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 (meta-abduction in Eco, ur-abduction in Peirce). (shrink)

The goal of this paper is a reassessment of Peirce’s doctrine of symbol. The paper discusses a common reading of Peirce’s doctrine, according to which all and only symbols are conventional signs. Against this reading, it is argued that neither are all Peircean symbols conventional, nor are all conventional signs Peircean symbols. Rather, a Peircean symbol is a general sign, i. e., a sign that represents a general object.

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. (shrink)

According to the received view, Charles S. Peirce's theory of diagrammatic reasoning is derived from Kant's philosophy of mathematics. For Kant, only mathematics is constructive/synthetic, logic being instead discursive/analytic, while for Peirce, the entire domain of necessary reasoning, comprising mathematics and deductive logic, is diagrammatic, i.e. constructive in the Kantian sense. This shift was stimulated, as Peirce himself acknowledged, by the doctrines contained in Friedrich Albert Lange's Logische Studien (1877). The present paper reconstructs Peirce's reading of Lange's book, and illustrates (...) what, according to Peirce, was right and what was problematic in Lange's account of reasoning. It further seeks to explain how Peirce's theory of deductive reasoning was a combination of Kant's philosophy of mathematics and Lange's philosophy of logic. (shrink)

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. (shrink)

Charles Sanders Peirce: Logic Charles Sanders Peirce was an accomplished scientist, philosopher, and mathematician, who considered himself primarily a logician. His contributions to the development of modern logic at the turn of the 20th century were colossal, original and influential. Formal, or deductive, logic was just one of the branches in which he exercized … Continue reading Peirce’s Logic →.

We examine Charles S. Peirce's mature views on the logic of science, especially as contained in his later and still mostly unpublished writings. We focus on two main issues. The first concerns Peirce's late conception of retroduction. Peirce conceived inquiry as performed in three stages, which correspond to three classes of inferences: abduction or retroduction, deduction, and induction. The question of the logical form of retroduction, of its logical justification, and of its methodology stands out as the three major threads (...) in his later writings. The other issue concerns the second stage of scientific inquiry, deduction. According to Peirce's later formulation, deduction is divided not only into two kinds but also into two sub-stages: logical analysis and mathematical reasoning, where the latter is either corollarial or theorematic. Save for the inductive stage, which we do not address here, these points cover the essentials of Peirce's latest thinking on the l.. (shrink)

_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. (shrink)

The adoption and reporting of CSR policies have important ethical and managerial implications that need scrutiny. This study answers the call of CSR scholars for further studies in controversial sectors by focusing on the voluntary reporting practices of companies that market products or services that generate addiction among consumers. It contributes to the debate on organizational legitimacy and corporate reporting by empirically analyzing whether and how corporations in the tobacco, alcohol and gambling industries disclose their CSR actions and what reactions (...) such disclosures generate in stakeholders. Drawing on legitimacy theory and organizational façades, we apply a consequent mixed-methods design (initiation approach) built on (i) a content analysis of reports prepared by a large set of companies listed on the European, British, US, Canadian, Australian and New Zealand stock exchanges and (ii) an experiment on how different actions taken by the companies (preventive vs. remedial) elicit different perceptions of company hypocrisy and action effectiveness. While previous analyses have focused on “sin” or “harm” industries, this is one of the first to assess how companies account for “addiction”, which is more difficult for them to report and legitimate due to long-term negative consequences. This study contributes to the literature on the instrumental use of CSR reporting by empirically investigating how addiction companies shape their organizational façades and manage organizational legitimacy through disclosure. Moreover, the experimental evidence advances the knowledge of how cognitive mechanisms influence stakeholders in terms of legitimacy assessment and the perceived hypocrisy/effectiveness of CSR disclosure. (shrink)

In the Posterior Analytics Aristotle contrasts demonstrations with syllogisms through signs. In the Prior Analytics he defines a sign as a demonstrative premise. One is thus led to ask: is a sign a demonstration? This book reconstructs the history of the notion of "demonstration through signs" from roughly the third through to the thirteenth century. It examines the work of Aristotle's Greek, Arabic, and Latin commentators, both within and outside the tradition of the Posterior Analytics.

Peirce considered the principal business of logic to be the analysis of reasoning. He argued that the diagrammatic system of Existential Graphs, which he had invented in 1896, carries the logical analysis of reasoning to the furthest point possible. The present paper investigates the analytic virtues of the Alpha part of the system, which corresponds to the sentential calculus. We examine Peirce’s proposal that the relation of illation is the primitive relation of logic and defend the view that this idea (...) constitutes the fundamental motive of philosophy of notation both in algebraic and graphical logic. We explain how in his algebras and graphs Peirce arrived at a unifying notation for logical constants that represent both truth-function and scope. Finally, we show that Shin’s argument for multiple readings of Alpha graphs is circular. (shrink)

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. (shrink)

