Il seguente lavoro si concentra su un confronto tra la filosofia di Peirce e quella di Cassirer, con particolare attenzione alla loro trattazione del problema della semiotica e della sua rilevanza in relazione alla teoria della conoscenza.

This thesis develops and defends a Peircean conception of the task of metaphysics and critically compares it with recent anti-metaphysical forms of pragmatism. Peirce characterises metaphysics in terms of its place within his hierarchical classification of the sciences. According to the classification, metaphysics depends on logic for principles and provides principles to the natural and social sciences. This arrangement of the sciences is defended by appeal to Peirce's account of philosophy as 'cenoscopy'. The dependence of the natural and social sciences (...) on cenoscopy is then argued for on the basis of Peirce's rejection of psychologism and in terms of the necessity of abductive inference. Peirce's position is then compared with recent forms of pragmatism. While it is less naturalistic, Peirce's position is defended on pragmatist grounds. An account of Peirce on truth is then developed. Peirce's account of truth in terms of an ideal limit of inquiry is defended as consistent with recent, more deflationary, approaches. The truth of 'abstract propositions' is a matter of local indefeasibility. These abstract propositions are related to the 'absolute truth', understood as a single non-abstract proposition. The truth of this proposition is then understood in terms of an identity theory. Two conceptions of Peircean metaphysics are presented. Both are 'abductive'. Their task is to explain the possibility of success in inquiry. However, only one proposal accepts the notion of an absolute truth. The 'absolutist' proposal is defended as an interpretation of Peirce and as a contemporary option for pragmatist philosophers. The thesis concludes by comparing recent anti-metaphysical arguments due to Huw Price with the Peircean position. Room for the absolutist proposal is defended by means of an account of recent exchanges between Price and Robert Brandom on dispositional modality. (shrink)

Christopher Hookway has been influential in promoting engagement with pragmatist and naturalist perspectives from classical and contemporary American philosophy. This book reflects on Hookway’s work on the American philosophical tradition and its significance for contemporary discussions of the understanding of mind, meaning, knowledge, and value. -/- Hookway’s original and extensive studies of Charles S. Peirce have made him among the most admired and frequently referenced of Peirce’s interpreters. His work on classical American pragmatism has explored the philosophies of William James, (...) John Dewey, and Josiah Royce, and examined the influence of pragmatist ideas outside of the United States. Additionally, Hookway has participated in a number of celebrated exchanges with some of the most high-profile figures of twentieth- and twenty-first-century philosophy, including Karl-Otto Apel, Philip Pettit, Hilary Putnam, and W.V.O. Quine, through which his treatments of a large range of topics in epistemology and the philosophies of mind and language have been developed and promoted. The chapters in this book—which include contributions from several of Hookway’s former students and colleagues—include studies of Hookway’s engagement with the works of Peirce, James, and Dewey, his contributions to virtue epistemology, and his discussions of hope and pragmatist metaphysics. -/- Pragmatic Reason will be of interest to researchers and advanced students working on American philosophy, the history of analytic philosophy, and epistemology. (shrink)

This essay focuses on Charles S. Peirce’s grammar of representation and its relevance for a logical conception of scientific inquiry. Closely relying on Peirce’s writings, one of his important trichotomies of signs will be discussed in particular: that distinguishing between substitutive signs, or “semes”, informational signs, or “phemes”, and persuasive signs, or “delomes”. According to Peirce, these three categories of signs result from an extension of the traditional division between “terms”, “propositions”, and “arguments” to all signs, understood as the foundational (...) elements with and on which the scientific mind operates. It is shown that such an extended view of logic, conceived as a “semiotic”, or general doctrine of signs, is consistent with Peirce’s metaphysical views on truth and reality. Logic-as-semiotic, and its three corresponding branches of stecheotic, critic, and methodeutic, is thus conceived as a requisite normative trivium for the practice of scientific inquiry, whose purpose is to represent reality truthfully. In the end, we aim to remind that Peirce’s semiotic epistemology must necessarily be contextualized within the frame of his comprehensive philosophy of the scientific “settlement of opinion”. (shrink)

