Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to “speak” of indeterminism, its inability to present us a worldview in which new information is created as time passes. In such a case, scientific determinism would only be an illusion due to the timeless mathematical language scientists use. To investigate this possibility it is necessary (...) to develop an alternative mathematical language that is both powerful enough to allow scientists to compute predictions and compatible with indeterminism and the passage of time. We suggest that intuitionistic mathematics provides such a language and we illustrate it in simple terms. (shrink)

This paper examines Derrida's interpretation of Jean Cavaill s's critique of phenomenology in On Logic and the Theory of Science . Derrida's main claim is that Cavaill s's arguments, especially the argument based on G del's incompleteness theorems, need not lead to a total rejection of Husserl's phenomenology, but only its static version. Genetic phenomenology, on the other hand, not only is not undermined by Cavaill s's critique, but can even serve as a philosophical framework for Cavaill s's own position. (...) I will argue that Derrida's approach to Cavaill s is fruitful, facilitating the exposition of some central Cavaill sian ideas, including the notion of dialectics. Nevertheless, it is important to evaluate Derrida's own arguments against static phenomenology. I undertake such an assessment in the last section of the paper, showing that G del's theorems do not in themselves warrant rejection of static phenomenology. I base this conclusion in part on G del's own understanding of phenomenology as a philosophical basis for mathematics. (shrink)

This is a survey of the concept of continuity. Efforts to explicate continuity have produced a plurality of philosophical conceptions of continuity that have provably distinct expressions within contemporary mathematics. I claim that there is a divide between the conceptions that treat the whole continuum as prior to its parts, and those conceptions that treat the parts of the continuum as prior to the whole. Along this divide, a tension emerges between those conceptions that favor philosophical idealizations of continuity and (...) those that are more readily available for mathematico-scientific use. (shrink)