- Diagrams, Diagrammatic Reasoning, History of Logic, Charles S. Peirce, Abduction, Philosophy of Logic, and 18 morePhilosophy of Science, History of Science, Philosophy of Technology, Philosophy Of Mathematics, Philosophy of Mind, Philosophy of Cognitive Science, Cognitive Science, Science and Technology Studies, Diagrammatic Logic, History and Philosophy of Logic, History of Analytic Philosophy, Logic, Philosophy Of Language, Philosophical Logic, Game Theory, Logical Constants, Peircean Semiotics, and H.P. Griceedit
- This is not an official website and may not be used for any bibliometric or review purposes. Research Topics: History... moreThis is not an official website and may not be used for any bibliometric or review purposes. Research Topics: History and Philosophy of Science; Logic, Language, Cognition, and Computation; Foundations of Scientific Reasoning; Generative AI in Higher Education. Director of the Peirce Research Centre; Research Director of large international research projects (DiaMind: Diagrammatic Mind - Cognitive Aspects of Iconicity; Abduction in the Age of Uncertainty), funded by the Academy of Finland, Estonian Research Council, and others.edit
In the common use of logic diagrams, the positive term is conveniently located inside the circle while its negative counterpart is left outside. This practice, already found in Euler's original scheme, leads to trouble when one... more
In the common use of logic diagrams, the positive term is conveniently located inside the circle while its negative counterpart is left outside. This practice, already found in Euler's original scheme, leads to trouble when one wishes to express the non-existence of the outer region or to tackle logic problems involving negative terms. In this chapter, we discuss various techniques introduced by Euler's followers to overcome this difficulty: some logicians modified the data of the problem at hand, others amended the diagrams, and another group changed the mode of representation. We also consider how modern diagrammatic systems represent negation.
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This chapter canvasses some of the most pertinent notions that Peirce allied to his conception of abduction: divination, trustworthiness, hope, investigand, economy, uberty, seduction, instinct, insight, and imagination. While such... more
This chapter canvasses some of the most pertinent notions that Peirce allied to his conception of abduction: divination, trustworthiness, hope, investigand, economy, uberty, seduction, instinct, insight, and imagination. While such notions may suggest Peirce sliding into psychologism about logic, Peirce's own texts show that we can give these concepts perfectly non-psychological, natural, and scientific glosses-namely those that integrate their logical, linguistic, cognitive, and semiotic meanings. Thus attempts to characterize abduction as the "heuristics" of the operation of one's psychology or cognitive architecture would leave the issue of the full nature and reach of abduction wanting.
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Peirce's novel, post-1903 interrogative construal of abductive logic is studied in terms of a dynamic approach. The information flow in abduction is interpreted by a dynamic mechanism over ranges. An abductive logic is proposed... more
Peirce's novel, post-1903 interrogative construal of abductive logic is studied in terms of a dynamic approach. The information flow in abduction is interpreted by a dynamic mechanism over ranges. An abductive logic is proposed that analyzes conjecture-making in scientific discovery. It explains how the updates on models representing the inquirers' information proceed when they are faced with new surprising facts. The formal semantics for this logic is given by neighborhood models. We apply our abductive logic to an analysis of some examples of scientific discovery. We thank the two anonymous reviewers of this journal for the abductive feedback that has contributed so much to the improvement of the present paper. We also thank the audience of the 15th Congress of Logic, Methodology and Philosophy of Science held in Helsinki, August 2015, in which a part of the present paper was presented in a special symposium on Pragmati(ci)st Philosophy of Science: Old and New organized by Chiara Ambrosio. * This work is supported by China National Fund of Humanities and Social Sciences (grant no. 14ZDB016).
