The deduction theorem and ecology

Abstract

The deduction theorem is based primarily on the formula [A superset of (B superset of C)] superset of [(A superset of B) superset of (A superset of C)]. The fisheries of Newfoundland, Iceland, and west Greenland have three aspects, a first aspect of abundance of cod or herring, aspect A, a second aspect of overfishing or overfishing plus hydrographic change, aspect B, and a third aspect of collapse of the cod-herring fishery or shift to shrimp, aspect C. Each aspect implies, connects to the next either in [A superset of (B superset of C)] sequence or in the [(A superset of B) superset of (A superset of C)] double sequence. The Mississippi River system has three parts, the drainage area of the inner U.S.A., part A, the plankton-rich, low salinity plume to the west of the Mississippi delta, part B, and the oxygen-depleted near-bottom layer of the plume, part C. These parts are connected, as shown by the implication connective, superset of . There are two indirect applications of the deduction theorem. The first is three aspects of hotspots, each hotspot being a region having a set of many indigenous species and having set of endangered species, the two sets being identical by having all the same species (the principle of extensionality). The second indirect application is three logically valid formulas that describe most of the natural world. A is contraposition, an example of which is: a vertebrate is adapted to year-round temperate temperature if it is functional (active) year-round; if and only if a vertebrate is not adapted to year-round temperate temperature only if it is not functional (not active) year-round. B is equivalence, an example of which is: if a North American bird species is adapted to its area, then its area is adapted to it, and if its area is adapted to the species, then the species is adapted to its area – equivalent to: species is adapted to area if and only if area is adapted to species. C is constructive dilemma, an example of which is: all insects are in diapause or non-diapause condition; all insects, if in diapause condition, are winter adapted; and all insects, if in non-diapause (winged) condition, are summer adapted: therefore, all insects are winter adapted or summer adapted. The three logically valid formulas, contraposition, equivalence, and constructive dilemma are thus parts of the larger logically valid formula of the deduction theorem. The empirical data, of considerable value in themselves, become of very great value when inserted into the validity formulas, which seem of limited value without the empirical input. Thus the intent of this several-layered study is just to probe into the underpinnings of nature and to attempt to create some order in our perception of these underpinnings.