In this paper, we intend to discuss if and in what sense semiosis (meaning process, cf. C. S. Peirce) can be regarded as an "emergent" process in semiotic systems. It is not our problem here to answer when or how semiosis emerged in nature. As a prerequisite for the very formulation of these problems, we are rather interested in discussing the conditions which should be fulfilled for semiosis to be characterized as an emergent process. The first step in this work (...) is to summarize a systematic analysis of the variety of emergence theories and concepts, elaborated by Achim Stephan. Along the summary of this analysis, we pose fundamental questions that have to be answered in order to ascribe a precise meaning to the term "emergence" in the context of an understanding of semiosis. After discussing a model for explaining emergence based on Salthe's hierarchical structuralism, which considers three levels at a time in a semiotic system, we present some tentative answers to those questions. (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)

In this paper I argue that, according to Peirce’s mature account of perception, we directly perceive generals, or "Thirds," in external reality which should be described as physical and not as mental. I argue against three other interpretations of the role of Thirdness in Peirce’s account: (I) we do not directly perceive Thirds, although they are involved in the interpretive and judgmental part of perception; (II) we directly perceive Thirds, but they are imposed on external objects by our minds; and (...) (III) we directly perceive Thirds in external objects, but external reality is comprised of the representations of an objective mind. I address questions about the role of the percept and the percipuum in his account, in what exact sense he thought that perception is interpretive, and how he thought it is even possible to directly perceive generals in the external world. (shrink)

In recent work, Cheryl Misak has developed a novel justification of deliberative democracy rooted in Peircean epistemology. In this article, the author expands Misak's arguments to show that not only does Peircean pragmatism provide a justification for deliberative democracy that is more compelling than the justifications offered by competing liberal and discursivist views, but also fixes a specific conception of deliberative politics that is perfectionist rather than neutralist. The article concludes with a discussion of whether the `epistemic perfectionism' implied by (...) the pragmatist argument could be endorsed by liberal democrats. Key Words: deliberative democracy • epistemology • liberalism • Cheryl Misak • Charles Peirce • perfectionism • pragmatism • truth. (shrink)

Scientific representation is a currently booming topic, both in analytical philosophy and in history and philosophy of science. The analytical inquiry attempts to come to terms with the relation between theory and world; while historians and philosophers of science aim to develop an account of the practice of model building in the sciences. This article provides a review of recent work within both traditions, and ultimately argues for a practice-based account of the means employed by scientists to effectively achieve representation (...) in the modelling sciences. (shrink)

This paper considers the relation between the American pragmatist Charles Sanders Peirce and the German idealist G. W. F. Hegel . While Peirce engaged with Hegel’s thought quite extensively, his often critical comments on the latter have made it hard to see any genuine common ground between the two; recent ways of reading Hegel, however, suggest how this might be possible, where the connections between their respective metaphysical positions and views of the categories are explored here. Issues relating to their (...) epistemology and philosophies of languages are considered in a companion article. (shrink)

Journal Name: Semiotica Issue: Ahead of print.

In this article, I examine the reconstruction that Peirce does on analytic/synthetic Kantian division, supported by his phenomenology, semiotic and pragmatism. The analysis of Peirce’s writings on mathematic suggests a notion of a posteriori and necessary analytical truths, that is, propositions that express one belief justified in experience, but whose generalization is valid for all the possible worlds. This was a new idea the time that Peirce formulated it, in 19th Century, and it contrasts with semantic-analytical tradition from Frege and (...) was contested by Quine in 1950’s. Peirce’s notion of analyticity is a result of his discovery of the logic of relatives, which led the philosopher to revise the deductive reasoning, dividing it into corollarial and theorematic, which in turn allow us to understand why mathematics is, simultaneously, deductive and non-trivial. (shrink)

In this paper we will show Peirce’s distinction between deduction, induction and abduction. The aim of the paper is to show how Peirce changed his views on the subject, from an understanding of deduction, induction and hypotheses as types of reasoning to understanding them as stages of inquiry very tightly connected. In order to get a better understanding of Peirce’s originality on this, we show Peirce’s distinctions between qualitative and quantitative induction and between theorematical and corollarial deduction, passing then to (...) the distinction between mathematics and logic. In the end, we propose a sketch of a comparison between Peirce and Whitehead concerning the two thinkers’ view of mathematics, hoping that this could point to further inquiries. (shrink)