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In Peirce studies and beyond, such as in the fields of the philosophy of logic and mathematics, mathematical practice and their histories, there have been two dominant ideas in the mainstream and recent research on diagrammatic... more
In Peirce studies and beyond, such as in the fields of the philosophy of logic and
mathematics, mathematical practice and their histories, there have been two dominant
ideas in the mainstream and recent research on diagrammatic reasoning and
representation. The first is that diagrams, especially logical diagrams, are visual in
senses in which symbolic notations are not. The second idea is that logical diagrams are
iconic in senses in which symbolic notations are not. In this paper we submit both of
these claims under critical scrutiny. We use Peirce‘s system of Existential Graphs,
which is the mainstay of diagrammatic reasoning in both its historical and systematical
senses, as the testing ground. We show that neither of these claims is well founded.
mathematics, mathematical practice and their histories, there have been two dominant
ideas in the mainstream and recent research on diagrammatic reasoning and
representation. The first is that diagrams, especially logical diagrams, are visual in
senses in which symbolic notations are not. The second idea is that logical diagrams are
iconic in senses in which symbolic notations are not. In this paper we submit both of
these claims under critical scrutiny. We use Peirce‘s system of Existential Graphs,
which is the mainstay of diagrammatic reasoning in both its historical and systematical
senses, as the testing ground. We show that neither of these claims is well founded.
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Assertive graphs (AGs) modify Peirce's Alpha part of Existential Graphs (EGs). They are used to reason about assertions without a need to resort to any ad hoc sign of assertion. The present paper presents an extension of... more
Assertive graphs (AGs) modify Peirce's Alpha part of Existential Graphs (EGs). They are used to reason about assertions without a need to resort to any ad hoc sign of assertion. The present paper presents an extension of propositional AGs to the Beta case by introducing two kinds of non-interdefinable lines. The absence of polarities in the theory of AGs necessitates Beta-AGs that resort to such two lines: standard lines that mean the presence of a certain method of asserting, and barbed lines that mean the presence of a general method of asserting. New rules of transformations for Beta-AGs are presented by which it is shown how to derive the theorems of quantificational intuitionistic logic. Generally, Beta-AGs offer a new non-classical system of quantification http://www.collegepublications.co.uk/downloads/ifcolog00044.pdf
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Research Interests: Cognitive Psychology, Cognitive Science, Applied Mathematics, Cognition, Deductive reasoning, and 15 moreArgumentation, Critical Discourse Analysis, Cognitive Linguistics, Cognitive Neuroscience, Argumentation Theory, Computational Mathematics, Argumentation Theory and Critical Thinking, Charles Sanders Peirce, Charles S Peirce, Argument Structure, Argumentation et analyse du discours, Argumentação Jurídica, Construction Logistics, Argumentação, and Argumentación
Residuation has become an important concept in the study of algebraic structures and algebraic logic. Relation algebras, for example, are residuated Boolean algebras and residuation is now recognized as a key feature of substructural... more
Residuation has become an important concept in the study of algebraic structures and algebraic logic. Relation algebras, for example, are residuated Boolean algebras and residuation is now recognized as a key feature of substructural logics. Early work on residuation can be traced back to studies in the logic of relations by De Morgan, Peirce and Schr¨oder. We know now that Peirce studied residuation enough to have listed equivalent forms that residuals may take and to have given a method for arriving at the different permutations. Here, we present for the first time a graphical treatment of residuation in Peirce’s Beta part of Existential Graphs (EGs). Residuation is captured by pairing the ordinary transformations of rules of EGs—in particular those concerning the cuts—with simple topological deformations of lines of identity. We demonstrate the effectiveness and elegance of the graphical presentation with several examples. While there might have been speculation as to whether Peirce recognized the importance of residuation in his later work, or whether residuation in fact appears in his work on EGs, we can now put the matter to rest. We cite passages where Peirce emphasizes the importance of residuation and give examples of graphs Peirce drew of residuals. We conclude that EGs are an effective means of enlightening this concept.