Charles Sanders Peirce is best known as the founder of pragmatism, but the name that he preferred for his overall system of thought was ‘‘synechism’’ because the principle of continuity was its central thesis. He considered time to be the paradigmatic example and often wrote about its various aspects while discussing other topics. This essay draws from many of those widely scattered texts to formulate a distinctively Peircean philosophy of time, incorporating extensive quotations into a comprehensive and coherent synthesis. Time (...) is not an existential subject with past, present, and future as its incompatible predicates, but rather a real law enabling things to possess contrary qualities at its different determinations, and Peirce identifies four classes of such states based on when and how they are realized. Because time is continuous, it is not composed of instants, and even the present is an indefinite lapse during which we are directly aware of constant change. The accomplished past is perpetually growing as the possibilities and conditional necessities of the future are actualized at the present, and the entire universe evolves from being utterly indeterminate toward being absolutely determinate. Nevertheless, time must return into itself even if events are limited to only a portion of it, a paradox that is resolved with the aid of projective geometry. Temporal synechism thus touches on a broad spectrum of philosophical issues including mathematics, phenomenology, logic, and metaphysics. (shrink)

Although Peirce frequently insisted that continuity was a core component of his philosophical thought, his conception of it evolved considerably during his lifetime, culminating in a theory grounded primarily in topical geometry. Two manuscripts, one of which has never before been published, reveal that his formulation of this approach was both earlier and more thorough than most scholars seem to have realized. Combining these and other relevant texts with the better-known passages highlights a key ontological distinction: a collection is bottom-up, (...) such that the parts are real and the whole is an ens rationis, while a continuum is top-down, such that the whole is real and the parts are entia rationis. Accordingly, five properties are jointly necessary and sufficient for Peirce’s topical continuum: rationality, divisibility, homogeneity, contiguity, and inexhaustibility. (shrink)

Two different versions of the ending of the first additament to C. S. Peirce's 1908 article, "A Neglected Argument for the Reality of God," appear in the Collected Papers but were omitted from The Essential Peirce. In one, he linked the hypothesis of God's Reality to his entire theory of logic as semeiotic, claiming that proving the latter would also prove the former. In the other, he offered a final outline of his cosmology, in which the Reality of God as (...) Ens necessarium is indispensable to both the origin and order of our existing universe of Signs. Exploring these passages, as well as the unpublished manuscript drafts of the article, provides important insights into the key concepts of instinct and continuity within Peirce's comprehensive system of thought. (shrink)

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 determined by (...) the senses of its constituent parts, and ‘decomposition’, which is the process of dividing a sentence into a predicate and a subject, and whose purpose is to both to explain how quantified sentences are constructed and to evidence a pattern within a sentence which it shares with other sentences. (shrink)

Os signos e as classes dos signos estão entre os tópicos mais importantes do sistema filosófico de Charles S. Peirce. As 10, 28, e 66 classes de signos são classificações desenvolvidas especialmente a partir de 1903 e representam um grande refinamento da divisão fundamental de signos – ícone, índice, símbolo. Nossa abordagem aqui define uma estratégia de visualização das classificações dos signos, com especial atenção para as 10 e 66 classes de signos. O livro está dividido em duas partes: (i) (...) bases teóricas, (ii) diagramas para as classes de signos. Na Parte I (bases teóricas), são apresentadas introdutoriamente as noções fundamentais das categorias fenomenológicas, classes de signos, as tricotomias e diagramas, assim como implicações gerais de nossa abordagem, metodologia e aplicações. Na Parte II (diagramas para as classes de signos), são apresentados e discutidos os modelos das classes, propostos por Peirce e seus comentadores, incluindo uma introdução detalhadamente documental de nossos modelos, 10cubes e 3N3, diagramas dinâmicos para as classes de signos. (shrink)

The aim of this article is to describe in some detail the actual relationship between Charles S. Peirce and Alfred N. Whitehead, paying particular attention to the Peircean notions of science and metaphysics, with the conviction that this contrast can help to understand better the scope and depth of C. S. Peirce’s thought.

