Peirce believed that his pragmaticism can be conclusively proven. Beginning in 1903, he drafted several attempts, ending by 1908 with a semeiotic proof. Around 1905, he exposes the proof using the theory of Existential Graphs . This paper modernizes the semantics Peirce proposed for EGs in terms of game-theoretic semantics . Peirce's 1905 proof is then reconstructed in three parts, by relating pragmaticism to the GTS conception of meaning, showing that Peirce's proof is an argument for a relational structure of (...) the meaning of intellectual signs that our interpretative and strategic practices give rise to, and bringing out the key links between EGs and pragmaticism. (shrink)
This paper examines the contemporary philosophical and cognitive relevance of Charles Peirce's diagrammatic logic of existential graphs (EGs), the ?moving pictures of thought?. The first part brings to the fore some hitherto unknown details about the reception of EGs in the early 1900s that took place amidst the emergence of modern conceptions of symbolic logic. In the second part, philosophical aspects of EGs and their contributions to contemporary logical theory are pointed out, including the relationship between iconic logic and images, (...) the problem of the meaning of logical constants, the cognitive economy of iconic logic, the failure of the Frege?Russell thesis, and the failure of the Language of Thought hypothesis. (shrink)
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examine Charles S. Peirce's mature views on the logic of science, especially as contained in his later and still mostly unpublished writings.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)
Charles S. Peirce’s pragmatist theory of logic teaches us to take the context of utterances as an indispensable logical notion without which there is no meaning. This is not a spat against compositionality per se , since it is possible to posit extra arguments to the meaning function that composes complex meaning. However, that method would be inappropriate for a realistic notion of the meaning of assertions. To accomplish a realistic notion of meaning (as opposed e.g. to algebraic meaning), Sperber (...) and Wilson’s Relevance Theory (RT) may be applied in the spirit of Peirce’s Pragmatic Maxim (PM): the weighing of information depends on (i) the practical consequences of accommodating the chosen piece of information introduced in communication, and (ii) what will ensue in actually using that piece in further cycles of discourse. Peirce’s unpublished papers suggest a relevance-like approach to meaning. Contextual features influenced his logic of Existential Graphs (EG). Arguments are presented pro and con the view in which EGs endorse non-compositionality of meaning. (shrink)
Charles Peirce's theory of proper names is intimately connected to a number of central topics in contemporary philosophy of language and logic. Several papers have appeared in the past in which Peirce's theory of names has been attested to be a precursor of the causal-historical theory of reference.2 The causal-historical theory in turn has customarily been pigeonholed as the 'new' theories of reference that have been emerging since the 1950s (Devitt 1981; Donellan 1966; Kripke 1980; Marcus 1950; Putnam 1973). Among (...) those who have seen Peirce as such a precursor of the new theory of reference are DiLeo (1997), Hilpinen (1995), Maddalena (2006), Pape (1987), and Thibaud (1987). Related recent publications on the .. (shrink)
Are knowledge and belief pivotal in science, as contemporary epistemology and philosophy of science nearly universally take them to be? I defend the view that scientists are not primarily concerned with knowing and that the methods of arriving at scientific hypotheses, models and scenarios do not commit us having stable beliefs about them. Instead, what drives scientific discovery is ignorance that scientists can cleverly exploit. Not an absence or negation of knowledge, ignorance concerns fundamental uncertainty, and is brought out by (...) retroductive inferences, which are roughly characterised as reasoning from effects to causes. I argue that recent discoveries in sciences that coped with under-structured problem spaces testify the prevalence of retroductive logic in scientific discovery and its progress. This puts paid to the need of finding epistemic justification or confirmation to retroductive methodologies. A scientist, never frightened of unknown unknowns, strives to advance the forefront of uncertainty, not that of belief or knowledge. Far from rendering science irrational, I conclude that catering well for the right conditions in which to cultivate ignorance is a key to how fertile retroductive inferences arise. (shrink)
