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LINGUISTIX&LOGIK, Tony Marmo's blog
Wednesday, 13 April 2005


Unexpected Substitutions

Context: The facts below (seem to) show that if (OP1) and (OP2) hold, they do not suffice, for they can only to account for the cases of unsuccessful substitutions, and the successful cases remain unexplained:

(OP1)Opaque context (classic version)
A sentential context φ containing an occurrence of a term t is opaque, if the substitution of co-referential terms is an invalid mode of inference with respect to this occurrence. (See Mckinsey 1998, Quine 1956)

(OP2)Church’ Substitutability of Identicals
Things are identical if the name of one can be substituted for that of the other without loss of truth.

Failure in Transparent Contexts

The first argument against the strict association between substitutability and opacity is that even in certain transparent contexts, i.e., where no propositional attitude is reported, the application of the substitutability principle does yield odd results. This evidences that one thing is independent from the other.
Consider the famous Fregean examples: since Venus has is styled Venus, morning star and evening star, the three expressions should be perfectly inter-exchangeable in a transparent context. But, if one takes the sentence (1a) and substitutes the evening star for Venus, the result (2b) is odd:
(1)a. Venus appears in the morning.==>
b. #The evening star appears in the morning.

An interpretation of Frege’s work traditionally attributes the oddity of (1b) to the sense versus referent distinction. Regardless of how to characterise it in theoretic terms of a semantic framework, it is clear that what is in question is not whether (1b) can be inserted into a believe clause, but the very presence of the adjective evening that modifies star in contradiction to the predicate appears in the morning.
Indeed there are numerous analogous examples that show called impossible syllogisms in transparent contexts, involving what is herein:
(2)a. Lepidopterans (can) fly.
b. Caterpillars are Lepidopterans. ==>
c. ƒ Caterpillars (can) fly.

In (2) there is no obvious evidence of a (hidden) propositional operator. Rather, what happens to (2) reflects revision of information and the defeasibility property of natural languages. Accordingly (2) states a default rule for the class of Lepidopterans, the exception being the stage of their lives when they are caterpillars. In other words, (2) is susceptible of reviewing, as most statements in natural languages. This same reasoning can be applied to sentences containing proper nouns, like (3):
(3) a. Captain Marvel looses his super-strength and his capacity to fly when he says the magic word.
b. Billy Batson is Captain Marvel. ==>
c. ƒ Billy Batson looses his super-strength and his capacity to fly when he says the magic word.

Sentence (3c) is the wrong depiction of the Comics book mentioned, since Billy Batson actually gains super-strength and the capacity to fly when he says the magic word (and consequently transforms into Captain Marvel).
Of course, in comparison, (6) cannot be explained solely in relation to defeasibility, although one could think of a context where it its uttered as a consequence of someone’s astronomical discovery, which forced him to review his former beliefs respecting the stars. The oddity of (6) has to do with issues of consistency, wherefrom one concludes that there is at least another fundamental semantic property involved.
Anyway, the examples above suffice to show that restrictions on substitutions transcend the case of propositional attitude ascriptions.

Non-Uniformity of Results in Opaque Contexts

The second argument is against the idea that attitude ascriptions always block Leibniz’ substitutability. Indeed, the substitution tests do not uniformly yield false results in all opaque context. On the contrary, some substitutions might yield even true results. Let us give one initial example, where the same object is designated by different names. Yet none of the possible alternative names or expressions to designate the same object changes the truth of the statement:
(4) Every visitor to the Louvre intends to see the Mona Lisa/ La Gioconda/ da Vinci’s most famous painting.

Of course, there are some tricks to make unlikely substitutions work. For instance, a true sentence like even Jameson believes that Peter Parker is a mere photographer does not normally yield a true result, if, as in (5a), one substitutes Spiderman for Peter Parker. But in a context like (5b) the substitution preserves the truth:
(5) a. ƒ Even Jameson believes that Spiderman is a mere photographer.
b. T The disguise is so convincing that even Jameson believes that Spiderman is a mere photographer. (See Berg 1988, Mckinsey 1999)

Posted by Tony Marmo at 01:05 BST

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