According to Charles S. Peirce and to Mariano Artigas, science is the collective and cooperative activity of all those whose lives are animated by the desire to discover the truth. The particular sciences are branches of a common tree. The unity of science is not achieved by the reduction of the special sciences to more basic ones: the new name for the unity of the sciences is cross-disciplinarity. This is not a union of the sciences themselves, but rather the unity (...) and dialogue of scientists, the real inquirers into the truth. In the light of Peirce’s and Artigas’s teachings, we can see that philosophers are in just the right place to call for this unity of sciences. This call should not be seen as promoting a return to the old scientism, but seeks a deep dialogue between the particular sciences and philosophy in order to deal with the presuppositions of the scientific enterprise. The key to the cross-disciplinarity of knowledge is not revolution, but rather shared efforts in a unique mixture of continuity and fallibilism, of affection and reason, of the attempt to understand others’ disciplines as well as our own. (shrink)

How anything acts depends upon what it is, both as a kind of thing and as a distinct individual of that kind: “agere sequitur esse” — action follows being. This is as true of signs as it is of lions or centipedes: therefore, in order to determine the range or extent of semiosis we need above all to determine the kind of being at stake under the name “sign”. Since Poinsot, in a thesis that the work of Peirce centuries later (...) confirmed, the proper being of signs as signs lies in a relation, a relationship irreducibly unifying three distinct terms: a foreground term representing another than itself — the representamen or sign vehicle; the other represented — the significate or object signified; and the third term to or for whom the other-representation is made — the interpretant, which need not be a person and, indeed, need not even be mental. The action of signs then is the way signs influence the world, including the world of experience and knowledge, but extending even to the physical world of nature beyond the living. It is a question of what is the causality proper to signs in consequence of the being proper to them as signs, an indirect causality, just as relations are indirectly dependent upon the interactions of individuals making up the plurality of the universe; and a causality that models what could or might be in contrast to what is here and now. To associate this causality with final causality is correct insofar as signs are employed in shaping the interactions of individual things; but to equate this causality with “teleology” is a fundamental error into which the contemporary development of semiotics has been inclined to fall, largely through some published passages of Peirce from an essay within which he corrects this error but in passages so far left unpublished. By bringing these passages to light, in which Peirce points exactly in the direction earlier indicated by Poinsot, this essay attempts a kind of survey of the contemporary semiotic development in which the full vista of semiosis is laid out, and shown to be co-extensive with the boundaries of the universe itself, wherever they might fall. Precisely the indirect extrinsically specificative formal causality that signs exercise is what enables the “influence of the future” according to which semiosis changes the relevance of past to present in the interactions of Secondness. Understanding of this point (the causality proper to signs) also manifests the error of reducing the universe to signs, the error sometimes called “pansemiosis”. (shrink)

While the topic of assertion has recently received a fresh wave of interest from Peirce scholars, to this point no systematic account of Peirce’s view of assertion has been attempted. We think that this is a lacuna that ought to be filled. Doing so will help make better sense of Peirce’s pragmatism; further, what is hidden amongst various fragments is a robust pragmatist theory of assertion with unique characteristics that may have significant contemporary value. Here we aim to uncover this (...) theory, and to show that assertion for Peirce is not a mere corollary of pragmatic conceptions of truth, judgement, and belief, but is rather a central aspect of his philosophy. (shrink)

Peirce maintains that facts and propositions are structurally isomorphic. When we understand how Peirce thinks they are isomorphic, we find that a common objection raised against epistemic conceptions of truth – that there are facts beyond the ken of discovery – holds no water against Peirce’s claim that truth is what would be believed after a sufficiently long and rigorous course of inquiry.

I argue against the tendency in the philosophy of science literature to link abduction to the inference to the best explanation (IBE), and in particular, to claim that Peireean abduction is a conceptual predecessor to IBE. This is not to discount either abduction or IBE. Rather the purpose of this paper is to clarify the relation between Peireean abduction and IBE in accounting for ampliative inference in science. This paper aims at a proper classification—not justification—of types of scientific reasoning. In (...) particular, I claim that Peireean abduction is an in-depth account of the process of generating explanatory hypotheses, while IBE, at least in Peter Lipton's thorough treatment, is a more encompassing account of the processes both of generating and of evaluating scientific hypotheses. There is then a two-fold problem with the claim that abduction is IBE. On the one hand, it conflates abduction and induction, which are two distinct forms of logical inference, with two distinct aims, as shown by Charles S. Peirce; on the other hand it lacks a clear sense of the full scope of IBE as an account of scientific inference. (shrink)