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Under its most fair-spoken interpretation, a form of knowledge that is known as de re knowledge means that an individual is picked in epistemic alternatives so that the identity of alternatives is not known to one who is making these... more
Under its most fair-spoken interpretation, a form of knowledge that is known as de re knowledge means that an individual is picked in epistemic alternatives so that the identity of alternatives is not known to one who is making these choices. However, if individuals can be chosen outright, so that a sentence including some propositional attitudes such as knowledge or belief becomes true, these individuals have to be taken as being the same across the alternatives, experiencing only their local manifestations or aspects in some particular alternatives. It is this interpretation that amounts to de re or specific reading of knowledge, and its logic can be implemented in game-theoretic semantics, where the relevant games are of imperfect information, and the syntax is an intensionalised version of Hintikka-Sandu independence-friendly (IF) first-order logic. The interpretation cannot operate independently of the issues concerning the identification of objects in a semantic theory. The identification semantics is here taken to include a number of cognitively meaningful modes, with repercussions to so-called puzzles of beliefs.
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The emergence of the Semantic Web suggests new perspectives to knowledge acquisition and representation, increasing the usefulness of possible-worlds semantics of epistemic logic (knowledge, belief and information). In this poster, it is... more
The emergence of the Semantic Web suggests new perspectives to knowledge acquisition and representation, increasing the usefulness of possible-worlds semantics of epistemic logic (knowledge, belief and information). In this poster, it is argued that possible worlds are a foundation of the Semantic Web, because one can (i) address the problem of the property of omniscience in logical approaches to knowledge, (ii) develop question-answering systems, interrogation and the semantics of questions, and (iii) see what the role model theory plays is in the Semantic Web research.
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Logiikassa on tavanomaista rakentaa lauseita, esittää väitteitä ja suorittaa muodollista päättelyä symbolisia merkkijärjestelmiä käyttäen. Valtaosa nykyaikaisen logiikan historiasta on ollut näiden symbolisten merkkijärjestelmien... more
Logiikassa on tavanomaista rakentaa lauseita, esittää väitteitä ja suorittaa muodollista päättelyä symbolisia merkkijärjestelmiä käyttäen. Valtaosa nykyaikaisen logiikan historiasta on ollut näiden symbolisten merkkijärjestelmien tutkimusta ja niiden sovelluksia. Symboliselle logiikalle vaihtoehdon tarjoavat ns. diagrammilogiikat. Niissä keskeistä on kuvallisuus (ikonisuus), merkkijärjestelmän ilmausten tietty rakenteellinen yhteys ilmausten edustamiin asioihin.
matisismiin liittyvää aineistoa hän tuotti 1890-luvulta alkaen. 2 (Apel 1995; Pietarinen & Snellman 2006). Yleisen tulkinnan ja merkityksen teorian, pragmatisismin, muotoilu fi losofi sta, loogista ja merkkiteoreettista käsitevälineistöä... more
matisismiin liittyvää aineistoa hän tuotti 1890-luvulta alkaen. 2 (Apel 1995; Pietarinen & Snellman 2006). Yleisen tulkinnan ja merkityksen teorian, pragmatisismin, muotoilu fi losofi sta, loogista ja merkkiteoreettista käsitevälineistöä käyttäen oli hänen merkit-tävin saavutuksensa. Pragmatismilla ja pragmatisismilla tarkoitetaan molemmilla kantaa, jonka mukaan kielen ulkoiseen maailmaan liittyvät käytännöt vaikuttavat ilmauksen merkitykseen. Peirce oli erittäin systemaattinen ajattelija ja pyrki luomaan arkkitehtonisen fi losofi an, joka on osa tieteitten kokonaisjärjestelmää, mutta hän ei koskaan luonut yleisesitystä pragmatisismista ja sen erityispiirteistä. Tutkijat ovat pyrkineet rakentamaan kuvaa tästä myöhemmän kauden ajat-telusta Peircen jälkeensä jättämien käsikirjoitusten perusteella. 3 Peirce on kuvannut oman fi losofi sen menetelmänsä vastaavan laboratoriotutkijan menetelmiä. Sen mukaan ilmausten ja merk-kien merkitys perustuu niiden tuottamiin koetuloksiin, jos vain se...
