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)

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)

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)

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)

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)

Abductive conclusions are drawn in a special, co-hortative mood. Abductive conclusions are representative interpretants that represent abduction as a form of reasoning that can convey a general conception of the truth. The truth is not asserted; abduction merely delivers the idea of a matter of course, rendering that idea comparatively simple and natural, hence assuring us of its justified assertibility. Hence abductive reasoning is at home in addressing ‘How Possible’-questions in science. Abductive reasoning concerns the question of how things might, (...) could or would conceivably be such that they can be plausibly asserted. Peirce took all reasoning to be diagrammatic and representable using the graphical method of logic. Yet no examples have previously been found in his large manuscript corpus of what such non-deductive graphs might look like. This paper proposes a new interpretation of a sole exception, a sketch of two graphs from a rejected page from 1903, which might be the only surviving example of Peirce’s abductive graphs. The proposed interpretation takes them to be representative interpretants of this special inverse type of inference. (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.

The background target of the research going into the present article is to forge an intellectual alliance between, on the one hand, active inference and the free-energy principle (FEP), and on the other, Charles S. Peirce’s theory of semiotics and pragmatism. In the present paper, the focus is on the allegiance between the nomenclatures of active and abductive inferences as the proper place to begin reaching at that wider target. The paper outlines the key conceptual elements involved in a naturalistic (...) rendering of Peirce’s late semiotic and logical notion of abductive reasoning. The target is a cognitive-biological model of abduction which preserves the functional integrity of an organism and fulfils the existential imperative for living beings’ evidence of existence. Such a model is an adaptation of Peirce’s late logical schema of abduction proposed in his largely unpublished works during the early 20th century. The proposed model is argued to be a feasible sketch also of recent breakthroughs in computational (sensu Bayesian) cognitive science. (shrink)

In this article I bring to light a group of scientific and philosophical ideas and intellectual currents from the early era of the significs movement, contemporaneous with the origins of early analytic philosophy. Significs was a strong candidate for the science of language, meaning, and communication during the new century. Its heyday coincided with the forums of the Vienna Circle, yet its intellectual and cultural climate persisted until fading in the turmoil of the mid-century's analytic thought.

This paper compares Peirce’s and Hintikka’s logical philosophies and identifies a cross-section of similarities in their thoughts in the areas of action-first epistemology, pragmaticist meaning, philosophy of science, and philosophy of logic and mathematics.

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)

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 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.

This paper compares Peirce’s and Hintikka’s logical philosophies and identifies a cross-section of similarities in their thoughts in the areas of action-first epistemology, pragmaticist meaning, philosophy of science, and philosophy of logic and mathematics.

Peirce aspired for the completeness of his logic cum the theory of signs in his 1903 Lowell Lectures and other late manuscripts. Semeiotic completeness states that everything that is a consequence in logical critic is derivable in speculative grammar. The present paper exposes the reasons why Peirce would fall short of establishing semeiotic completeness and thus why he would not continue seeking a perfect match between the theories of grammar and critic. Some alternative notions are then proposed.

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)

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.

Peirce wrote in late 1901 a text on formal logic using a special Dragon-Head and Dragon-Tail notation in order to express the relation of logical consequence and its properties. These texts have not been referred to in the literature before. We provide a complete reconstruction and transcription of these previously unpublished sets of manuscript sheets and analyse their main content. In the reconstructed text, Peirce is seen to outline both a general theory of deduction and a general theory of consequence (...) relation. The two are the cornerstones of modern logic and have played a crucial role in its development. From the wider perspective, Peirce is led to these theories by three important generalizations: propositions to all signs, truth to scriptibility, and derivation to transformability. We provide an exposition of such proposed semiotic foundation for logical constants and point out a couple of further innovations in this rare text, including the sheet of assertion, correction as a dual of deduction and the nature of conditionals as variably strict conditionals. (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)