The paper gives a detailed reconstruction and discussion of Peirce’s doctrine of propositions, so-called Dicisigns, developed in the years around 1900. The special features different from the logical mainstream are highlighted: the functional definition not dependent upon conscious stances nor human language, the semiotic characterization extending propositions and quasi-propositions to cover prelinguistic and prehuman occurrences of signs, the relations of Dicisigns to the conception of facts, of diagrammatical reasoning, of icons and indices, of meanings, of objects, of syntax in Peirce’s (...) logic-as-semiotics. (shrink)

I develop an account of scientific representations building on Charles S. Peirce's rich, and still underexplored, notion of iconicity. Iconic representations occupy a central place in Peirce's philosophy, in his innovative approach to logic and in his practice as a scientist. Starting from a discussion of Peirce's approach to diagrams, I claim that Peirce's own representations are in line with his formulation of iconicity, and that they are more broadly connected to the pragmatist philosophy he developed in parallel with his (...) scientific work. I then defend the contemporary relevance of Peirce's approach to iconic representations, and specifically argue that Peirce offers a useful ‘third way’ between what Mauricio Suárez has recently described as the ‘analytical’ and ‘practical’ inquiries into the concept of representation. As a philosophically minded scientist and an experimentally inclined philosopher, Peirce never divorced the practice of representing from questions about what counts as a representation... (shrink)

Uma seção da Gramática Especulativa de C.S.Peirce – Dez classes de signos – recebeu, a partir de 1903, um importante tratamento diagramático. Neste artigo, são apresentados e discutidos dois diagramas desenvolvidos por Peirce para as dez classes, incluindo esboços desses modelos.

In the last decade of his life C.S. Peirce began to formulate a purely geometrical theory of continuity to supersede the collection-theoretic theory he began to elaborate around the middle of the 1890s. I argue that Peirce never succeeded in fully formulating the later theory, and that while that there are powerful motivations to adopt that theory within Peirce’s system, it has little to recommend it from an external perspective.

Koopman’s book revolves around the notion of transition, which he proposes is one of the central ideas of the pragmatist tradition but one which had not previously been fully articulated yet nevertheless shapes the pragmatist attitude in philosophy. Transition, according to Koopman, denotes “those temporal structures and historical shapes in virtue of which we get from here to there”. One of the consequences of transitionalism is the understanding of critique and inquiry as historical pro...

George M. Searle (1839-1918) and Charles S. Peirce worked together in the Coast Survey and the Harvard Observatory during the decade of 1860: both scientists were assistants of Joseph Winlock, the director of the Observatory. When in 1868 George, a convert to Catholicism, left to enter the Paulist Fathers, he was replaced by his brother Arthur Searle. George was ordained as a priest in 1871, was a lecturer of Mathematics and Astronomy at the Catholic University of America, and became the (...) fourth superior general of his congregation from 1904 to 1909. Among the books he wrote for non-Catholic audiences was Plain Facts for Fair Minds (1895). On the 8th of August of 1895, Peirce found that book in a bookstore and the following day wrote a letter to George Searle developing his strong reservations about the question of the infallibility of the Pope. This letter (L 397) is almost unknown amongst Peirce's scholars. -/- After describing these historical circumstances as a framework, the aim of my paper is to describe Peirce's arguments against papal infallibility presented by George Searle in his book, and the contrast between the genuine scientific attitude and the putative metaphysical notion of absolute truth that is —according to Peirce— behind Searle's defense of infallibility. In this sense, Peirce's fallibilism will be explained with some detail, giving an account also of his practical infallibilism: "The assertion that every assertion but this is fallible, is the only one that is absolutely infallible. But though nothing else is absolutely infallible, many propositions are practically infallible; such as the dicta of conscience" (Minute Logic, CP 2.75, c. 1902). -/- Finally, having in mind the present interest in Peirce's religious ideas it will be suggested that some of Peirce's ideas on infallibility are nearer to contemporary understanding of that issue than Searle's defense. "I would with all my heart join the ancient church of Rome if I could. But your book," —Peirce writes to Searle— "is an awful warning against doing so." -/- . (shrink)

Argues that the path to the good life does not consist in working toward some abstract concept of the good, but rather by ameliorating the problems of the practices and institutions that make up our practical life.

