In this essay, I discuss some observations by Peirce which suggest he had some idea of the substantive metalogical differences between logics which permit both quantifiers and relations, and those which do not. Peirce thus seems to have had arguments?which even De Morgan and Frege lacked?that show the superior expressiveness of relational logics.

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examine Charles S. Peirce's mature views on the logic of science, especially as contained in his later and still mostly unpublished writings.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)

This paper reconstructs the Peircean interpretation of Kant's doctrine on the syntheticity of mathematics. Peirce correctly locates Kant's distinction in two different sources: Kant's lack of access to polyadic logic and, more interestingly, Kant's insight into the role of ingenious experiments required in theorem-proving. In this second respect, Kant's analytic/synthetic distinction is identical with the distinction Peirce discovered among types of mathematical reasoning. I contrast this Peircean theory with two other prominent views on Kant's syntheticity, i.e. the Russellian and the (...) Beckian views, and show how Peirce's interpretation of Kant solves the dilemma that each of these two views faces. I also show that Hintikka's criterion for Kant's synthetic judgments, i.e. a new individual introduced by the -instantiation rule, does not capture the most important characteristic of Peirce's theorematic reasoning, i.e. the process of choosing a correct individual. (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)

Abductive reasoning takes place in forming``hypotheses'''' in order to explain ``facts.'''' Thus, theconcept of abduction promises an understanding ofcreativity in science and learning. It raises,however, also a lot of problems. Some of them will bediscussed in this paper. After analyzing thedifference between induction and abduction (1), Ishall discuss Peirce''s claim that there is a ``logic''''of abduction (2). The thesis is that this claim can beunderstood, if we make a clear distinction between inferential elements and perceptive elements of abductive reasoning. For (...) Peirce, the creative act offorming explanatory hypotheses and the emergence of``new ideas'''' belongs exclusively to the perceptive side of abduction. Thus, it is necessary to study the roleof perception in abductive reasoning (3). A furtherproblem is the question whether there is arelationship between abduction and Peirce''s concept of``theorematic reasoning'''' in mathematics (4). Both forms of reasoning could be connected, because both arebased on perception. The last problem concerns therole of instincts in explaining the success ofabductive reasoning in science, and the question whether the concept of instinct might be replaced bymethods of inquiry (5). (shrink)

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 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.

The aim of the paper is to try and make one’s ideas clearer about such concepts as “logic,” “psychology,” “mind,” “normativity,” rationality,” as they were conceived by Peirce, in order to elucidate his genuine position as far as the relationship between logic and pychology is concerned, whether he was or was not a straightforward “anti psychologist” in logic, and from such analyses, to make some suggestions about the contemporary relevance of Peirce’s original views on such isues.

In this paper I propose to read and understand gestures as logical tools within a synthetic paradigm of knowledge. This interpretation of gesture is drawn from a new pragmatist reading of reasoning in general, and synthetic reasoning in particular. Complete gestures are actions with a beginning and an end that bear a meaning. It is our regular way to embody vague ideas into singular actions with general meaning. The tool is forged by a dense blending of icons, indices, and symbols (...) and by a complexity of phenomenological characteristics as feelings, actual actions, general concepts and habits. The paper illustrates this new way to look at gestures and different kinds of complete and incomplete gestures. (shrink)

Prior to the Second World War, Peirce was virtually unknown in Finnish philosophical discussions. This was not the case of pragmatism altogether. For example, James’s ideas were well received and discussed in Finland at some length around the time of his death in 1910, including the translation of several of James’s books and writings into Finnish. A central figure in this discussion was the most prominent Finnish philosopher at that time, Eino Kaila, who also founded the psychological labora...