Radical Reductionism in Logic
By now it should be clear that biology has something to do with logic. But the Reducibility Thesis implies something stronger than that, namely, that biology is all there is to logic. The latter position I shall call radical reductionism. Radical reductionism in logic regards logic as completely reducible to biology with no leftovers. (Caution: The term radical reductionism refers here to radical evolutionary reductionism in logical theory. It is to be distinguished from the historical radical reductionism of Hume, Locke, and Carnap. Although there may be some common ground, the present theory departs sharply from earlier reductionist systems in regarding logic as itself reducible. )
Radical reductionism is an extreme position. There may be consistent philosophies of logic that are less extreme while still preserving some role for biology. The extreme philosophy is presented here with the idea that it is important to understand reductionism in its pure form before introducing compromises. It can then be decided more intelligently what compromises are called for, if any.
The claims of radical reductionism raise profound questions about what logic is and what systems of logic should be expected to accomplish. It might have been possible to ignore the hard questions if only the same laws of logic were obtained whether one started out from biology or from a more traditional starting point. But that is not the situation in which we find ourselves. It has become evident that some perfectly acceptable evolutionary models give rise to logics that are significantly nonclassical. The question of how these nonclassical logics are to be regarded brings matters to a head. It would appear that radical reductionism and classicism are in direct conflict (Cooper 1989).