Trata-se de fazer um recorte temático na história da filosofia ocidental, comparando três noções básicas de ciência: a aristotélica-tomista, segundo a qual ciência é conhecimento dedutivo, com base em certos princípios supremos, de estabelecimento de verdades; a baconiana, segundo a qual ciência é um procedimento indutivo de descoberta de verdades; e a peirciana, segundo a qual ciência é um modo de vida, uma atividade investigativa concreta, de descoberta da verdade. Aristóteles; Demonstração; Dedução; Tomás de Aquino; Princípios; Bacon; Indução; Peirce; Inquirição; (...) Comunidade de inquirição; Ciência. (shrink)

Charles S. Peirce, polymath, philosopher, logician, lived a life of often wild extremes and, when he died in 1914, had earned a vile reputation as a debauched genius. Yet he created a unified, profound and brilliant work, both published and unpublished, a fact difficult to explain. In my 1993 biography, I proposed three hypotheses to account for his Jekyll-Hyde character: his obsession with the puzzle of meaning, two neurological pathologies, trigeminal neuralgia and left-handedness, and the powerful influence of his father. (...) After publication, further research has led me to propose two additional hypotheses to explain his extraordinary life: manic-depressive illness and mystical experience, the last greatly influencing the development of his doctrine of semeiotic, of which his logic of science is a part. (shrink)

In his Logical Investigations Edmund Husserl criticizes John Stuart Mill’s account of meaning as connotation, especially Mill’s failure to separate the distinction between connotative and non-connotative names from the distinction between the meaningful and the meaningless. According to Husserl, both connotative and non-connotative names have meaning or “signification”, that is, what Gottlob Frege calls the sense (“Sinn”) of an expression. The distinction between connotative and non-connotative names is a distinction between two kinds of meaning (or sense), attributive and non-attributive meaning (...) (“attributive und nicht-attributive Bedeutung”). Attributive (connotative) names denote (refer to) objects through their attributes, whereas a non-attributive name means a thing directly (“direkt”). In this paper I examine the concepts of attributive and non-attributive meaning by means of the semiotic theory of Charles S. Peirce, and compare Peirce’s account with the views of Frege, Husserl, Alexius Meinong, and David Kaplan and Gareth Evans. (shrink)

Charles S. Peirce frequently mentioned reading Richard Whately's Elements of Logic when he was 12 years old. Throughout his life, Peirce emphasized the importance of that experience. This valorization of Whately is puzzling at first. Early in his career Peirce rejected Whately's central logical doctrines. What valuable insight concerning logic was robust enough to survive these specific rejections? Peirce recommended a biographical approach to understanding his philosophy. This essay follows that suggestion by considering Peirce's reading of Whately in a larger (...) life context. Surprisingly many factors in Charles Peirce's personal and intellectual development were at play when he read Whately. His father, Benjamin Peirce, oversaw rigorous home schooling intended to train young Charley for a brilliant intellectual career. Laboratory experience with qualitative chemical analysis exposed the boy to the logic of scientific investigation, specifically to the hypothetico-deductive method of inquiry. However, tensions between father and son developed over Charles' wish to devote his life to studying the logic of science. The two also disagreed upon the value of formal science. Against this background we will review relevant logical doctrines of Whately's book, as well as his innovative formalizing practice of logical inquiry. Then we will see that it was Whately's lessons about formal science that were of such importance to Peirce. (shrink)

I address the philosophical debate over whether the mathematical theory of probability arose on the basis of empirical observations or of purely theoretical speculations. The debate tends to pose a strict dichotomy between empirical problem-solving and pure theorizing. I alternatively suggest that, in the case of mathematical probability, an empirical problem-context acted as an enabling condition for the possibility of mathematical innovation, but that the activity of the early mathematical probabilists gradually became the study of a theoretical system of ideas. (...) This case has some implications for a more general philosophical view on the context of mathematical discovery. ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ----------------------------------------. (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)

