quantifying in use of a quantifier outside of an opaque construction to attempt to bind a variable within it, a procedure whose legitimacy was first questioned by Quine. An opaque construction is one that resists substitutivity of identity. Among others, the constructions of quotation, the verbs of propositional attitude, and the logical modalities can give rise to opacity. For example, the position of ‘six’ in: (1) ‘six’ contains exactly three letters is opaque, since the substitution for ‘six’ by its codesignate ‘immediate successor of five’ renders a truth into a falsehood: (1H) ‘the immediate successor of five’ contains exactly three letters. Similarly, the position of ‘the earth’ in: (2) Tom believes that the earth is habitable is opaque, if the substitution of ‘the earth’ by its codesignate ‘the third planet from the sun’ renders a sentence that Tom would affirm into one that he would deny: (2H) Tom believes that the third planet from the sun is habitable. Finally, the position of ‘9’ (and of ‘7’) in: (3) Necessarily (9 ( 7) is opaque, since the substitution of ‘the number of major planets’ for its codesignate ‘9’ renders a truth into a falsehood: (3H) Necessarily (the number of major planets ( 7). Quine argues that since the positions within opaque constructions resist substitutivity of identity, they cannot meaningfully be quantified. Accordingly, the following three quantified sentences are meaningless: (1I) (Ex) (‘x’ ( 7), (2I) (Ex) (Tom believes that x is habitable), (3I) (Ex) necessarily (x ( 7). (1I), (2I), and (3I) are meaningless, since the second occurrence of ‘x’ in each of them does not function as a variable in the ordinary (nonessentialist) quantificational way. The second occurrence of ‘x’ in (1I) functions as a name that names the twenty-fourth letter of the alphabet. The second occurrences of ‘x’ in (2I) and in (3I) do not function as variables, since they do not allow all codesignative terms as substituends without change of truth-value. Thus, they may take objects as values but only objects designated in certain ways, e.g., in terms of their intensional or essential properties. So, short of acquiescing in an intensionalist or essentialist metaphysics, Quine argues, we cannot in general quantify into opaque contexts.
See also INTENSIONALITY , MEANING , SUB- STITUTIVITY SALVA VERITAT. R.F.G.