FORMALISATIONS OF EVOLUTIONARY BIOLOGY

Publisher Summary A formalization of a theory is an abstract representation of the theory expressed in a formal deductive framework for which there is a complete specification of what constitutes a well-formed-formula (wff) and all the permissible rules of inference. In the early part of the 20th-century, formalization in science was virtually synonymous with the representation of a theory in first-order predicate logic with identity. In the latter part of the 1960's, an alternative conception was developed in which theories were represented in set theory or in a state space. This conception was widely called “the semantic conception.” It builds on earlier work on modeltheoretic semantics of formal systems. Consequently, a theory can be formalized in first-order predicate logic with identity, in set theory, in matrix algebra and, indeed, any branch of mathematics that satisfies a wff and all the permissible rules of inference. The label “semantic conception” captures the rejection of the logical empiricist method of providing semantics but it does not reflect fully the rejection of first-order predicate logic as the appropriate formal calculus.

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