The Evolution of Reason: Logic as a Branch of Biology

By William S. Cooper | Go to book overview

9
The Evolutionary Derivation
of Nonclassical Logics

There are respectable population models that are not logically classical. Such models give rise to evolutionarily stable logics, but the logics are nonstandard. The models are perfectly legitimate biologically, even though their logics involve departures from classical laws.

Three such models will be examined as case studies. Two of them (Models 5 and 6) have already appeared in the evolutionary literature in life-history tree form (Cooper 1981). One (Model 5) has also been analyzed in some detail in other papers (Cooper and Kaplan 1982; Kaplan and Cooper 1984), and has been reviewed in the context of related models (Godfrey-Smith 1996; Lomnicki 1988).


MODEL 5: A CHANGING ENVIRONMENT

Model 1 was a constant growth model. Each character-defined population of interest had a constant per-season rate of increase. Implicit in the constant growth supposition was the assumption that the environment does not change from season to season in ways that affect the growth rate. Such environments are said to be temporally homogeneous.

Dropping the temporal homogeneity restriction from Model 1 (but leaving everything else intact) produces a more general model, Model 5. In Model 5 the relevant environmental factors can change from season to season and the growth rate with them. Obviously the new model is capable of greater descriptive realism, for most real environments do fluctuate to at least some extent.

In Model 5 it will be assumed for simplicity that the environmental changes occur randomly through time. That is, knowing what the

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