One of the least explored areas of C.S. Peirce's wide range of work is his contributions to psychology and the philosophy of mind. This dissertation examines the corpus of this work, especially as it relates to the subjects of mind, habit, instinct, sentiment, emotion, perception, consciousness, cognition, and community. The argument is that Peirce's contributions to these areas of investigation were both highly original and heavily influenced by the main intellectual currents of his time. An effort has been made to (...) present Peirce's philosophy without apology, within the conceptual framework and idiom of its time, and without appeal to a comprehensive view that Peirce never articulated. Nevertheless, as several noted interpreters have argued, much of this work can be viewed through the lens of Peirce's innovative theory of signs and the notion of the semiotic triad as its central unifying feature, despite the fact that the general theory was itself under continuous refinement and remained incomplete at the time of his death. Another hermeneutical device employed is William James' better known and more accessible work which, when juxtaposed with Peirce's ideas, serves to bring them into sharper relief. While general and historical in the presentation of material, this study seeks, at the same time, to engage the criticism of contemporary Peirce scholars in an attempt to account for several of the conundrums inherent in Peirce's work. Among the problems with implications for his philosophy of mind and theory of inquiry are the limitations of his theory of continuity, his negative view of the self, his somewhat ambiguous position on the relation of psychology to logic, and the metaethical puzzle arising from application of his theory of probable inference to truly fateful decisions. These problems provide an interesting perspective and lend balance to the truly insightful contributions Peirce made to the discovery of the mind. (shrink)

In this Paper I interpret Charles S. Peirce’s method of prescision as a transcendental method. In order to do so, I argue that Peirce’s pragmatism can be interpreted in a transcendental light only if we use a non‐justificatory understanding of transcendental philosophy. I show how Peirce’s prescision is similar to some abstracting procedure that Immanuel Kant used in his Critique of Pure Reason. Prescision abstracts from experience and thought in general those elements without which such experience and thought would be (...) unaccountable. Similarly, in the Aesthetics, Kant isolated the a priori forms of intuition by showing how they could be abstracted from experience in general, while experience in general cannot be thought without them. However, if Peirce’s and Kant’s methods are similar in this respect, they reached very different conclusions. (shrink)

Any description of the emergence and evolution of different types of meaning processes (semiosis, sensu C.S.Peirce) in living systems must be supported by a theoretical framework which makes it possible to understand the nature and dynamics of such processes. Here we propose that the emergence of semiosis of different kinds can be understood as resulting from fundamental interactions in a triadically-organized hierarchical process. To grasp these interactions, we develop a model grounded on Stanley Salthe's hierarchical structuralism. This model can be (...) applied to establish, in a general sense, a set of theoretical constraints for explaining the instantiation of different kinds of meaning processes (iconic, indexical, symbolic) in semiotic systems. We use it to model a semiotic process in the immune system, namely, B-cell activation, in order to offer insights into the heuristic role it can play in the development of explanations for specific semiotic processes. (shrink)

I articulate Charles S. Peirce’s philosophy of mathematical education as related to his conception of mathematics, the nature of its method of inquiry, and especially, the reasoning abilities required for mathematical inquiry. The main thesis is that Peirce’s philosophy of mathematical education primarily aims at fostering the development of the students’ semeiotic abilities of imagination, concentration, and generalization required for conducting mathematical inquiry by way of experimentation upon diagrams. This involves an emphasis on the relation between theory and practice and (...) between mathematics and other fields including the arts and sciences. For achieving its goals, the article is divided in three sections. First, I expound Peirce’s philosophical account of mathematical reasoning. Second, I illustrate this account by way of a geometrical example, placing special emphasis on its relation to mathematical education. Finally, I put forth some Peircean philosophical principles for mathematical education. (shrink)

