Verisimilitude and Shared Tests

Abstract

In rather similar ways Professors Miller and Tich' have denied that, given Popper's formulation of verisimilitude, one false theory may be a closer approximation to truth than its false competitor. In effect, the authors maintain that any increase in the truth content of the succeeding theory will be accompanied by a corresponding increase in the falsity content of that theory. Given this argument, Newton's theory could not, pace Popper, be said to possess more verisimilitude than Kepler's. The problem with Popper's formulation of the notion of verisimilitude, which allows for the sort of remarks proffered by Tichy and Miller, rests with the comparability of truth and falsity contents with respect to empirical content. In the course of this essay I shall endeavor to explain this problem and suggest a means for its circumvention. According to Popper, it may be said of two false but internally consistent competing theories with comparable truth and falsity contents that theory B a closer approximation to truth than theory A if and only if either the truth content, i.e., the true logical consequences, but not the falsity content, i.e., the false logical consequences, of B exceeds that of A, or when the falsity content but not the truth content of A exceeds that of B. More precisely, theory B possesses more verisimilitude than theory A if and only if B's falsity content a sub-set of A's falsity content while B's truth content not also a sub-set of A's truth content, or when A's truth content a sub-set of B's truth content while A's falsity content not also a part of B's falsity content ([3] and [4]). If I am correct, problems with Popper's notion of verisimilitude arise with respect to the phrase is not also a part of. These problems shall hopefully become evident as a result of the consideration of the arguments proffered by TichV ([ 5]) and Miller ([ 2]). If theory B false, then there a false statment, e.g., x, comprising part of the content of BAssuming that the truth content of theory A a sub-set of the truth content of theory B, there also a statement, e.g., y, which a member of the truth content of B which exceeds the truth content of A. Nonetheless, the conjunction of x and y belongs to the falsity content of B but not to the falsity content of A. Therefore, the falsity content of B 607