Ajatus tieteestä ja tieteellisestä tutkimuksesta ihmiskunnan hyvinvoinnin ja teknologian takeena ei ole kovin iäkäs, eikä se myöskään ole universaali. Länsimaisen elämänpiirin ulkopuolella teknologiset innovaatiot eivät pitkään nojanneet... more
Ajatus tieteestä ja tieteellisestä tutkimuksesta ihmiskunnan hyvinvoinnin ja teknologian takeena ei ole kovin iäkäs, eikä se myöskään ole universaali. Länsimaisen elämänpiirin ulkopuolella teknologiset innovaatiot eivät pitkään nojanneet tieteellisiin toiminta-ja ajatustapoihin, eivätkä ne sitä aina ole tehneet länsimaissakaan. Vielä tuoreempi on käsityksemme tieteen metodologiasta ja tieteellisen tutkimuksen perusluonteesta, tuskin paljoa yli satavuotias. Kuinka tieteelliset käsitykset viime kädessä muotoutuvat? Miten tieteellinen keksiminen ja innovointi on mahdollista? Tiede perustuu arvauksille. Tämä on perustavaa laatua oleva tosiseikka, joka herättää myös paljon kysymyksiä. Arvausten luonne ymmärretään helposti väärin. Tieteellinen arvaaminen ei tee tieteenteosta satunnaista spekulaatiota. Arvaaminen ei ole epärationaalista, impulsiivista tai tee tieteen tarkoituksesta samaa kuin kirjallisuus fiktiosta. Siitä ei seuraa skeptisismiä, ajatusta, että tiedolla tulee olla absoluutt...
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DESCRIPTION Working Paper, Diagrammatic Mind Research Group
We show that Neil Tennant's critical study of Jaakko Hintikka's book The Principles of Mathematics Revisited is based on systematic misunderstandings and misrepresentations of the content of the book.
Participants of the workshop. Contributors. Preface. Introduction: Reference and the Semantics of Anaphora K. von Heusinger, U. Egli. Historical Aspects of Anaphoric Relations. Anaphora from Athens to Amsterdam U. Egli. Understanding the... more
Participants of the workshop. Contributors. Preface. Introduction: Reference and the Semantics of Anaphora K. von Heusinger, U. Egli. Historical Aspects of Anaphoric Relations. Anaphora from Athens to Amsterdam U. Egli. Understanding the Semantics of 'relativa grammaticalia': Some Medieval Logicians on Anaphoric Pronouns R. Hulsen. Meaning in Motion J. Groenendijk, M. Stokhof. Quantification and Scope. Scope Matters D. Farkas. Scope Ambiguities with Negative Quantifiers H. de Swart. Definiteness Effect: The Case of Russian E. Paducheva. Persistence, Polarity, and Plurality S. Neale. Anaphoric Reference. Anaphoric Relations Across Attitude Contexts R. van Rooy. The Grammar of the Attitudes H. Slater. Choice Functions and the Semantics of Indefinites. Some Remarks on Choice Functions and LF-Movement A. von Stechow. What Makes Choice Natural? Y. Winter. The Reference of Indefinites K. von Heusinger. Representation and Interpretation. Reference and Inference: The Case of Anaphora J. Peregrin. Coreference and Representationalism P. Dekker. Underspecified Semantics R. Muskens. Index of Subjects. Index of Names.
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Extensive games of imperfect information, together with the associated semantic machinery, can be brought to bear on logical aspects of quantum-theoretic phenomena. Among other things, this kinship implies that propositional logic of... more
Extensive games of imperfect information, together with the associated semantic machinery, can be brought to bear on logical aspects of quantum-theoretic phenomena. Among other things, this kinship implies that propositional logic of informational independence is useful in understanding such quantum theoretic issues as non-locality and EPR-type paradoxes, and that quantum logic exhibits the overall game-theoretical notion of uncertainty.