In his later years, Peirce devoted much energy to the project of a book on logic, whose intended title was “Logic, considered as Semeiotic.” That the science of logic is better considered as semeiotic is indeed one of the most fundamental tenets of Peirce’s mature philosophy of logic. But what is the primary motivation for considering logic as semeiotic and what advantages did Peirce see in doing so? If logic is to be considered as semeiotic, this can only mean that (...) its objects and their functioning are to be described in purely semeiotical terms. But did Peirce succeed in providing such a description? This paper focuses on the semeiotical functioning of the fundamental triad of logic: terms (rhemes), propositions (dici-signs), and arguments; it also discusses the idea of an extension of the science of logic and offers examples of the kind of extension that Peirce had in mind. (shrink)

Facebook, the second largest social network on the Web with around 60 million members, is one of the fastest-growing and best-known sites on the Internet today. With the U.S. now accounting for only about a third of all Facebook users, we are starting to see a gradual shift away from its original demographic of college-age users. Very surprisingly, indeed, in the past months Facebook has been literally invaded by Italians, Which is the reason for this huge success of Facebook? One (...) of the reasons is that clearly young Italians' discontent and frustration with the current political situation and with their political representatives is finding in the Web a channel to let youth voice be heard. Facebook is also a media for channelling Italians' emotions, self representation, and symbolic environment at the same speed of their telefonino : indeed Facebook not only provides multimedia content and a high interactive environment, but it also provides personalised features. In other words, it is my personal content which is available on the web and it make me feel as if I was in the centre of a virtually worldly networked stage. We will argue Facebook is realizing what Guy Debord calls "the invasive forces of the 'spectacle' - "a social relation between people that is mediated by images": Facebook is seen as an alternative tool able to amplify an individual's alienation and narcissism, which, are a consequence of the mercantile form of social organization which has reached its climax in capitalism. Under Marxist theory, Facebook does not appear what Jaron Lanier claims to be collaborative communities. We finally argue that Facebook is not a promising example of a new shift from capitalism to a new form of economy based on openness, peering, sharing and global action -- which they called Wikinomics; but rather new disguised forms of advanced capitalism aimed at eroding space to more challenging modes of Internet collectivism. (shrink)

It is well-known that by 1882, Peirce, influenced by Cayley’s, Clifford’s and Sylvester’s works on algebraic invariants and by the chemical analogy, had already achieved something like a diagrammatic treatment of quantificational logic of relatives. The details of that discovery and its implications to some wider issues in logical theory merit further investigation, however. This paper provides a reconstruction of the genesis of Peirce’s logical graphs from the early 1880s until 1896, covering the period of time during which he already (...) was acquainted with the works of his Johns Hopkins colleagues on the mathematical theory of graphs and was reaching the very first forms of his theory and method of... (shrink)

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. (shrink)

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. (shrink)

In 1898 C. S. Peirce declares that the medieval doctrine of consequences had been the starting point of his logical investigations in the 1860s. This paper shows that Peirce studied the scholastic theory of consequentiae as early as 1866–67, that he adopted the scholastics’ terminology, and that that theory constituted a source of logical doctrine that sustained Peirce for a lifetime of creative and original work.

Journal Name: Semiotica Issue: Ahead of print.

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... (shrink)

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. (shrink)

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.. (shrink)

The problem of the unity of the proposition—what distinguishes a proposition from a mere list of constituents, so that the former is able to say something while the latter is not?—is as old as philosophy. It is evoked at the end of Plato’s Sophist, where the Stranger affirms that when one makes a statement “he does not merely give names, but he reaches a conclusion by combining verbs with nouns” ; and it is discussed by Aristotle in De Interpretatione, where (...) it is said that since “falsity and truth have to do with combination and separation”, then “the first single statementmaking sentence is the affirmation, next is the negation” ; but “every statement-making.. (shrink)

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. (shrink)

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. (shrink)

In the earliest phase of his logical investigations, Peirce adopts Mill's doctrine of real Kinds as discussed in the System of Logic and adapts it to the logical conceptions he was then developing. In Peirce's definition of natural class, a crucial role is played by the notion of information: a natural class is a class of which some non-analytical proposition is true. In Peirce's hands, Mill's distinction between connotative and non-connotative terms becomes a distinction between symbolic and informative and pseudo-symbolic (...) and non-informative forms of representation. A symbol is for Peirce a representation which has information. Just as for Mill all names of Kind connote their being such, so for Peirce all symbols profess to correspond to a natural class. (shrink)

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. (shrink)

According to an established reconstruction,1 Augustine of Hippo in the fourth century CE was the first to perform a complete fusion between the theory of signs and the theory of language. Before Augustine, these were considered separate fields of investigation. Aristotle had presented his theory of language in the De Interpretatione, in which the “things in the voice” are said to be “symbols” of the “affections of the soul”, and his theory of inference from signs in the Analytics, where a (...) σημεῖον is a species of enthymeme reconstructible in either of the three syllogistic figures. Similarly, in their theory of language the Stoics... (shrink)

The “sign of consequence” is a notation for propositional logic that Peirce invented in 1886 and used at least until 1894. It substituted the “copula of inclusion” which he had been using since 1870.

The “sign of consequence” is a notation for propositional logic that Peirce invented in 1886 and used at least until 1894. It substituted the “copula of inclusion” which he had been using since 1870.

Journal Name: Semiotica - Journal of the International Association for Semiotic Studies / Revue de l'Association Internationale de Sémiotique Volume: 2013 Issue: 195 Pages: 331-355.

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... (shrink)