•  177
    The Sign of Consequence
    The Digital Encyclopedia of Peirce Studies 1 1-5. 2016.
    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.
  •  70
    New Light on Peirce's Conceptions of Retroduction, Deduction, and Scientific Reasoning
    with Ahti-Veikko Pietarinen
    International Studies in the Philosophy of Science 28 (4): 353-373. 2014.
    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examine Charles S. Peirce's mature views on the logic of science, especially as contained in his later and still mostly unpublished writings.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 stand…Read more
  •  62
    Peirce's Continuous Predicates
    Transactions of the Charles S. Peirce Society 49 (2): 178. 2013.
    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 alwa…Read more
  •  53
    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, …Read more
  •  53
    “Logic, considered as Semeiotic”: On Peirce's Philosophy of Logic
    Transactions of the Charles S. Peirce Society 50 (4): 523. 2014.
    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 functio…Read more
  •  52
    Peirce and the Unity of the Proposition
    Transactions of the Charles S. Peirce Society 50 (2): 201. 2014.
    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 tr…Read more
  •  47
    Eco and Peirce on Abduction
    European Journal of Pragmatism and American Philosophy 10 (1). 2018.
    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, …Read more
  •  34
    Introduction: History and Philosophy of Logical Notation
    History and Philosophy of Logic 39 (1): 1-2. 2018.
    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, …Read more
  •  33
    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 Lan…Read more
  •  31
    Peirce’s Logic
    with Ahti-Veikko Pietarinen
    Internet Encyclopedia of Philosophy. 2015.
    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 →.
  •  30
    Inferences from Signs: Peirce and the Recovery of the σημεῖον
    Transactions of the Charles S. Peirce Society 52 (2): 259. 2016.
    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 σημεῖο…Read more
  •  30
    From Mitchell to Carus: Fourteen Years of Logical Graphs in the Making
    Transactions of the Charles S. Peirce Society 52 (4): 539. 2016.
    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 t…Read more
  •  29
    Analysis and decomposition in Peirce
    Synthese 198 (1): 687-706. 2018.
    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 determi…Read more
  •  28
    Charles S. Peirce and the Medieval Doctrine of consequentiae
    History and Philosophy of Logic 37 (3): 244-268. 2016.
    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.
  •  27
    Reprint of: Assertion and denial: A contribution from logical notations
    with Ahti-Veikko Pietarinen
    Journal of Applied Logic 25. 2017.
  •  24
    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 …Read more
  •  24
    Peirce on assertion and other speech acts
    Semiotica 2019 (228): 29-54. 2019.
    Journal Name: Semiotica Issue: Ahead of print
  •  23
    Peirce on Symbols
    Archiv für Geschichte der Philosophie 103 (1): 169-188. 2021.
    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.
  •  23
    Signs and demonstration in Aristotle
    British Journal for the History of Philosophy 26 (3): 410-428. 2018.
    ABSTRACTIn this paper, I explore the contrast drawn by Aristotle in two parallel passages of the Posterior Analytics between ‘signs’ and ‘demonstration’. I argue that while at APo. I.6 Aristotle contrasts demonstration proper with a deductively valid sign-syllogism, at APo. II.17 the contrast is rather between a demonstration proper and a deductively invalid sign-syllogism.
  •  20
    Peirce on the justification of abduction
    Studies in History and Philosophy of Science Part A 84 12-19. 2020.
  •  18
    Peirce's Continuous Predicates
    Transactions of the Charles S. Peirce Society 49 (2): 52. 2013.
  •  18
    Neat, Swine, Sheep, and Deer: Mill and Peirce on Natural Kinds
    British Journal for the History of Philosophy 23 (5): 911-932. 2015.
    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 in…Read more
  •  17
    Assertion and denial: A contribution from logical notations
    with Ahti-Veikko Pietarinen
    Journal of Applied Logic 25 1-22. 2017.
  •  16
    Icons, Interrogations, and Graphs: On Peirce's Integrated Notion of Abduction
    Transactions of the Charles S. Peirce Society 56 (1): 43. 2020.
    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 th…Read more
  •  16
    Notational Differences
    Acta Analytica 35 (2): 289-314. 2020.
    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 “mu…Read more
  •  14
    Peirce on Proper Names
    Journal of the History of Philosophy 59 (3): 483-510. 2021.
  •  14
    Peirce, Leibniz, and the threshold of pragmatism
    Semiotica 2013 (195): 331-355. 2013.
    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
  •  14
    Aristotelian Abductions: A Reply to Flórez
    Transactions of the Charles S. Peirce Society 55 (2): 185. 2019.
    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, s…Read more