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Oratio Obliqua, Oratio Recta: An Essay on Metarepresentation. Francois Recanati. Cambridge, MA: MIT Press, 2000.360 pp.
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Visual and other non-symbolic representational forms and reasoning about them are increasingly visible in the intersections of logic, computer science and linguistics. Peirce's system of existential graphs, putting forth... more
Visual and other non-symbolic representational forms and reasoning about them are increasingly visible in the intersections of logic, computer science and linguistics. Peirce's system of existential graphs, putting forth "actions of the mind in thought" by "moving pictures of ...
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I examine the conceptual interplay between semantic and pragmatic aspects of linguistic meaning from the game-theoretic standpoint, and find a negative result: that which is semantic and that which is pragmatic in language cannot be... more
I examine the conceptual interplay between semantic and pragmatic aspects of linguistic meaning from the game-theoretic standpoint, and find a negative result: that which is semantic and that which is pragmatic in language cannot be distinguished by rule-governed and structural features of game theory. The difference is whether players entertain epistemic relationships with respect to the solution concepts and strategy profiles in the game-theoretic analysis of linguistic meaning.
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ABSTRACT This paper argues that despite some surface similarities, pragmaticism as a philosophy of mathematics proposed by Charles Peirce is incompatible with mathematical structuralism and fictionalism. Pragmaticism has to do with... more
ABSTRACT This paper argues that despite some surface similarities, pragmaticism as a philosophy of mathematics proposed by Charles Peirce is incompatible with mathematical structuralism and fictionalism. Pragmaticism has to do with experimentation and observation concerning the forms of relations in diagrammatic and iconic representations of mathematical entities. It does not presuppose mathematical foundations although it has these representations as its objects of study. But these objects do have a reality which structuralism and fictionalism deny.
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. Three aspects of structural information in extensive form of games are discussed. First, the way strategies are dened in extensive games, as coding the appropriate amount of information about histories, leaves the possibility of... more
. Three aspects of structural information in extensive form of games are discussed. First, the way strategies are dened in extensive games, as coding the appropriate amount of information about histories, leaves the possibility of performing a transformation of imperfect information games into perfect information ones. Such a transformation is described here, and it is shown that subgame perfect equilibrium can be preserved. Second, the structure of extensive games with simultaneous moves is discussed, and it is argued that this class of games can be seen both as imperfect and perfect information games. A need for additional information partition is pointed out for these games, to capture the notion of imperfect recall. Third, it is suggested that extensive games in general benet from a wider and more dynamic concept of information set, generalising away from the requirement of players making decisions at the sets. In some cases, these dynamic sets are argued to be indisp...
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Peirce's later writings centre on his mature philosophy of pragmaticism, which he set out developing around the mid-1890s. My purpose is to argue for three interrelated theses: (i) that Peirce believed his pragmaticism to incorporate... more
Peirce's later writings centre on his mature philosophy of pragmaticism, which he set out developing around the mid-1890s. My purpose is to argue for three interrelated theses: (i) that Peirce believed his pragmaticism to incorporate the notion of abduction, (ii) that pragmaticism is a consequence of several fundamental assumptions that he believed can be shown to build a logically sound argument for its correctness, and (iii) that abduction features in pragmaticism in contributing to the argument in terms of two fundamental steps towards its conclusion.
According to the orthodox view of pragmatics, the esteemed notion of the common ground was introduced into the modern theory in the wake of the speech-act theories by David Lewis (1969), Stephen Schiffer (1972), and Robert Stalnaker... more
According to the orthodox view of pragmatics, the esteemed notion of the common ground was introduced into the modern theory in the wake of the speech-act theories by David Lewis (1969), Stephen Schiffer (1972), and Robert Stalnaker (1974), who applied the concept of mutual or common knowledge and belief. ½ I will challenge this view. While these writers acknowledged that H. Paul Grice foresaw the central role of the common ground (his preferred terms was the " common-ground status " of discourse particles and assertions), it has not been noted that he was influenced by Peirce's pragmatic philoso-phy and his many writings on topics closely related to speech acts, assertions, conventional utterances, interpretants as implicatures, rationality, cooperation, dialogue strategies, and several other key pragmatic factors in communication. Peirce also acknowledged the importance of common knowledge in the very existence of the common ground. In this chapter I will trace the d...