This volume aims to provide the elements for a systematic exploration of certain fundamental notions of Peirce and Husserl in respect with foundations of science by means of drawing a parallelism between their works. Tackling a largely understudied comparison between these two contemporary philosophers, the authors highlight the significant similarities in some of their fundamental ideas. This volume consists of eleven chapters under four parts. The first part concerns methodologies and main principles of the two philosophers. An introductory chapter outlines (...) central historical and systematical themes arising out of the recent scholarship on Peirce and Husserl. The second part is on logic, its Chapters dedicated to the topics from Peirce’s Existential Graphs and the philosophy of notation to Husserl’s notions of pure logic and transcendental logic. The third part includes contributions on philosophy of mathematics. Chapters in the final part deal with the theory of cognition, consciousness and intentionality. The closing chapter provides an extended glossary of central terms of Peirce’s theory of phaneroscopy, explaining them from the viewpoint of the theory of cognition. (shrink)

Introduction to the Special Issue in Logica Universalis on Jaakko Hintikka’s Logical Philosophy, with biographical and bibliographical remarks.

This paper proposes to recover the topic of the philosophy of scientific method from its late nineteenth-century roots. The subject matter of scientific method sprouted from key inferential ingredients identified by Charles Peirce. In this paper, the historical path is traversed from the viewpoint of contemporary Cognitive Structural Realism (CSR). Peirce’s semiotic theory of methods and practices of scientific inquiry prefigured CSR’s reliance on embodied informational structures and experimentation upon forms of relations that model generic scientific domains. Three results are (...) shown to follow from this convocation: (i) a naturalization of Peirce’s interconnected abductive, deductive and inductive stages of the logic of science, here characterized de novo in terms of CSR. (ii) a perspective to scientific modeling that incorporates processes of abstraction and generalization as originated from Peirce’s logic of science, and (iii) diagrammatic reasoning as a pivotal method in analyzing scientific reasoning in experimental practices. (shrink)

This is the first book to collect research on game-theoretic tools in the analysis of language with particular reference to semantics and pragmatics. Games are significant, because they pertain equally to pragmatics and semantics of natural language. The book provides an overview of the variety of ways in which game theory is used in the analysis of linguistic meaning and shows how games arise in pragmatic as well as semantic investigations.

Carl Sagan famously lamented how “we live in a society exquisitely dependent on science and technology, in which hardly anyone knows about science and technology. This is a clear prescription for disaster”. One might add that in contemporary societies, people know about the philosophy of science and technology even less.

The paper proposes a way to naturalise Charles S. Peirce’s conception of the scientific method, which he specified in terms of abduction, deduction and induction. The focus is on the central issue of the economy of research in abduction and self-correction by error reduction in induction. We show how Peirce’s logic of science receives support from modern breakthroughs in computational neuroscience, and more specifically from Karl Friston’s statements of active inference and the Free Energy Principle, namely the account of how (...) organisms’ capacity to decrease the discrepancy between the expected value and actual outcomes entails the minimisation of errors in their hypotheses about the world. A scientific account of organisms’ capacity to choose policies and form expectations is aligned with Peirce’s theories of abduction and induction, and especially with the economy of research. The upshot is the recovery of Peirce’s theory of the logic of science in the context of active inquiry. (shrink)

Abstraction and generalization are two processes of reasoning that have a special role in the construction of scientific theories and models. They have been important parts of the scientific method ever since the nineteenth century. A philosophical and historical analysis of scientific practices shows how abstraction and generalization found their way into the theory of the logic of science of the nineteenth-century philosopher Charles S. Peirce. Our case studies include the scientific practices of Francis Galton and John Herschel, who introduced (...) composite photographs and graphical methods, respectively, as technologies of generalization and thereby influenced Peirce’s logic of abstraction. Herschel’s account of generalization is further supported by William Whewell, who was very influential on Peirce. By connecting Herschel’s scientific technology of abstraction to Peirce’s logical technology of abstraction—namely, diagrams—we highlight the role of judgments in scientific observation by hypostatic abstractions. We also relate Herschel’s discovery-driven logic of science and Peirce’s open-ended diagrammatic logic to the use of models in science. Ultimately, Peirce’s theory of abstraction is a case of showing how logic applies to reality. (shrink)