How to model meaning processes (semiosis) in artificial semiotic systems? Once all computer simulation becomes tantamount to theoretical simulation, involving epistemological metaphors of world versions, the selection and choice of models will dramatically compromise the nature of all work involving simulation. According to the pragmatic Peircean based approach, semiosis is an interpreter-dependent process that cannot be dissociated from the notion of a situated (and actively distributed) communicational agent. Our approach centers on the consideration of relevant properties and aspects of Peirce’s (...) pragmatic concept of semiotics. Upon developing this approach, we have no pretensions of our being able to present an exhaustive analysis of the differences between Peirce and other theoretical positions. Nevertheless, our contribution will serve to demonstrate how theorists contribute toward revealing certain fundamental ‘semiotic constraints’ that will be of interest and importance. (shrink)

Against the view that symbol-based semiosis is a human cognitive uniqueness, we have argued that non-human primates such as African vervet monkeys possess symbolic competence, as formally defined by Charles S. Peirce. Here I develop this argument by showing that the equivocal role ascribed to symbols by “folk semiotics” stems from an incomplete application of the Peircean logical framework for the classification of signs, which describes three kinds of symbols: rheme, dicent and argument. In an attempt to advance in the (...) classifying semiotic processes, Peirce proposed several typologies, with different degrees of refinement. Around 1903, he developed a division into ten classes. According to this typology, symbols can be further analysed in three subclasses (rheme, dicent, argument). I proceed to demonstrate that vervet monkeys employ dicent symbols. There are remarkable implications of this argument since ‘symbolic species theory’ fails to explore the vast Peircean semiotic philosophy to frame questions regarding the emergence and evolution of symbolic processes. (shrink)

Philosophers and social scientists of diverse orientations have suggested that the pragmatics of semiosis is germane to a dynamic account of meaning as process. Semiosis, the central focus of C. S. Peirce's pragmatic philosophy, may hold a key to perennial problems regarding meaning. Indeed, Peirce's thought should be deemed seminal when placed within the cognitive sciences, especially with respect to his concept of the sign. According to Peirce's pragmatic model, semiosis is a triadic, time-bound, context-sensitive, interpreter-dependent, materially extended dynamic process. (...) Semiosis involves inter-relatedness and inter-action between signs, their objects, acts and events in the world, and the semiotic agents who are in the process of making and taking them. (shrink)

Charles S. Peirce (1839-1914) made relevant contributions to deductive logic, but he was primarily interested in the logic of science, and more especially in what he called 'abduction' (as opposed to deduction and induction), which is the process whereby hypotheses are generated in order to explain the surprising facts. Indeed, Peirce considered abduction to be at the heart not only of scientific research, but of all ordinary human activities. Nevertheless, in spite of Peirce's work and writings in the field of (...) methodology of research, scarce attention has been paid to the logic of discovery over the last hundred years, despite an impressive development not only of scientific research but also of logic. -/- Having this in mind, the exposition is divided into five parts: 1) a brief presentation of Peirce, focusing on his work as a professional scientist; 2) an exposition of the classification of inferences by the young Peirce: deduction, induction and hypothesis; 3) a sketch of the notion of abduction in the mature Peirce; 4) an exposition of the logic of surprise; and finally, by way of conclusion, 5) a discussion of this peculiar ability of guessing understood as a rational instinct. -/- . (shrink)

Nicholas Rescher embraces a more objectivist, realist, analytic pragmatism than the pragmatism which has been in vogue in the last two decades. He rejects any pragmatism for which there is no truth, reality, or objectivity but only conversations or solidarity within this or that vocabulary. Rescher has argued that pragmatism, far from being anti-realist, provides the only good argument for realism and for our ability to operate the causal model of inquiry about the real world. I examine this kind of (...) pragmatist argument, point out its pitfalls, and argue that Rescher avoids them. (shrink)

Taking as its exegetic point of departure Peirce's outline of a semiotic theory of cognition from the mid 1890s, this paper explores the relevance of this outline to a theory of learning and also to a broader, normative vision of education. Firstly, besides providing for fallibilism in philosophical inquiry Peirce's outline accords with critical strategies of his fellow pragmatists, such as William James's detection of the ‘psychologist's fallacy’ and John Dewey's rejection of the ‘philosophical fallacy’. It is pointed out that (...) this merit of Peirce's outline is due to his abstract and often neglected notion of a prespecialised scientific intelligence. Secondly, the paper shows that Peirce's semiotic approach to prescientific learning processes conditioning all kinds of theoretical activity may indeed complement James's and Dewey's contributions: giving careful attention to the work of linguistic and paralinguistic signs in such learning processes Peirce's analysis captures indexical and iconic aspects, as well as symbolic aspects of linguistic interaction and experientially constrained dialogue. Following Peirce's analysis the paper considers how the iconicity of linguistic structure, ostensive acts and the practical situatedness of language use are pre‐conditions of experiential learning in every day life as well as in scientific learning. It is also shown how this semiotic analysis is connected with Peirce's important notion of abduction. Finally, it is pointed out that a broader vision of education may issue from Peirce's semiotic analysis and that such a vision would emphasise that the life experience of individuals entering educational institutions should be made to bear on the objectives as well as the teaching practices of educational institutions. (shrink)