Arvoisat kuulijat, tarkoitukseni tässä on perustella (eli ei siis mitenkään varsinaisesti todistaa, sillä sellainen tehtävä ei liene vapaan tahdon ongelman ollessa kyseessä ensinkään mahdollinen), että suuresta houkutuksestaan huolimatta... more
Arvoisat kuulijat, tarkoitukseni tässä on perustella (eli ei siis mitenkään varsinaisesti todistaa, sillä sellainen tehtävä ei liene vapaan tahdon ongelman ollessa kyseessä ensinkään mahdollinen), että suuresta houkutuksestaan huolimatta sellaista suurta ja yleistä kysymystä kuin " Onko vapaata tahtoa olemassa vai ei " ei voi tehdä mielekkääksi. Emme voi kysyä, haluan siis esittää, onko meillä tahdon vapautta vai ei, ajautumatta syvälliseen paradoksiin. Sen sijaan voimme pyrkiä löytämään tapoja muotoilla vapaan tahdon luonnetta koskevia eräänlaisia 'pieniä' kysymyksiä, joilla itse asiassa voi olla joitakin niin sanottuun 'jokapäiväiseen elämään' liittyviä ja tällaista 'puhdasta olemassaoloa' jotenkin kouriintuntuvampi merkitys. Voihan nimittäin olla esimerkiksi niin, että 'pienistä' kysymyksistä tuleekin suuria. Ja vaikka niihinkään ei välttämättä saada sellaisia vastauksia, joissa voisimme lopullisesti levätä, on jo mielekkäiden kysymysten ...
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"[...] a "must-have" for both the Peircean scholar and any other philosopher who wishes to relate Peirce's thinking on language and logic to other major thinkers and logical themes of the twentieth century (and beyond)." Robert W. Burch,... more
"[...] a "must-have" for both the Peircean scholar and any other philosopher who wishes to relate Peirce's thinking on language and logic to other major thinkers and logical themes of the twentieth century (and beyond)."
Robert W. Burch, Texas A&M University, USA, in 'Project Muse - Scholarly Journals Online'
"Ahti-Veikko Pietarinen’s Signs of Logic is a ground-breaking contribution to Peircean semiotics, impressive in its scope and depth. It is the first book where Peirce’s pragmatic theory of meaning, logic of existential graphs, and theory of communication are presented in a unified game-theoretical framework. This work is indispensable to all serious students of Peirce’s philosophy of logic, language, and communication."
Risto Hilpinen, Professor of Philosophy, University of Miami, Coral Gables, USA
"Charles Peirce, America’s great scientific philosopher, was convinced that his late logic could contribute significantly to ‘man’s future intellectual development’, but he never got the chance to make his case. Now, a century later, Pietarinen shows that Peirce was right and that Peirce’s semiotic and logic can inform the theory of games and strategy and contribute to a general theory of intelligent agency. This is cutting edge philosophy and it is much to Pietarinen’s credit that he has been able to find such up-to-date relevance and significance in Peirce’s century old writings."
Nathan Houser, Professor of Philosophy, Director of the Institute for American Thought, Director and General Editor of the Peirce Edition Project
"In this magisterial work Ahti-Veikko Pietarinen has performed the valuable service of demonstrating the extent that Peirce’s logic admits of systematic expression, notwithstanding the scatter and fragmentariness of his writings. Even more impressive is the success of Signs of Logic in establishing Peirce’s remarkable prescience as anticipator of developments ranging from game-theoretic logic to dialogue logic, from Gricean pragmatics to the economics of cognitive practice, and so on. Signs of Logic is essential reading for the Peirce scholar and for any one interested in the development of logic in the century just past and beyond."