4Es approaches to cognition draw an unconventional picture of cognitive processes and of the mind. Instead of conceiving of cognition as a process that always takes place within the boundaries of the skull and the skin, these approaches hold that cognition is a situated process that often extends beyond human agents’ physical boundaries. In particular, supporters of the extended mind theory and of the enactive approach claim that embodied action in a perceptually complex environment is constitutive of cognitive processes, and (...) thus of the mind. (Chapter 1). Although both draw an extended picture of cognition and of the mind, supporters of the extended mind and supporters of the enactive approach disagree on the value of internal representations in perceptually-guided action. The extended mind theory holds that we need to posit internal action-oriented representations (AORs). AORs are valuable -the argument goes- because they account for action-selection, action-control, and for the prediction of incoming perceptual information. Advocates of the enactive approach to cognition, instead, argue against AORs. Firstly, they argue that AORs do not fulfill the necessary conditions for the identification of representational entities. Therefore, that of AOR is an ill-conceived epistemic construct. Secondly, they argue that AORs are expressive of an internalist prejudice, which makes the extended mind theory weaker than it should be from an explanatory and metaphysical point of view. I endorse both these arguments advanced by supporters of the enactive approach. Moreover, through a semiotic analysis of the construct and of the workings of AORs, I show that AORs are not active at all. Hence, I argue that AORs do not do the job they are supposed to do: extending the mind’s boundaries by explaining our perceptual relation with the world as an active, embodied, and world-involving process. Therefore, I suggest that the construct of AOR ought to be dismissed - at least in current projects in 4Es cognition (Chapter 2). I argue that similar arguments apply to recent attempts to make predictive processing accounts of perceptually-guided action more aligned with 4Es approaches to cognitive science by appealing to predictive internal models of our perceptual world. I thus propose an alternative explanation of the key features of perceptually-guided action that AORs and these internal models are supposed to be grasp. Action-control, action-selection, and the anticipatory aspects of action-perception loops can be explained by appealing to embodied actions in a field of relevant affordances, which are perceived as such based on the agent’s motor skills and motives. Furthermore, I suggest that, by combining the enactive approach to cognition with an analysis of the indexical features of our perceptual environment, we can explain perceptually-guided action in a way that truly accounts for our minds as entities that often extend beyond our skulls and skin. And we can do so without holding onto spooking entities like AORs and internal predictive models. (Chapter 3). (shrink)

A teoria convergente da verdade de Peirce é uma abordagem intuitiva e razoável da verdade. No seu sentido mais geral, vincula a verdade aos resultados da investigação. De acordo com a máxima pragmática, Peirce percebeu que as consequências práticas de afirmações verdadeiras são de trazer investigações à fruição e resolver opinião. No entanto, a teoria da verdade de Peirce é muitas vezes difamada e mal-entendida. Argumenta-se, aqui, que uma vez que se entende que a teoria convergente é uma inferência e (...) generalização oriunda do notável teorema matemático conhecido como a Lei dos Grandes Números, e como esse teorema fornece certeza matemática à indução como o cerne do método científico, muitos dos problemas desaparecem. Parte do mal-entendido também se deve ao fato que Peirce tinha três sentidos distintos de convergência, os quais muitos comentadores confundem ou interpretam erroneamente. Com esse entendimento, será mostrado que ao contrário das análises de Cheryl Misak e Christopher Hookway, Peirce argumenta que investigação persistente por bons métodos não é apenas um ideal regulador para atingir a verdade – uma esperança intelectual – mas uma possibilidade comprovada matematicamente que já resultou em verdades estabelecidas. (shrink)

Translation, according to Charles S. Peirce, is semiotic mediation. In sign processes in general, the sign mediates between the object, which it represents, and its interpretant, the idea it evokes, the interpretation it creates, or the action it causes. To what extent does the way a translator mediates correspond to what a sign does in semiosis? The paper inquires into the parallels between the agency of the sign in semiosis and the agency of the interpreter (and translator) in translation. It (...) argues that some of the limits and limitations of translatability are also the limits of the sign in semiosis. Since genuine icons and genuine indices do not convey meaning they are strictly speaking also untranslatable. Nevertheless, icons and indices also serve as mediators in learning how to translate. (shrink)

