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)

Journal Name: Semiotica Issue: Ahead of print.

In this paper, we focus on the development of geometric cognition. We argue that to understand how geometric cognition has been constituted, one must appreciate not only individual cognitive factors, such as phylogenetically ancient and ontogenetically early core cognitive systems, but also the social history of the spread and use of cognitive artifacts. In particular, we show that the development of Greek mathematics, enshrined in Euclid’s Elements, was driven by the use of two tightly intertwined cognitive artifacts: the use of (...) lettered diagrams; and the creation of linguistic formulae. Together, these artifacts formed the professional language of geometry. In this respect, the case of Greek geometry clearly shows that explanations of geometric reasoning have to go beyond the confines of methodological individualism to account for how the distributed practice of artifact use has stabilized over time. This practice, as we suggest, has also contributed heavily to the understanding of what mathematical proof is; classically, it has been assumed that proofs are not merely deductively correct but also remain invariant over various individuals sharing the same cognitive practice. Cognitive artifacts in Greek geometry constrained the repertoire of admissible inferential operations, which made these proofs inter-subjectively testable and compelling. By focusing on the cognitive operations on artifacts, we also stress that mental mechanisms that contribute to these operations are still poorly understood, in contrast to those mechanisms which drive symbolic logical inference. (shrink)

Kelly suggested that it was useful to consider anyone as functioning as a scientist, in the business of applying theories, making hypotheses and predictions and testing them out in the practice of everyday life. One of Charles Peirce’s major contributions was to develop the disciplines of logic and the philosophy of science. We can deepen and enrich our understanding of Kelly’s vision by looking at what Peirce has to say about the process of science. For Peirce, the essence of science (...) was the application of the laws of inference. He developed a much broader concept of logic, elaborating the processes of deduction and induction and adding to these the logic of hypothetical inference, or ‘abduction’, even as Kelly broadened it further in his “departure from classical logic”. Examining the implications of these three forms of inference allows us to elaborate the dynamics involved in the process of construing, ordinacy and the cycles of experience, creativity and decision making. This is the second of a three part series examining the relationship between the work of Peirce and Kelly. The third will include a look at phenomenology, bipolarity, the self, dialogical process and sociological considerations. (shrink)