Francesco Bellucci

Existential graphs as an instrument of logical analysis: Part I. Alpha

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.

New Light on Peirce's Conceptions of Retroduction, Deduction, and Scientific Reasoning

We examine Charles S. Peirces mature views on the logic of science, especially as contained in his later and still mostly unpublished writings (1907–1914). We focus on two main issues. The first concerns Peirces 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 Peirces later formulation, deduction is divided not only into two kinds (corollarial and theorematic) 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 Peirces latest thinking on the logic of science and reasoning.

The Iconic Moment. Towards a Peircean Theory of Diagrammatic Imagination

Einstein famously said, “Imagination is more important than knowledge”. But how to study imagination and how to represent and communicate what the content of imagination may be in the context of scientific discovery? In 1908 Peirce stated that deduction consists of “two sub-stages”, logical analysis and mathematical reasoning. Mathematical reasoning is further divisible into “corollarial and theorematic reasoning”, the latter concerning an invention of a new icon, or “imaginary object diagram”, while the former results from “previous logical analyses and mathematically reasoned conclusions”. The iconic moment is clearly stated here, as well as the imaginative character of theorematic reasoning. But translating propositions into a suitable diagrammatic language is also needed: A diagram is for Peirce “a concrete but possibly changing mental image of such a thing as it represents”. “A model”, he held, “may be employed to aid the imagination; but the essential thing to be performed is the act of imagining” (MS 616, 1906). Peirce had observed that the importance of imagination in scientific investigation is in supplying an inquirer, not with any fiction but, in quite stark contrast to what fiction is, with “an inkling of truth”. Since Peirce’s limit notion of truth precludes gaining any direct insight into the truth, in rational inquiry the question of what the truth may be or what it could be needs to be tackled by imagination. This imaginative faculty is aided by diagrams which are iconic in nature. The inquirers who imagine the truth “dream of explanations and laws”. Imagination becomes a crucial part of the method for attaining truth, that is, of the logic of science and scientific inquiry, so much so that Peirce took it that “next after the passion to learn there is no quality so indispensable to the successful prosecution of science as imagination”. In this paper we investigate aspects of scientific reasoning and discovery that seem irreplaceably dependent on a Peircean understanding of imagination, abductive reasoning and diagrammatic representations.

Exploring Peirce’s speculative grammar: The immediate object of a sign

The paper argues against what I call the “Fregean interpretation” of Peirce’s distinction between the immediate and the dynamic object of a sign, according to which Peirce’s dynamic object is akin to Frege’s Bedeutung , while Peirce’s immediate object is akin to Frege’s Sinn . After having exposed the Fregean interpretation, I briefly reconstruct the genesis of Peirce’s notion of immediate object in his semiotic writings of the years 1904–1909 and defend the view that, according to Peirce, only propositions have immediate objects. Includes: Comment by Helmut Pape (pp. 416–418).

Diagrammatic Reasoning: Some Notes on Charles S. Peirce and Friedrich A. Lange

According to the received view, Charles S. Peirces theory of diagrammatic reasoning is derived from Kants 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 Langes Logische Studien (1877). The present paper reconstructs Peirces reading of Langes book, and illustrates what, according to Peirce, was right and what was problematic in Langes account of reasoning. It further seeks to explain how Peirces theory of deductive reasoning was a combination of Kants philosophy of mathematics and Langes philosophy of logic.

Neat, Swine, Sheep, and Deer: Mill and Peirce on Natural Kinds

In the earliest phase of his logical investigations (1865–1870), Peirce adopts Mills doctrine of real Kinds as discussed in the System of Logic and adapts it to the logical conceptions he was then developing. In Peirces 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 Peirces hands, Mills 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.

H. Paul Grice’s Lecture Notes on Charles S. Peirce’s Theory of Signs

This document provides a transcription of a significant unpublished manuscript by Paul Grice on Charles Peirce’s Theory of Signs, deposited in the H. Paul Grice Papers, BANC MSS 90/135, The Bancroft Library, University of California, Berkeley. Grice’s notes concern the theory of signs, semeiotic, of the American logician, scientist and philosopher Charles Sanders Peirce (1839–1914). The material was probably intended as the text for lectures. The MS consists of 46 non-numbered sheets. The editors have prepared the transcription from a copy of the original manuscript located in the Bancroft Library.

Logic, Psychology, and Apperception: Charles S. Peirce and Johann F. Herbart

Since his first writings, C. S. Peirce defended an unpsychological approach to logic. His authority was J. F. Herbart, who in his Lehrbuch zur Einleitung in die Philosophie had affirmed that “in logic it is necessary to ignore everything that is psychological.” This would become a standard reference for Peirce’s philosophy of logic. Moreover, it was from Herbart’s conception of apperception that Peirce inherited the “synechistic” law of mind first exposed in 1892. This paper explores Peirce’s lifelong “Herbartian” antipsychologism, reviews Herbart’s notion of apperception and indicates its significance for Peirce’s law of mind.

Su Peirce filosofo del linguaggio

The paper argues that if there is a philosophy of language in Peirce, this is to be sought in his conception of speculative grammar. I reconstruct the evolution of Peirce’s speculative grammar in the period 1894-1906 and I show that while in the 1890s speculative grammar is considered as a theory of the proposition, beginning 1903 Peirce conceives it as a general classification of signs, which also includes a pioneeristic speech act theory

Habits of Reasoning: On the Grammar and Critics of Logical Habits

We explain the grammar and the critics of the habits of reasoning, using Peirce’s 1903 Lowell Lectures and the related Syllabus as the key textual source. We establish what Peirce took sound reasoning to be, and derive a major soundness result concerning his logic as semeiotic: an argument is valid if for any object that the premises represent, the conclusion represents it as well, which in semeiotic terms translates to a sign being a valid argument if for any object that the sign represents, the interpretant sign represents it as well. The perfect adherence of the grammar to the critics is evidenced by the un-eliminability of leading principles. Just as a logical leading principle is an un-eliminable element of reasoning, because any attempt to use it as a premise engenders an infinite regress, so a logical representative interpretant is a habit that cannot be rendered a sign. The logical representative interpretant is a principle not itself a premise, a rule not itself subject to rules, a habit not itself a sign.