the first book of the Posterior Analytics...

In Die Grundgesetze der Arithmetik (I, §48), Frege introduces his rule of the fusion of horizontals, according to which if an occurrence of the horizontal stroke is followed by another occurrence of the same stroke, either in isolation or “contained” in a propositional connective, the two occurrences can be fused with each other. However, the role of this rule, and of the horizontal sign more generally, is controversial; Michael Dummett notoriously claimed, for instance, that the horizontal is “wholly superfluous” in Frege's logical system. In this paper, we challenge Dummett's view by providing a comprehensive analysis of the significance of the horizontal stroke. After some preliminary remarks, we argue that even if Frege's connectives in some sense “contain” the horizontal, yet they are total functions. Then, we take up the question of the sense expressed by the horizontal, and we claim that, unlike other sentential operators, the horizontal is not sense‐compositional. Finally, we consider the semantic and pragmatic aspects of Frege's horizontal in connection to his judgment stroke and the double judgment stroke. Contra Dummett, we argue that the horizontal is a special and indispensable element of Frege's logic.

Peirce’s claims that methodeutic “concerns abduction alone” and that “pragmatism contributes to the security of reasoning but hardly to its uberty” are explained. They match as soon as a third claim is taken into account, namely that “pragmatism is the logic of abduction,” not of deduction or induction. Since methodeutic concerns abduction and not deduction or induction, it follows that pragmatism is a maxim of methodeutic. Then, since pragmatism contributes to the security of reasoning but not to its uberty, it follows that methodeutic contributes to the security of the only reasoning it is concerned with, namely abduction. We then explain two related issues of methodeutic of abduction. First, in addition to the maxim of pragmatism, which suggests how to choose among experimental hypotheses contributing to the security of reasoning, there is the maxim of simplicity, which suggests hypotheses that are preferable for investment and which contributes to uberty of reasoning. Second, a third maxim of abduction is economy, which suggests adopting hypotheses that contribute to the advantageousness of reasoning even when pragmatism and simplicity cease to apply. These three maxims—experientiality for security, simplicity for uberty, and economy for advantageousness—are the bedrocks of Peirce’s methodeutic of abduction.

Abstract:"Issues of Pragmaticism" (1905) contains the only published version of Peirce's doctrine of "critical common-sensism." One of the claims of that doctrine is that common sense beliefs are invariably vague. In this paper, we seek to explain this claim. We begin by providing a philological reconstruction of the drafts of "Issues of Pragmaticism" and a comparison of Peirce's several, successive expositions of critical common-sensism across those drafts. Then we examine Peirce's theory of vagueness; we show that there is both a "subjectal" and a "predicative" variety of vagueness, and that Peirce construes predicative vagueness according to three distinct models. Finally, we assess in what sense, i.e., according to which of the three models, common sense beliefs may be said to be invariably vague.

_Peirce’s Speculative Grammar: Logic as Semiotics _offers a comprehensive, philologically accurate, and exegetically ambitious developmental account of Peirce’s theory of speculative grammar. The book traces the evolution of Peirce’s grammatical writings from his early research on the classification of arguments in the 1860s up to the complex semiotic taxonomies elaborated in the first decade of the twentieth century. It will be of interest to academic specialists working on Peirce, the history of American philosophy and pragmatism, the philosophy of language, the history of logic, and semiotics.

Cet article soutient que s’il existe une philosophie du langage chez Peirce, il faut la chercher dans sa conception de la grammaire spéculative. Je reconstitue l’évolution de la grammaire spéculative de Peirce dans la période 1894- 1906, et je montre que, tandis que dans les années 1890 la grammaire spéculative est considérée comme une théorie de la proposition, Peirce la conçoit dès 1903 comme une classification générale des signes, incluant une théorie des actes de langage tout à fait pionnière.

The article offers an analysis of Peirce's notion of “rhema.” It examines and explains Peirce's definition of the rhema; it identifies and solves two problems that are direct consequences of the definition. The first problem is that proper names, while classified as rhemata, do not satisfy Peirce's definition of the rhema. The second problem is that Peirce also calls “rhemata” the results of propositional analysis that however do not satisfy his own definition of the rhema. Peirce himself solves the first problem by generalizing the notion of rhema into that of “seme.” I argue that we can solve the second problem if, following M. Dummett, we distinguish propositional analysis from propositional decomposition.