The following two articles comprise two sets of Charles Peirce’s manuscripts, “Recent Developments of Existential Graphs and their Consequences for Logic” (MS 498, MS 499, MS 490 & S-36, 1906) and “Assurance through Reasoning” (MS 669 & MS 670, 1911), written for the National Academy of Sciences meetings in 1906 and 1911. The papers are deposited at Houghton Library, Harvard University. Only some parts of MS 470 have been published before, and in somewhat defective form. Although “Assurance” follows “Recent Developments” (...) chronologically, given the expository style of the former it is recommended to be read before “Recent Developments”. As the title indicates, in the latter Peirce goes on to describe his latest discoveries concerning the method and the logic of existential graphs. The transcription reproduces all significant deletions that appear in the original sheets. Editorial comments and additions are given in brackets. [Alt.:] means the beginning of an alternative sequence. [Del. (shrink)
I argue that many of the pragmatic notions that are commonly attributed to 1-1. P. Grice, or are reported to be inspired by his work on pragmatics, such as assertion, conventional implicature, cooperation, common ground, common knowledge, presuppositions and conversational strategies, have their origins in C. S. Peirce's theory of signs and his pragmatic logic and philosophy. Both Grice and Peirce rooted their theories in normative rationality, anti-psychologism and the relevance of assertions. With respect to the post-Gricean era of pragmatics, (...) theories of relevance may be seen to have been geared, albeit unconsciously, upon Peirce's pragmatic agenda. (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)
This paper explores the intertwining of uncertainty and values. We consider an important but underexplored field of fundamental uncertainty and values in decision-making. Some proposed methodologies to deal with fundamental uncertainty have included potential surprise theory, scenario planning and hypothetical retrospection. We focus on the principle of uncertainty transduction in hypothetical retrospection as an illustrative case of how values interact with fundamental uncertainty. We show that while uncertainty transduction appears intuitive in decision contexts it nevertheless fails in important ranges of (...) strategic game-theoretic cases. The methodological reasons behind the failure are then examined. (shrink)
This paper addresses the theoretical notion of a game as it arisesacross scientific inquiries, exploring its uses as a technical andformal asset in logic and science versus an explanatory mechanism. Whilegames comprise a widely used method in a broad intellectual realm(including, but not limited to, philosophy, logic, mathematics,cognitive science, artificial intelligence, computation, linguistics,physics, economics), each discipline advocates its own methodology and aunified understanding is lacking. In the first part of this paper, anumber of game theories in formal studies are critically (...) surveyed. Inthe second part, the doctrine of games as explanations for logic isassessed, and the relevance of a conceptual analysis of games tocognition discussed. It is suggested that the notion of evolution playsa part in the game-theoretic concept of meaning. (shrink)
A century ago, Charles S. Peirce proposed a logical approach to modalities that came close to possible-worlds semantics. This paper investigates his views on modalities through his diagrammatic logic of Existential Graphs (EGs). The contribution of the gamma part of EGs to the study of modalities is examined. Some ramifications of Peirce’s remarks are presented and placed into a contemporary perspective. An appendix is included that provides a transcription with commentary of Peirce’s unpublished manuscript on modality from 1901.
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 →.
I will show that the semantic structure of a new imperfect-information propositional logic can be described in terms of extensive forms of semantic games. I will discuss some ensuing properties of these games such as imperfect recall, informational consistency, and team playing. Finally, I will suggest a couple of applications that arise in physics, and most notably in quantum theory and quantum logics.
