Popper's verisimilitude is the excess of truth content over falsity content. It is shown that his measures of truth and falsity content are at variance with his respective concepts. It is further shown that both his actual measure of verisimilitude and measures based on measures of truth and falsity content consistent with his definition of the concepts, have undesirable properties. Moreover, any measure of verisimilitude based solely on content and truth value does not capture the notion of closeness to truth. A new concept of verisimilitude is proposed, based on a metric in the space of state descriptions.
1, STATE DESCRIPTIONS, RANGE AND CONTENT, AND LOGICAL PROBABILITY
We define a state description (SD) as the strongest (most informative) consistent statement in a language system. It suffices here to consider the simplest example of a language system, a sentential calculus with n primitive sentences.
A SD then is a conjunction of the n primitive sentences, each of' which may or may not be preceded by a negation sign. There are N = 2 n SDs. Any two SDs are incompatible. Given a statement a, there is the set of SDs with which it is compatible, its range; and the set of SDs with which it is incompatible, its content. A statement is logically equivalent to the disjunction of the SDs in its range. The range of a tautology is the universal set, its content the empty set; the range of a contradiction is the empty set, its content the universal set.
Logically equivalent statements have the same range and the s~tme content. In this article we consider statements as represented by their range', or content, i.e. we consider logically equivalent statements as identical, we do not care for their formulation.
Exactly one SD in the language system is true, for which we write 't'. A statement is true if t is in its range.
A measure of the range of a statement a is a logical probability p(a); Theory and Decision 8 (1977) 369-375. All Rights Reserved.