Taking as its exegetic point of departure Peirce's outline of a semiotic theory of cognition from the mid 1890s, this paper explores the relevance of this outline to a theory of learning and also to a broader, normative vision of education. Firstly, besides providing for fallibilism in philosophical inquiry Peirce's outline accords with critical strategies of his fellow pragmatists, such as William James's detection of the ‘psychologist's fallacy’ and John Dewey's rejection of the ‘philosophical fallacy’. It is pointed out that (...) this merit of Peirce's outline is due to his abstract and often neglected notion of a prespecialised scientific intelligence. Secondly, the paper shows that Peirce's semiotic approach to prescientific learning processes conditioning all kinds of theoretical activity may indeed complement James's and Dewey's contributions: giving careful attention to the work of linguistic and paralinguistic signs in such learning processes Peirce's analysis captures indexical and iconic aspects, as well as symbolic aspects of linguistic interaction and experientially constrained dialogue. Following Peirce's analysis the paper considers how the iconicity of linguistic structure, ostensive acts and the practical situatedness of language use are pre‐conditions of experiential learning in every day life as well as in scientific learning. It is also shown how this semiotic analysis is connected with Peirce's important notion of abduction. Finally, it is pointed out that a broader vision of education may issue from Peirce's semiotic analysis and that such a vision would emphasise that the life experience of individuals entering educational institutions should be made to bear on the objectives as well as the teaching practices of educational institutions. (shrink)

Meinongian 'objects' are evoked in an effort to critique and expand upon traditional theories of reference. The argument stems from an account of Peirce's categories of meaning in light of vague, contradictory, inconsistent, general, incomplete, and incompleteable signs. In addition to signs as either 'true', 'false', or meaningless, the function of imaginary numbers reveals the possibility of a sign's being both 'true' and 'false' or neither 'true' nor 'false', over time, and dialogically speaking. This demands a tolerance for vagueness, ambiguity, (...) contradiction, and incessantly changing meaning. (shrink)

This multifaceted essay emerges from a host of sources within diverse academic settings. Its central thesis is guided by physicist John A. Wheeler's thoughts on the quantum enigma. Wheeler concludes, following Niels Bohr, that we are co-participants within the universal self-organizing process. This notion merges with concepts from Peirce's process philosophy, Eastern thought, issues of topology, and border theory in cultural studies and social science, while surrounding itself with such key terms as complementarity, interdependence, interrelatedness, vagueness, generality, incompleteness, inconsistency, and (...) mestizaje. Ultimately, a sense of semiosic process pervades in light of combined homogenous and hetergenous tendencies. (shrink)

Arguably, a theory of assertion should be able to provide (i) a definition of assertion, and (ii) a set of conditions for an assertion to be appropriate. This paper reviews two strands of theories that have attempted to meet this challenge. Commitment-based accounts à la Peirce define assertion in terms of commitment to the truth of the proposition. Restriction-based accounts à la Williamson define assertion in terms of the conditions for its appropriate performance. After assessing the suitability of these projects (...) to meet the desiderata of a theory of assertion, I argue that a speech act theoretic account à la Searle is more suitable for this purpose: it integrates the core intuitions of both restriction-based and commitment-based accounts while avoiding their respective problems, and has the further advantage of determining how assertion fits into a more general theory of illocutionary acts. (shrink)

Terrence Deacon's views about the origin of language are based on a particular notion of a symbol. While the notion is derived from Peirce's semiotics, it diverges from that source and needs to be investigated on its own terms in order to evaluate the idea that the human species has crossed the symbolic threshold. Deacon's view is defended from the view that symbols in the animal world are widespread and from the extreme connectionist view that they are not even to (...) be found in humans. Deacon's treatment of symbols involves a form of holism, as a symbol needs to be part of a system of symbols. He also appears to take a realist view of symbols. That combination of holism and realism makes the threshold a sharp threshold, which makes it hard to explain how the threshold was crossed. This difficulty is overcome if we take a mild realist position towards symbols, in the style of Dennett. Mild realism allows intermediate stages in the crossing but does not undermine Deacon's claim that the threshold is difficult to cross or the claim that it needs to be crossed quickly. (shrink)

