Theory of adaptation: application of symbolic logic

Abstract

The theory of adaptation takes up, first, completely symbolized expressions in which the basic element is the dyadic term Axy, x is adapted to y. When this is combined with a monadic term such as Ey, y is a moist environment, in ( y)( Axy⊃ Ey), validity can be achieved by reversal and denial (transposition): ( y)( A xy⊃ E y)≡( y)(∼ E y⊃∼ A xy). This provides a full and complete description when applied as follows: the North American forest x is adapted only to moist environments if and only if it is not adapted to any non-moist environments. Then dyadic–dyadic, monadic–dyadic–dyadic, and monadic–dyadic–monadic–dyadic combinations are presented and exemplified. The theory of adaptation takes up, second, incompletely symbolized expressions such as: (x)(Fx v Hx), (x)[(Fx⊃Gx)·(Hx⊃Ix)], ∴ (x)(Gx v Ix)′ , which provides the structure for this description of temperate insects: all undergo diapause or nondiapause; all, if undergoing diapause, are winter adapted, and if undergoing nondiapause, are summer adapted; therefore, all are winter adapted or summer adapted. The phrases winter adapted, G x, and summer adapted, I x, are incomplete symbolizations since they are brief versions of (∃ y)( W y· A xy), x is adapted to winter, and of (∃ y)( S y· A xy), x is adapted to summer. The brief versions, however, make elaborations and extensions of the basic formulation possible. The formulas of complete symbolization provide for affirmation or denial of adaptation or no decision. Thus, in addition to the example of the North American forest other examples are species of the lizard Anolis, each of which is well adapted in its niche but not well adapted outside its niche, the associations of the North American forest which are tall, densely packed and adapted in moist regions but short, scattered, and unadapted in non-moist regions, and species of Gilia which are adapted to their habitats unless these habitats are not adapted to them. Then in small-to-moderate forest gaps regrowth of prevalent, adapted primary species contrasts with the regrowth of unadapted, non-prevalent pioneer species. But it cannot be decided whether the lizard Anolis allogus in a smaller niche on Cuba is adapted to this or is not adapted to this when comparing it to Anolis oculatus in its larger niche on Dominica. The formulas of incomplete symbolization provide only affirmation of adaptation. Examples in addition to the diapause—nondiapause case are for diatoms which are dark or light adapted and ciliates which are myxotrophically or heterotrophically adapted. Then, evolutionary pathways to warm bloodedness of fish include being adapted to fast swimming in tuna fish, or northern distribution in lamnid sharks, or deep diving in swordfish. And finally four basic evolutionary pathways include anaerobic and aerobic photosynthesis and thus adaptation to the lighted planetary surface and include chemosynthesis in two ways and thus adaptation to the dark ocean floor.