This article presents and defends an integrated view of the placebo effect, termed “affective-meaning-making” model, which draws from theoretical reflection, clinical outcomes, and neurophysiological findings. We consider the theoretical limitations of those proposals associated with the “meaning view” on the placebo effect which leave the general aspects of meaning unspecified, fail to analyze fully the role of emotions and affect, and establish no clear connection between the theoretical, physiological, and psychological aspects of the effect. We point out that a promising (...) way to overcome these limitations is given by grounding the placebo effect on Peirce’s theory of meaning, in which the role of the meaning constitution and change is placed in logical and objective structures. We also show the connection between our theoretical proposal and the appraisal theory and integrate it with emotion regulation. (shrink)

Peirce's misfortunes to get some of his most important works published provide an interesting window into publication and editorial practices that prevailed at the turn of the 20th century in the United States. Also, what Peirce had to face appears not that different from what many have experienced in the world of contemporary academic publishing. Peirce's manuscripts were routinely deemed too technical, lengthy, or of limited interest to the general readership and scholars who were not experts of the area. But (...) who is supposed to be the expert when the matter presented is altogether new? Unscientific attitudes persist in today's publication culture, too, where a would-be academic quickly learns to err on the side... (shrink)

Modern explainable AI methods remain far from providing human-like answers to ‘why’ questions, let alone those that satisfactorily agree with human-level understanding. Instead, the results that such methods provide boil down to sets of causal attributions. Currently, the choice of accepted attributions rests largely, if not solely, on the explainee’s understanding of the quality of explanations. The paper argues that such decisions may be transferred from a human to an XAI agent, provided that its machine-learning algorithms perform genuinely abductive inferences. (...) The paper outlines the key predicament in the current inductive paradigm of ML and the associated XAI techniques, and sketches the desiderata for a truly participatory, second-generation XAI, which is endowed with abduction. (shrink)

The Annual Biosemiotic Achievement Award was established at the annual meeting of the International Society for Biosemiotic Studies (ISBS) in 2014, in conjunction with Springer and _Biosemiotics_. It seeks to recognize papers published in the journal that present novel and potentially important contributions to biosemiotic research, its scientific impact, and its future prospects. Here the winner of the Biosemiotic Achievement Award for 2022 is announced: The award goes to Sigmund Ongstad for his article “Simple Utterances but Complex Understanding? Meta-studying the (...) Fuzzy Mismatch between Animal Semantic Capacities in Varied Contexts”. (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)

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)

This article investigates Charles Peirce’s development of logical calculi for classical propositional logic in 1880–1896. Peirce’s 1880 work on the algebra of logic resulted in a successful calculus for Boolean algebra. This calculus, denoted byPC, is here presented as a sequent calculus and not as a natural deduction system. It is shown that Peirce’s aim was to presentPCas a sequent calculus. The law of distributivity, which Peirce states in 1880, is proved using Peirce’s Rule, which is a residuation, inPC. The (...) transitional systems of the algebra of the copula that Peirce develops since 1880 paved the way to the 1896 graphical system of the alpha graphs. It is shown how the rules of the alpha system reinterpret Boolean algebras, answering Peirce’s statement that logical graphs supply a new system of fundamental assumptions to logical algebra. A proof-theoretic analysis is given for the connection betweenPCand the alpha system. (shrink)

This volume presents mathematical game theory as an interface between logic and philosophy.

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)

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)

This paper presents an enrichment of the Gabbay–Woods schema of Peirce’s 1903 logical form of abduction with illocutionary acts, drawing from logic for pragmatics and its resources to model justified assertions. It analyses the enriched schema and puts it into the perspective of Peirce’s logic and philosophy.

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)