Wittgenstein’s language games can be put into a wider service by virtue of elements they share with some contemporary opinions concerning logic and the semantics of computation. I will give two examples: manifestations of language games and their possible variations in logical studies, and their role in some of the recent developments in computer science. It turns out that the current paradigm of computation that Girard termed Ludics bears a striking resemblance to members of language games. Moreover, the kind of (...) interrelations that are emerging could be scrutinised from the viewpoint of logic that virtually necessitates game-theoretic conceptualisations, demonstrating the fact that the meaning of utterances may, in many situations, be understood as Wittgenstein’s language games of ‘showing or telling what one sees’. This provides motivation for the use of games in relation to logic and formal semantics that some commentators have called for. Many of the ideas can be traced to C.S. Peirce, for whom signs were vehicles of strategic communication. The conclusion about Wittgenstein is that the notions of saying and showing converge in his late philosophy. (shrink)
A century ago, Charles S. Peirce proposed a logical approach to modalities that came close to possible-worlds semantics. This paper investigates his views on modalities through his diagrammatic logic of Existential Graphs. The contribution of the GAMMA part of EGs to the study of modalities is examined. Some ramifications of Peirce's remarks are presented and placed into a contemporary perspective. An appendix is included that provides a transcription with commentary of Peirce's unpublished manuscript on modality from 1901.
Charles Peirce’s alpha system \ is reformulated into a deep inference system where the rules are given in terms of deep graphical structures and each rule has its symmetrical rule in the system. The proof analysis of \ is given in terms of two embedding theorems: the system \ and Brünnler’s deep inference system for classical propositional logic can be embedded into each other; and the system \ and Gentzen sequent calculus \ can be embedded into each other.
The following two review papers have a common origin. Pietarinen’s book Signs of Logic and Stjernfelt’s book Diagrammatology were both published in the same Synthese Library Series being published by Springer. The two books also share the common topic of diagrammatic reasoning in Charles Peirce’s work. Beginning in a conference Applying Peirce held in Helsinki in conjunction with the World Congress of Semiotics in June 2007, two authors have commented upon these books under the headline of Synthese Library Book Session (...) on several occasions, including the Aarhus meeting on Signs and Meaning held in February 2008, the Diagrammatology and Diagram Praxis workshop in Lisboa in March 2009, and the Peirce and Early Analytic Philosophy symposium in Helsinki in June 2009. Therefore, these two review papers form a continuing discussion on the contributions Peirce’s diagrammatic epistemology and logic will have to a broad range of issues at the intersections of philosophy, logic, cognitive sciences and beyond. (shrink)
We describe Peirce’s 1903 system of modal gamma graphs, its transformation rules of inference, and the interpretation of the broken-cut modal operator. We show that Peirce proposed the normality rule in his gamma system. We then show how various normal modal logics arise from Peirce’s assumptions concerning the broken-cut notation. By developing an algebraic semantics we establish the completeness of fifteen modal logics of gamma graphs. We show that, besides logical necessity and possibility, Peirce proposed an epistemic interpretation of the (...) broken-cut modality, and that he was led to analyze constructions of knowledge in the style of epistemic logic. (shrink)
The theory of existential graphs, which Peirce ultimately divided into four quadrants , is a rich method of analysis in the philosophy of logic. Its $$\upbeta $$ β -part boasts a diagrammatic theory of quantification, which by 1902 Peirce had used in the logical analysis of natural-language expressions such as complex donkey-type anaphora, quantificational patterns describing new mathematical concepts, and cognitive information processing. In the $$\upbeta $$ β -quadrant, he came close to inventing independence-friendly logic, the idea of which he (...) found indispensable in fulfilling the tasks –. (shrink)
It is of common use in modern Venn diagrams to mark a compartment with a cross to express its non-emptiness. Modern scholars seem to derive this convention from Charles S. Peirce, with the assumption that it was unknown to John Venn. This paper demonstrates that Venn actually introduced several methods to represent existentials but felt uneasy with them. The resistance to formalize existentials was not limited to diagrammatic systems, as George Boole and his followers also failed to provide a satisfactory (...) symbolic representation for them. This difficulty points out issues that are inherent to the very nature of existentials. This paper assesses the various methods designed for the representation of existential statements with Venn diagrams. First, Venn’s own attempts are discussed and compared with other solutions proposed by his contemporaries and successors, notably Lewis Carroll and Peirce. Since disjunctives hold an important role in an effective representation of existentials, their representation is also discussed. Finally, recent methods for the diagrammatic representation of existing individuals, rather than mere existence, are surveyed. (shrink)
