On the mathematical representation of phenomena of emergence

This paper is a philosophical enquiry into the role that mathematics play in the articulation of science. It is conducted, in its essentials, in the spirit of Wittgenstein's views on the nature and function of philosophy, which are to lay bare, as it were, the manner in which we do whatever it is that we do, and then to examine the claims that we make for the deed. My conclusions should be easily accessible to those familiar with his thinking on the subject of science.

The case that has inspired the writing of this paper is not that of biology, nor is it the biological theory of evolution; rather, the case I have kept in mind while writing this paper is that of cognitive science, sometimes presented as a “science of mind” by its practitioners. It is primarily a computational theory characterized by two distinct approaches, one internal, the gist of which is that the brain/mind distinction is definitely passé; the other external, based on the view that the mark of human mentation is to be found in the ordinary use of old expressions to convey new meanings, i.e. in the Cartesian test for the existence of other minds, and its simpler computational version, the Turing test. Two intuitions underlie the paper: one, that language is obviously an adaptive characteristic of human organisms: one learns one's own mother's tongue, and feral children cannot conceptualize if first exposed to language after reaching puberty; two, empirical evidence supports the view that the “knowing brain” is different architecturally from the “untutored” one. These intuitions warrant regarding man's cognitive apparatus as an evolutionary system, and the “mind” as an emergent property.