Francesco Bellucci

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.

The paper seeks to explain in what sense pragmatism was for Peirce a doctrine of logic. It is argued that pragmatism is a doctrine of logic for Peirce because its maxim, the pragmatic maxim, is a maxim of the methodeutic of abduction, i.e., concerns the method of selecting hypotheses for experimental testing. The paper also connects this idea to Peirce’s 1913 thesis according to which pragmatism contributes to the security but not to the uberty of reasoning. The connection consists in that by excluding hypotheses that cannot be tested, the maxim renders the whole process of reasoning more secure, while any explanatory hypotheses is “uberous” in Peirce’s sense as any other.

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.

This paper provides an analysis of the notational difference between Beta Existential Graphs, the graphical notation for quantificational logic invented by Charles S. Peirce at the end of the 19th century, and the ordinary notation of first-order logic. Peirce thought his graphs to be “more diagrammatic” than equivalently expressive languages for quantificational logic. The reason of this, he claimed, is that less room is afforded in Existential Graphs than in equivalently expressive languages for different ways of representing the same fact. The reason of this, in turn, is that Existential Graphs are a non-linear, occurrence-referential notation. As a non-linear notation, each graph corresponds to a class of logically equivalent but syntactically distinct sentences of the ordinary notation of first-order logic that are obtained by permuting those elements that in the graphs lie in the same area. As an occurrence-referential notation, each Beta graph corresponds to a class of logically equivalent but syntactically distinct sentences of the ordinary notation of first-order logic in which the identity of reference of two or more variables is asserted. In brief, Peirce’s graphs are more diagrammatic than the linear, type-referential notation of first-order logic because the function that translates the latter to the graphs does not define isomorphism between the two notations.

The Syllabus for Certain Topics of Logic is a long treatise that Peirce wrote in October and November to complement the material of his 1903 Lowell Lectures. The last of the eight lectures was on abduction, first entitled “How to Theorize” and then “Abduction.” Of abduction, the Syllabus states that its “conclusion is drawn in the interrogative mood ”.1 This is not the first time that Peirce associates abduction to interrogations,2 but the statement is significant because it is the first time that the “interrogative mood” is ascribed to speculative grammar. At the same time, such...

Expressively equivalent logical languages can enunciate logical notions in notationally diversified ways. Frege’s Begriffsschrift, Peirce’s Existential Graphs, and the notations presented by Wittgenstein in the Tractatus all express the sentential fragment of classical logic, each in its own way. In what sense do expressively equivalent notations differ? According to recent interpretations, Begriffsschrift and Existential Graphs differ from other logical notations because they are capable of “multiple readings.” We refute this interpretation by showing that there are at least three different kinds of such multiple readings. While readings of the first kind do not capture any essential difference among notations but only among vocabularies, corresponding to readings of the second and the third kind two general parameters according to which notations may differ are defined: linearity vs. non-linearity, and tabularity vs. non-tabularity. This answers the question of how there can be substantially different but expressively equivalent logical notations.

A rose is a rose is a rose is a rose.As is well known, according to Charles S. Peirce one of the principal tasks of logic is the analysis of reasoning. This was indeed the explicit purpose of his logical algebras and graphical logic, and Peirce often credits himself with possessing a special gift for logical analysis. Yet he surprisingly also holds that “absolute completeness of logical analysis is no less unattainable [than] is omniscience. Carry it as far as you please, and something will always remain unanalyzed.” 1 The question thus arises as to what Peirce could have meant by saying that, in logical analysis, something remains unanalyzed. This question, important..

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.

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...

Peirce seems to maintain two incompatible theses: that a sentence is multiply analyzable into subject and predicate, and that a sentence is uniquely analyzable as a combination of rhemata of first intention and rhemata of second intention. In this paper it is argued that the incompatibility disappears as soon as we distinguish, following Dummett’s work on Frege, two distinct notions of analysis: ‘analysis’ proper, whose purpose is to display the manner in which the sense of a sentence is determined by the senses of its constituent parts, and ‘decomposition’, which is the process of dividing a sentence into a predicate and a subject, and whose purpose is to both to explain how quantified sentences are constructed and to evidence a pattern within a sentence which it shares with other sentences.

This paper argues that Umberto Eco had a sophisticated theory of abductive reasoning and that this theory is fundamentally akin to Peirce’s both in the analysis and in the justification of this kind of reasoning. The first section expounds the essentials of Peirce’s theory of abduction, and explains how Peirce moved from seeing abduction as a kind of reasoning to seeing it as a stage of the larger process of inquiry. The second section deals with one of Eco’s paradigmatic examples of abduction, i.e., William of Baskerville’s abduction concerning the horse Brunellus in the overture of The Name of the Rose, and shows that, just like in Peirce’s three-stages model of inquiry, William’s abductions are verified by means of deduction and induction. The third section examines the problem of the justification of abductive reasoning, and argues that both Peirce and Eco solved this problem through the idea that the justification of abduction is itself abductive.

Peirce and Frege both distinguished between the propositional content of an assertion and the assertion of a propositional content, but with different notational means. We present a modification of Peirce’s graphical method of logic that can be used to reason about assertions in a manner similar to Peirce’s original method. We propose a new system of Assertive Graphs, which unlike the tradition that follows Frege involves no ad hoc sign of assertion. We show that axioms of intuitionistic logic can be derived from AGs, and argue that AGs analyse and represent assertions and illocutionary content in a way which is motivated both by its logical properties and its historical connection with the ideas that led to the development of the graphical method.

We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. We conclude that Frege, and even more so Peirce, developed new notations not to make drawing logical conclusions easier but in order to answer the needs of logical analysis.