: This paper discusses the American scientist and philosopher Charles S. Peirce's (1839–1914) classification of the sciences from the contemporary perspective of interdisciplinary studies. Three theses are defended: (1) Studies on interdisciplinarity pertain to the intermediate class of Peirce's classification of all science, the sciences of review (retrospective science), ranking below the sciences of discovery (heuretic sciences) and above practical science (the arts). (2) Scientific research methods adopted by interdisciplinary inquiries are cross-categorial. Making them converge to an increasing extent with (...) the sciences of discovery, especially the methodeutic of normative logic, is one of the future challenges for studies on interdisciplinarity. (3) The overall structure of Peirce's classification, were it to be applied in today's situation, would not, in any major respect, be radically different from what it was designed to reflect a hundred years ago, in spite of the virtually exponential creation and production of new domains and the massive increase in investment in research and scientific publication. Accordingly, charges that the sciences of discovery are becoming ever more fragmented are not new. (shrink)
This special issue of Synthese on Peirce’s Logic and Philosophy of Language collects papers by Rocco Gangle & Gianluca Caterina, Chuangshen He, Risto Hilpinen, Matthew Moore, Charles S. Peirce, Ahti-Veikko Pietarinen and Frederik Stjernfelt.Charles Sanders Peirce was a scientist, philosopher, mathematician and semiotician, as well as one of the undisputed giants in the founding of modern logic. He advanced virtually endless areas in exact sciences. He worked throughout his long career as a scientist, logician, philosopher, mathematician, and meaning analyst. As (...) an advocate of developing and applying new methods and theories to improve logical analysis, his innovations included algebraic methods, quantification theory, semantics and pragmatics of communication, ethics and philosophy of notation, as well as comprehensive systems of diagrammatic logics which he termed existential graphs. Peirce held an exceptionally wide conception of logic, conceived as semeiotic, which he to .. (shrink)
How are we to understand the talk about properties of structures the existence of which is conditional upon the assumption of the reality of those structures? Mathematics is not about abstract objects, yet unlike fictionalism, modal-structuralism respects the truth of theorems and proofs. But it is nominalistic with respect to possibilia. The problem is that, for fear of reducing possibilia to actualities, the second-order modal logic that claims to axiomatise modal existence has no real semantics. There is no cross-identification of (...) higher-order mathematical entities and thus we cannot know what those entities are. I suggest that a scholastic notion of realism, interspersed with cross-identification of higher-order entities, can deliver the semantics without collapse. This semantics of modalities is related to Peirce's logic and his pragmaticist philosophy of mathematics. (shrink)
In this commentary, I reply to the fourteen papers published in the Sign Systems Studies special issue on Peirce’s Theory of Signs, with a view on connecting some of their central themes and theses and in putting some of the key points in those papers into a wider perspective of Peirce’s logic and philosophy.
I argue that many of the pragmatic notions that are commonly attributed to H. P. Grice, or are reported to be inspired by his work on pragmatics, such as assertion, conventional implicature, cooperation, common ground, common knowledge, presuppositions and conversational strategies, have their origins in C. S. Peirce's theory of signs and his pragmatic logic and philosophy. Both Grice and Peirce rooted their theories in normative rationality, anti-psychologism and the relevance of assertions. With respect to the post-Gricean era of pragmatics, (...) theories of relevance may be seen to have been geared, albeit unconsciously, upon Peirce's pragmatic agenda. (shrink)
I argue that in aiming to integrate the notions of representation and resemblance in the arts, philosophy of sciences and cognitive sciences one needs to focus on those processes of reasoning and creative inquiry that exploit our faculties of imagination and mental imagery, create novel and useful metaphors based on iconic types of meaning, and may result in discovery through the interactive practices of artists and scientists. To address these matters within the confines of Goodmanian conventionalist and symbolic theories of (...) logic, thought and language is unlikely to deliver these points. A comprehensive philosophy of signs, however, might do the job. (shrink)