Sunday, October 15, 2006

Preliminaries on how to make a Kettle of Fish without the kettle or the fish.

As stated in the post (and broken up), on Frege’s view, sentences of the form:

(1) a = b

and

(2) s believes that a is F

do not imply

(3) s believes that b is F

This is because, as also mentioned in the post, according to Frege, once a proper name (the ‘a’ or ‘b’) is used within the scope of an intentional verb it is to be thought of as being connected to the reference of the sign and the sense of the sign. Or, as put by Frege:

“It is natural, now, to think of there being connected with a sign (name, combination of words, letter), besides that to which the sign refers, which may be called the reference of the sign, also what I should like to call the sense of the sign, wherein the mode of presentation is contained.”(p.24)

But why do we need to have such a complicated explanation of a sign or proper name within the scope of an intentional verb? Why do we need both sense and reference?

On Frege’s view, when evaluating a sign within an intentional context a very complicated reaction is taking place in which the sign corresponds or expresses its sense, which stands for or designates its reference. But this is not all:

“We are therefore driven into accepting the truth value of a sentence as constituting its reference. By the truth value of a sentence I understand the circumstance that it is true or false. … Every declarative sentence concerned with the reference of its words is therefore to be regarded as a proper name, and its reference, …is either the True or the False.”(p.29)

So, this means that, the sense (or mode of presentation) of ‘a’ in (2) is not necessarily the same as the sense of ‘b’ in (3). The mode of presentation of (2) can be different than (3), for Frege. And, in effect you can have different truth values for (2) and (3).

For Frege the inference in the SI or paradox case is not false, it is invalid. The truth of (1) and (2) does not imply or transfer to (3). In other words, one is a different kettle of fish than the other and should therefore not be eaten together. So, according to Priest’s analysis, Frege avoids the problems presented by SI because, ‘a’ and ‘b’ in statements (2) and (3) are not interchangeable because their senses are different. He then concludes that: “(In a sense then, the failure of SI is merely syntactic, since we are not dealing with co-referring expressions.)” (p.40)

Loosely Frege does reject a syntactic version of SI in intentional contexts, but not all contexts. And because it is not in all contexts, the conclusion of Priest on behalf of Frege that ‘we are not dealing with co-referring terms’ is a little hasty and is far too simply put to capture what Frege’s view really is.

Priest seems to be half heartedly agreeing that we should reject a syntactic version of SI. But why? I believe part of the answer can be found in footnote 9 on p. 41 of Priest, in which he finds difficulties with accounts “which makes it impossible for a variable to bind inside and outside an epistemic context simultaneously in the natural way.” This is what he sees as the one of the unfortunate conclusions facing Frege’s account. As he illustrates with the inference and conclusion found on p. 41. According to Priest, on Frege’s view, one cannot maintain a person as an individual concept. (As a side note, I think this is a great misinterpretation of Frege’s view, and that perhaps a different take on both the account as a whole and the particular section in which he discusses subordinate clauses might change and in fact help Priest in constructing a solution to the SI problem.)

So, part of Priest’s view is that he wishes have variables that bind both inside and outside an epistemic context simultaneously. He rejects a syntactic version of SI, because he does not want co-referring expressions. If they are co-referring then the variable contained therein cannot be bound both inside and out simultaneously. The key word here, simultaneously. As he later explains he wishes to have “cases of true sentences where one quantifies into an intentional context, but where no instantiation is to be found.”(p. 43). And the only way for him to do this is to have substitutional quantification in both ordinary and intentional contexts. You cannot have substitutional quantification if the expressions are co-referring.

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