Scientific evidence and scientific values under risk and uncertainty are strictly connected from the point of view of Peirce’s pragmaticism. In addition, economy and statistics play a key role in both choosing and testing hypotheses. Hence we may show also the connection between the methodology of the economy of research and statistical frequentism, both originating from pragmaticism. The connection is drawn by the regulative principles of synechism, tychism and uberty. These principles are values that have both epistemic and non-epistemic dimension. (...) They concern both the decisions to test a hypothesis as well as inductive risk. The validity of this result stems from the values cost–benefit analysis imposes on scientific inquiry. Values associated with the economy of research are important not only in the pre-test phases of generating hypotheses but also when hypotheses are effectively tested. Peirce took these economic considerations to leave room for an interpretation of probability which is not only a frequentist and propensity-theoretic but also a conceptualist one referring to degrees of belief. We show that this leeway nonetheless agrees with the theory of the economy of scientific methods. (shrink)

Charles S. Peirce introduces the distinction between a token and a type into semiotics and philosophy by using as an example two ways of individuating words:(P1) A common mode of estimating the amount of matter in a MS. or printed book is to count the number of words. There will ordinarily be about twenty the's on a page, and of course they count as twenty words. In another sense of the word "word," however, there is but one word "the" in (...) the English language; and it is impossible that this word should lie visibly on a page or be heard in any voice, for the reason that it is not a Single thing or Single event. It does not exist; it only determines things that do exist. Such a definitely significant Form, I propose.. (shrink)

According to Peirce one of the most important philosophical problems is continuity. Consequently, he set forth an innovative and peculiar approach in order to elucidate at once its mathematical and metaphysical challenges through proper non-classical logical reasoning. I will restrain my argument to the definition of the different types of discrete collections according to Peirce, with a special regard to the phenomenon called ?premonition of continuity? (Peirce, 1976, Vol. 3, p. 87, c. 1897).

Peirce considera a matemática uma ciência informativa realmente capaz de aumentar nosso conhecimento. Isso significa que a matemática não é limitada à análise conceitual, mas possui um objeto real de investigação. O coração da visão peirciana da matemática é que o raciocínio matemático não é desenvolvido somente por meio de conceitos gerais, mas lida com um inevitável elemento de individualidade. A conclusão de uma inferência indutiva pode conter informação que não está absolutamente presente nas suas premissas, podendo vir a ser (...) somente por meio de trabalho concreto por parte do matemático. Peirce descreve esse trabalho como observação e experimentação sobre diagramas individuais. Enquanto a idéia de um elemento individual na matemática já está presente em Kant (e pode também ser traçada até Aristóteles), a sua base está na diferença entre Kant e Peirce acerca da análise categorial. A abordagem semiótica peirciana da matemática implica uma mudança, do plano do objeto denotado para o do próprio signo. Isso vale tanto para as inferências geométricas como para as inferências algébricas, que Peirce pode igualar nesse aspecto. Em ambos os casos, o elemento individual da matemática deve ser encontrado dentro do próprio diagrama, sem referência ao objeto denotado. Enquanto o diagrama é em todo caso um token, isso não pode explicar sua individualidade essencial, para cujo fim a justaposição indicial de suas partes deve ser examinada. (shrink)

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.

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 Lange's Logische Studien (1877). The present paper reconstructs Peirce's reading of Lange's book, and illustrates (...) what, according to Peirce, was right and what was problematic in Lange's account of reasoning. It further seeks to explain how Peirce's theory of deductive reasoning was a combination of Kant's philosophy of mathematics and Lange's philosophy of logic. (shrink)

We explore the technical details and historical evolution of Charles Peirce's articulation of a truth table in 1893, against the background of his investigation into the truth-functional analysis of propositions involving implication. In 1997, John Shosky discovered, on the verso of a page of the typed transcript of Bertrand Russell's 1912 lecture on ?The Philosophy of Logical Atomism? truth table matrices. The matrix for negation is Russell's, alongside of which is the matrix for material implication in the hand of Ludwig (...) Wittgenstein. It is shown that an unpublished manuscript identified as composed by Peirce in 1893 includes a truth table matrix that is equivalent to the matrix for material implication discovered by John Shosky. An unpublished manuscript by Peirce identified as having been composed in 1883?1884 in connection with the composition of Peirce's ?On the Algebra of Logic: A Contribution to the Philosophy of Notation? that appeared in the American Journal of Mathematics in 1885 includes an example of an indirect truth table for the conditional. (shrink)