Wittgenstein's discussion of rule-following is widely regarded to have identified what Kripke called "the most radical and original sceptical problem that philosophy has seen to date". But does it? This paper examines the problem in the light of Charles Peirce's distinctive "scientific hierarchy". Peirce identifies a phenomenological inquiry which is prior to both logic and metaphysics, whose role is to identify the most fundamental philosophical categories. His third category, particularly salient in this context, pertains to general predication. Rule-following scepticism, the (...) paper suggests, results from running together two questions: "How is it that I can project rules?", and, "What is it for a given usage of a rule to be right?". In Peircean terms the former question, concerning the irreducibility of general predication (to singular reference), must be answered in phenomenology, while the latter, concerning the difference between true and false predication, is answered in logic. A failure to appreciate this distinction, it is argued, has led philosophers to focus exclusively on Wittgenstein's famous public account of rule-following rightness, thus overlooking a private, phenomenological dimension to Wittgenstein's remarks on following a rule which gives the lie to Kripke's reading of him as a sceptic. (shrink)

This entry explores Charles Peirce's account of truth in terms of the end or ‘limit’ of inquiry. This account is distinct from – and arguably more objectivist than – views of truth found in other pragmatists such as James and Rorty. The roots of the account in mathematical concepts is explored, and it is defended from objections that it is (i) incoherent, (ii) in its faith in convergence, too realist and (iii) in its ‘internal realism’, not realist enough.

Enactivism has influentially argued that the traditional intellectualist ‘act-content’ model of intentionality is insufficient both phenomenologically and naturalistically, and minds are built from world-involving bodily habits – thus, knowledge should be regarded as more of a skilled performance than an informational encoding. Radical enactivists have assumed that this insight must entail non-representationalism concerning at least basic minds. But what if it could be shown that representation is itself a form of skilled performance? I sketch the outline of such an account (...) from the perspective of Peirce’s pragmatist semiotics, which theorises signs as habits of associating specific cues with appropriate acts and schemas of ensuing experience. Within this framework, I argue, a naturalistic account of propositional structure can be constructed which transcends the symbolic – and in some instances even the linguistic – sphere, and offers new insights regarding the Information Processing Challenge, and the Hard Problem of Content. (shrink)

Argument-forms exist which are valid over finite but not infinite domains. Despite understanding of this by formal logicians, philosophers can be observed treating as valid arguments which are in fact invalid over infinite domains. In support of this claim I will first present an argument against the classical pragmatist theory of truth by Mark Johnston. Then, more ambitiously, I will suggest the fallacy lurks in certain arguments for physicalism taken for granted by many philosophers today.

This paper presents a comprehensive account of Peirce's post-1900 theory of abduction. The account aims at bringing together various strands of discussion in Peirce's work, showing how their interaction creates a more coherent picture of his thoughts on abductive reasoning as manifest after the turn of the century. The discussion is of a historical nature, rather than a critical assessment.

Artykuł bada relację między korespondencją a konwergencją w teorii prawdy Charlesa S. Peirce’a. Analiza kontekstu wprowadzenia pragmatycznej koncepcji prawdy, a także jej struktury logicznej prowadzi do wniosku, że stanowisko Peirce’a należy rozumieć raczej jako reformę klasycznego pojęcia prawdy niż jego odrzucenie. W szczególności podjęte zostaje zagadnienie nominalistycznej i realistycznej interpretacji klasycznych i nieklasycznych ujęć prawdy oraz krytyka propozycji pogodzenia aktualistycznej i kontrfaktycznej interpretacji warunku konwergencji.

