Many important concepts of the calculus are difficult to grasp, and they may appear epistemologically unjustified. For example, how does a real function appear in “small” neighborhoods of its points? How does it appear at infinity? Diagrams allow us to overcome the difficulty in constructing representations of mathematical critical situations and objects. For example, they actually reveal the behavior of a real function not “close to” a point but “in” the point. We are interested in our research in the diagrams (...) which play an optical role –microscopes and “microscopes within microscopes”, telescopes, windows, a mirror role, and an unveiling role. In this paper we describe some examples of optical diagrams as a particular kind of epistemic mediator able to perform the explanatory abductive task of providing a better understanding of the calculus, through a non-standard model of analysis. We also maintain they can be used in many other different epistemological and cognitive situations. (shrink)

Computational philosophy (CP) aims at investigating many important concepts and problems of the philosophical and epistemological tradition in a new way by taking advantage of information-theoretic, cognitive, and artificial intelligence methodologies. I maintain that the results of computational philosophy meet the classical requirements of some Peircian pragmatic ambitions. Indeed, more than a 100 years ago, the American philosopher C.S. Peirce, when working on logical and philosophical problems, suggested the concept of pragmatism(pragmaticism, in his own words) as a logical criterion to (...) analyze what words and concepts express through their practical meaning. Many words have been spent on creative processes and reasoning, especially in the case of scientific practices. In fact, many philosophers have usually offered a number of ways of construing hypotheses generation, but they aim at demonstrating that the activity of generating hypotheses is paradoxical, obscure, and thus not analyzable. Those descriptions are often so far from Peircian pragmatic prescription and so abstract to result completely unknowable and obscure. To dismiss this tendency and gain interesting insight about the so-called logic of scientific discovery we need to build constructive procedures, which could play a role in moving the problem-solving process forward by implementing them in some actual models. The computational turn gives us a new way to understand creative processes in a strictly pragmatic sense. In fact, by exploiting artificial intelligence and cognitive science tools, computational philosophy allows us to test concepts and ideas previously conceived only in abstract terms. It is in the perspective of these actual computational models that I find the central role of abduction in the explanation of creative reasoning in science. I maintain that the computational philosophy analysis of model-based and manipulative abduction and of external and epistemic mediators is important not only to delineate the actual practice of abduction, but also to further enhance the development of programs computationally adequate in rediscovering, or discovering for the first time, for example, scientific hypotheses or mathematical theorems. The last part of the paper is devoted to illustrating the problem of the extra-theoretical dimension of reasoning and discovery from the perspective of some mathematical cases derived from calculus and geometry. (shrink)

Little, Brown, 1992 Review by Glenn Branch on Jul 5th 1999 Volume: 3, Number: 27.

Since the 1980s consensus opinion is that the mind is like a collection of specialised modules each tasked for a specific purpose. The author seeks to elucidate and account for this theory and explain what it means to be human in this context.

Theoretical and manipulative abduction conjectures and manipulations : the extra-theoretical dimension of scientific discovery. -- Non-explanatory and instrumental abduction : plausibility, implausibility, ignorance preservation. -- Semiotic brains and artificial minds : how brains make up material cognitive systems. -- Neuromultimodal abduction : pre-wired brains, embidiment, neurospaces. -- Animal abduction : from mindless organisms to srtifactual mediators. -- Abduction, affordances, and cognitive niches : sharing representations and creating chances through cognitive niche construction. -- Abduction in human and logical agents : hasty (...) generalizers, hybrid abducers, fallacies. -- Morphodynamical abduction : causation of hypotheses by attractors dynamics. (shrink)