It is a common thought that mathematics can be not only true but also beautiful, and many of the greatest mathematicians have attached central importance to the aesthetic merit of their theorems, proofs and theories. But how, exactly, should we conceive of the character of beauty in mathematics? In this paper I suggest that Kant's philosophy provides the resources for a compelling answer to this question. Focusing on §62 of the ‘Critique of Aesthetic Judgment’, I argue against the common view (...) that Kant's aesthetics leaves no room for beauty in mathematics. More specifically, I show that on the Kantian account beauty in mathematics is a non-conceptual response felt in light of our own creative activities involved in the process of mathematical reasoning. The Kantian proposal I thus develop provides a promising alternative to Platonist accounts of beauty widespread among mathematicians. While on the Platonist conception the experience of mathematical beauty consists in an intellectual insight into the fundamental structures of the universe, according to the Kantian proposal the experience of beauty in mathematics is grounded in our felt awareness of the imaginative processes that lead to mathematical knowledge. The Kantian account I develop thus offers to elucidate the connection between aesthetic reflection, creative imagination and mathematical cognition. (shrink)

The research on which the present paper makes a point in aimed at designing a cognitive model of Albert Einstein's discovery that is based on fundamental Einstein's publications and placed, ideally, at a meso-level, between macro-historical and micro-cognitive reconstructions (e.g. protocol analysis). As in a cognitive-historical analysis, we will trace some discovery heuristics in the construction of representations, that are on a continuum with those we employ in ordinary problem solving. Firstly, some theory-specific, reflexive heuristics—named orientative heuristics—are traced: inner perfection, (...) explain-or-assume, explanatory correspondence, and covariance/invariance. Then, other well-known abstractive heuristics as analogical and imagistic reasoning, thought experiment, limiting case analysis (e.g. Nersessian 1992) are shown occurring in Einstein's key-publications. A sketch of a socio-cognitive model for his discovery is then presented following two suggestions: (a) an idea of Van Fraassen about discovery phases, and (b) the Humean distinction between beliefs and ideas. (shrink)

Organizational research constitutes a differentiated, complex and fragmented field with multiple contradicting and incommensurable theories that make fundamentally different claims about the social and organizational reality. In contrast to natural sciences, the progress in this field can’t be attributed to the principle of truthlikeness where theories compete against each other and only best theories survive and prove they are closer to the truth and thus demonstrate scientific knowledge accumulation. We defend the structural realist view on the nature of organizational theories (...) in order to demonstrate that despite the multiplicity of isolated and competing explanations of organization-environment relations these theories are still logically compatible and mutually consistent which, in turn, assures theoretical progress in the field. Although postulating different and incompatible ontologies, three most successful organization-environments theories, namely, contingency theory, new institutionalism and population ecology share the same explanations of the relations between organizations and environments at the structural level. Without this principle one would say that what occurs in the field of organization theory is a change rather than a progress. (shrink)