John Woods, Professor, FRSC, Dept. of Philosophy, University of British Columbia, Canada, and Charles S. Peirce Professor of Logic, Dept. of Computer Science, King’s College London, UK
"Pietarinen’s book fills an important void in the contemporary understanding of Peirce’s logical heritage. Its thorough intertwining of Peirce’s game-theoretic ideas and Peirce’s existential graphs opens up an immense panorama. Combining precision and perspective, mathematical detail and philosophical architectonics, the work presents one of the best available accounts of Peirce’s kinetic thought."
Fernando Zalamea, Profesor Asociado, Departamento de Matemáticas, Universidad Nacional de Colombia
Robert W. Burch, Texas A&M University, USA, in 'Project Muse - Scholarly Journals Online'
"Ahti-Veikko Pietarinen’s Signs of Logic is a ground-breaking contribution to Peircean semiotics, impressive in its scope and depth. It is the first book where Peirce’s pragmatic theory of meaning, logic of existential graphs, and theory of communication are presented in a unified game-theoretical framework. This work is indispensable to all serious students of Peirce’s philosophy of logic, language, and communication."
Risto Hilpinen, Professor of Philosophy, University of Miami, Coral Gables, USA
"Charles Peirce, America’s great scientific philosopher, was convinced that his late logic could contribute significantly to ‘man’s future intellectual development’, but he never got the chance to make his case. Now, a century later, Pietarinen shows that Peirce was right and that Peirce’s semiotic and logic can inform the theory of games and strategy and contribute to a general theory of intelligent agency. This is cutting edge philosophy and it is much to Pietarinen’s credit that he has been able to find such up-to-date relevance and significance in Peirce’s century old writings."
Nathan Houser, Professor of Philosophy, Director of the Institute for American Thought, Director and General Editor of the Peirce Edition Project
"In this magisterial work Ahti-Veikko Pietarinen has performed the valuable service of demonstrating the extent that Peirce’s logic admits of systematic expression, notwithstanding the scatter and fragmentariness of his writings. Even more impressive is the success of Signs of Logic in establishing Peirce’s remarkable prescience as anticipator of developments ranging from game-theoretic logic to dialogue logic, from Gricean pragmatics to the economics of cognitive practice, and so on. Signs of Logic is essential reading for the Peirce scholar and for any one interested in the development of logic in the century just past and beyond."
John Woods, Professor, FRSC, Dept. of Philosophy, University of British Columbia, Canada, and Charles S. Peirce Professor of Logic, Dept. of Computer Science, King’s College London, UK
"Pietarinen’s book fills an important void in the contemporary understanding of Peirce’s logical heritage. Its thorough intertwining of Peirce’s game-theoretic ideas and Peirce’s existential graphs opens up an immense panorama. Combining precision and perspective, mathematical detail and philosophical architectonics, the work presents one of the best available accounts of Peirce’s kinetic thought."
Fernando Zalamea, Profesor Asociado, Departamento de Matemáticas, Universidad Nacional de Colombia
Peirce's manuscript MS 479 (1903) on Euler diagrams was partially printed in the Collected Papers in 1933 (CP 4.347-4.371). That transcription omitted some paragraphs, figures and important variants of the main text. Some diagrams were... more
Peirce's manuscript MS 479 (1903) on Euler diagrams was partially printed in the Collected Papers in 1933 (CP 4.347-4.371). That transcription omitted some paragraphs, figures and important variants of the main text. Some diagrams were reproduced misleadingly or imprecisely. Another important and unpublished paper (MS 481, 1896) presents a novel extension of Euler's diagrams. Among the discarded pages of a published article MS 1147 (1901) there is a variant on logical graphs with examples of novel extensions of Euler diagrams. MS 855 (1911) contains a draft with existentials and shading. We restore Peirce's original drawings from these four manuscripts and explain their main innovations. Euler diagrams were not designed to reason about relative terms, and Peirce's interest in them was not mathematical application or problem solving but showing the basic elements of syllogistic reasoning.