George Bealer

Functionalism would be mistaken if there existed a system of deviant relations (an “anti-mind”) that had the same functional roles as the standard mental relations. In this paper such a system is constructed, using “Quinean transformations” of the sort associated with Quine’s thesis of the indeterminacy of translation. For example, a mapping m from particularistic propositions (e.g., that there exists a rabbit) to universalistic propositions (that rabbithood is manifested). Using m, a deviant relation thinking* is defined: x thinks* p iff x thinks m(p). Such deviant relations satisfy the commonly discussed functionalist psychological principles. Finally, a more complicated system of deviant relations is constructed, one satisfying sophisticated principles dealing with the self-conscious rational mind.

This is the only complete logic for properties, relations, and propositions (PRPS) that has been formulated to date. First, an intensional abstraction operation is adjoined to first-order quantifier logic, Then, a new algebraic semantic method is developed. The heuristic used is not that of possible worlds but rather that of PRPS taken at face value. Unlike the possible worlds approach to intensional logic, this approach yields a logic for intentional (psychological) matters, as well as modal matters. At the close of the paper, the origin of incompleteness in logic is investigated. The culprit is found to be the predication relation, a relation on properties and relations that is expressed in natural language by the copula.

This paper begins with a brief summary of the Self-consciousness Argument, developed in the author’s paper “Self-consciousness.” (This argument is designed to refute the extant versions of functionalism -- American functionalism, Australian functionalism, and language-of-thought functionalism.) After this summary is given, two thesis are defended. The first is that the Self-consciousness Argument is not guilty of a Fregean equivocation regarding embedded occurrences of mental predicates, as has been suggested by many commentators, including Mark McCullagh. The second thesis is that the Self-consciousness Argument cannot be avoided by weakening the psychological theory upon which Ramsified functional definitions are based. Specifically, it does no good to excise psychological principles involving embedded mental predicates. Why? Because functional definitions based on the resulting sparse theories are exposed to an interesting new family of counterexamples.