Naturalized logic and chain sets

Abstract

The natural sciences are differentiated from mathematics by the presence and absence, respectively, of the requirement of agreement with experience. The information sciences, headed by mathematical logic, straddle this boundary. Their truth content is determined by whether we consider them to be purely mathematical theories or theories that are adapted in the best possible way to the means of expression and the thinking apparatus with which nature has endowed the human brain. A comparison is performed from the standpoint of agreement with experience between traditional logic and chain-set logic. The latter combines a two-valued logic with a multiple-valued one by attaching possibility and probability values to chains consisting of 1's, 0's, and b's, corresponding to assertion, negation, and lack of information, respectively. A single chain-set array can represent and, or, and if … then connectives between many different items, as well as uncertain information. One of the most radical differences between chain-set versus traditional logic is the treatment of the if then connective. The Paris-Rome example shows that the chain-set treatment of this connective is nearer to a scientifically true theory than traditional logic. Quantification, tree-formed classification structures, and fuzzy sets are special cases of chain sets. Chain sets are easy to use, and they build a bridge between the fields of two-valued logic, fuzzy set theory and multiple-valued logic, probability theory, and set theory without fuzzifying any of them. They also allow an operational definition of the difference between Kant's synthetic (factual) and analytic (logical) truth.