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)

This paper defends a key aspect of the Peircean conception of truth—the idea that truth is in some sense epistemically-constrained. It does so by exploring parallels between Peirce’s epistemology of inquiry and that of Wittgenstein in On Certainty. The central argument defends a Peircean claim about truth by appeal to a view shared by Peirce and Wittgenstein about the structure of reasons. This view relies on the idea that certain claims have a special epistemic status, or function as what are (...) popularly called ‘hinge propositions’. (shrink)

In an epistemology of contextualism, how robust does consensus need to be for critique to be practically effective? In ‘Relativism and the Critical Potential of Philosophy of Education’ Frieda Heyting proposes a form of contextualism, but her argument raises a number of problems. The kinds of criteria that her version of contextualism will furnish provide, at best, the potential only for an immanent form of critique from within a particular practice, and the possibility that practitioners alone will adopt a general (...) stance of critique. By their nature, the criteria that Heyting endorses will be too transient and ephemeral to assist in any larger project that might be aimed at making effective criticism of the status quo. Further problems are exposed to do with the conditions needed to make critique effective when Heyting's normative argument is situated in the Realpolitik of contemporary education. Drawing on the work of Charles Sanders Peirce, and in a manner intended to be complementary to Heyting's normative argument, the paper offers some suggestions regarding the role that doubt might play in justifying criticisms of the status quo. (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)

Following the guiding thread of Peirce’s use of diagrammatic syntax in his system of existential graphs , which depends crucially on the role of the Sheet of Assertion, we introduce the notion of Sheet of Indication as the basis for a general diagrammatic semantics applicable to a wide range of diagrams. We then show how Peirce’s EG-alpha graphs may be understood as instances of SIs and how logically coherent models of the graphs are represented in the SI semantics.

Charles Peirce is often credited for being among the first, perhaps even the first, to develop a scientific metaphysics of indeterminism. After rejecting the received view that Peirce developed his views from Darwin and Maxwell, I argue that Peirce's view results from his synthesis of Immanuel Kant's critical philosophy and George Boole's contributions to formal logic. Specifically, I claim that Kant's conception of the laws of logic as the basis for his architectonic, when combined with Boole's view of probability, yields (...) Peirce's metaphysics of probabilistic laws. Indeterminism provides, therefore, an excellent illustration of how Peirce attempted to use logic to clarify metaphysical problems.Since everyone must have conceptions of things in general, it is most important that they should be carefully constructed. I shall enter into no criticism of the different methods of metaphysical research, but shall merely say that in the opinions of several great thinkers, the only successful mode yet lighted upon is that of adopting our logic as our metaphysics. (W1: 490, 1866)2. (shrink)

Although the Cambridge Professor of Mental Philosophy and Logic James Ward was once one of Britain's most highly regarded Psychologists and Philosophers, today his work is unjustly neglected. This is because his philosophy is frequently misrepresented as a reactionary anti-naturalistic idealist theism. In this article, I argue, first, that this reading is false, and that by viewing Ward through the lens of pragmatism we obtain a fresh interpretation of his work that highlights the scientific nature of his philosophy and his (...) original and promising theory of ‘evolutionary Kantianism’, with its applications to the philosophy of mind, epistemology, and metaphysics. Second, I show that reading Ward as a pragmatist provides us with (1) a more complex history of the reception of pragmatism at Cambridge at the turn of the twentieth century than the straightforwardly hostile one traditionally told; and (2) a more detailed understanding of the wide range of philosophical problems to which pragmatism was deemed at this time to have an appropriate application. (shrink)

This article offers an analysis of the cognitive role of diagrammatic movements in the theater. Based on the recognition of a theatrical work’s inherent ability to provide new insights concerning reality, the article concentrates on the way by which actors’ movements on stage create spatial diagrams that can provide new insights into the spectators’ world. The suggested model of theater’s epistemology results from a combination of Charles S. Peirce’s doctrine of diagrammatic reasoning and David Lewis’s theoretical account of the truth (...) value of counterfactual conditionals. I argue that in several theatrical works – in particular those whose central image is dominated by movements – the relation of what Lewis names “comparative overall similarity” between the fictional and the actual world is based on diagrammatic homology. The cognitive process involved in deciphering them is, hence, based on diagrammatic reasoning. The main emphasis of the analysis is on the previously unnoticed but important cognitive role of observation in the theater: the idea that observation takes an active role in the reasoning process that enables the spectators to form new knowledge about their actual world. Samuel Beckett’s plays Quad and Come and Go serve here as case studies. (shrink)

In this paper, it will be shown that Peirce was of two minds about whether his scientific fallibilism, the recognition of the possibility of error in our beliefs, applied to mathematics. It will be argued that Peirce can and should hold a theory of fallibilism within mathematics, and that this position is more consistent with his overall pragmatic theory of inquiry and his general commitment to the growth of knowledge. But to make the argument for fallibilism in mathematics, Peirce's theory (...) of fallibilism must be reconceived to incorporate two different kinds of fallibilism, which correspond to two different kinds of truth claims. (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)

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)

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)