We apply a framework developed by C. S. Peirce to analyze the concept of clarity, so as to examine a pair of rival mathematical approaches to a typical result in analysis. Namely, we compare an intuitionist and an infinitesimal approaches to the extreme value theorem. We argue that a given pre-mathematical phenomenon may have several aspects that are not necessarily captured by a single formalisation, pointing to a complementarity rather than a rivalry of the approaches.

This study is an exploration of the place of perspectivism in the philosophy of Henri Bergson. His work is compared with that of Thomas Nagel in terms of the mutual concern of these two philosophers to reconcile our increasingly objecti vist and impersonal understanding of reality with the perspectival apprehension of the world that living and conscious beings instantiate. It argues that Bergson's philosophy of time holds the key both to comprehending and to balancing the demands made upon us by (...) these conflicting interests. It is seldom that Bergson's name is thought of in this connection, his concerns more often than not being identified with some thesis about time, movement, or vital forces. One purpose of the present work, therefore, is to contest this interpretive slant, not merely by offering an alternative image of Bergson, but also by critically exploring his employment of perspectivism (both positive and negative). We pursue this goal through the double strategy of both unravelling the inconsistencies in Bergson's· treatment of perspective and separating his own argument from the multitude of myths, opinions, and interpretations, sympathetic and unsympathetic, that have arisen around what is currently understood by "Bergsonism". In retrieving his thought from such philosophical ghettoes as "vitalism," "spiritualism," and "psychologism," we will argue for a Bergsonian perspectivism which ultimately resides in a thesis propounding the primacy of perception. One consequence of this is the demotion of memory's importance within his thought. Not that the orthodox image of Bergsonism that retains the privileged place of memory is wrong. Rather, we argue that there is enough in Bergson's peculiar picture of perception to obviate the need for memory in his philosophy, and, moreover, that it is actually more Bergsonian that memory should be so discharged. (shrink)

We suggest that, far from establishing an inconsistency in the standard theory of the geometrical linear continuum, Zeno’s Paradox of Extension merely establishes an inconsistency between the standard theory of geometrical magnitude and a misguided system of length measurement. We further suggest that our resolution of Zeno’s paradox is superior to Adolf Grünbaum’s now standard resolution based on Lebesgue measure theory.