1908-2000 AD Willard van Orman Quine [WMQTR]

Stanford Encyclopedia of Philosophy link

Interview by Bryan Magee

Quotes from Willard van Orman Quine:

Word and Object, p. 142.”When a singular term is used in a sentence purely to specify its object, and the sentence is true of the object, then certainly the sentence will stay true when any other singular term is substituted that designates the same object. Here we have a criterion for what may be called purely referential position: the position must be subject to substituitivity of identity.”

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On the statement Cicero believes “Catiline saw the evening star.”

(I’m constructing an example for my purposes, for I want an example with belief and 2 definite descriptions – really I only need 1 description).

I think Quine used the example more regarding modal logic – that does not matter here.

Quine, in word and object (and elsewhere) would say that since “the evening star = the morning star.”, we should be able to infer:
Cicero believes “Catiline saw the morning star.”

But, in fact, Cicero might not believe this. (I realized they are expired – but this is hypothetical anyway.)

Quine bases this inference on substitutivity of identity. (word & object, p. 142).

But really “the evening star = the morning star” in Principia Mathematica is (according to definitions) (See PM *14.03)
(let Fx = x is an evening star & Gx = x is a morning star.)

(Eb)((x)(Fx equ x = b)) & (Ec) ((x) Gx equ x = c) & b = c)

Now this is not of the form of identity statement to which substitutivity of identity applies. That is x=y where x and y are singular terms.
The identity statement involving descriptions must be analyzed.

If this were not true, then “On Denoting” would not have solved Russell’s puzzle about George IV and the author of Waverley.
See Collected Papers of Bertrand Russell Vol 4. p. 414.)
Note: It is believed Bertrand Russell used this example because his grandparents used to make fun of George IV, rather than any significance of Sir Scott.

If one could substitute “Sir Scott” for “the author of Waverley” in “George IV wondered whether Sir Scott was the author of Waverley,” then “On Denoting” would not have achieved Bertrand Russell’s purpose. Bertrand Russell did not think George IV had such an interest in the law of identity.

Most similar problems can be solved by using definite descriptions such as:
the thing meant by the name n by person p at time t.
This is how such names should be analyzed.
This does not mean people consciously think of this.
Also one might need:
the universal meant by the predicate f by person p at time t

I think it is really even more complicated.
One must distinguish objects, mental symbols, words, tokens of words, etc.

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From Introduction to Mathematical Philosophy by Bertrand Russell, p. 12.

“A class or collection may be defined in two ways that at first might seem like something quite distinct. We may enumerate its members, as you say, “The collection I mean is Brown, Jones, and Robinson.” Or we may mention a defining property, as when we speak of “mankind” or “the inhabitants of London.” The definition which enumerates is called definition by “extension,” and the one which mentions a defining property called a definition by “intension.” Of these two kinds of definition, the one by intension is logically more fundamental. This is shown by two considerations: (1)that the extensional definition can always be reduced to an intensional one; (2) that the intensional one often cannot even theoretically be reduced to the extensional one.”

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“Necessarily (the Evening Star = the Evening Star)”

Susan Haack takes this example up on Kindle location 1326 of Philosophy of Logics.

But really “the evening star = the evening star” in Principia Mathematica is (according to definitions) See Principia Mathematica *14.03
(let Fx = x is an evening star)

(Eb)((x)(Fx equ x = b)) & (Ec) ((x) Fx equ x = c) & b = c)

But this is not true unless the evening star exists, so it is not necessarily true.

I think all Quine’s objections to modal logic rest on this sort of error.
I have not, of course, had time to review all his objections.

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On extensional vs. intensional interpretation of predicates

But really “the evening star = the morning star” in Principia Mathematica is (according to definitions) See Principia Mathematica *14.03
(let Fx = x is an evening star & Gx = x is a morning star.)

(Eb)((x)(Fx equ x = b)) & (Ec) ((x) Gx equ x = c) & b = c)

This is an empirical fact, but if predicates are interpreted extensionally, then F = G.
Then F may be substituted for G and it is not a significant statement.
For it to be significant, predicates must be interpreted intensionally.

Correction (3/19/2018) – It would have the significance that either existed.

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On “Necessarily (the number of planets > 7).”

Since 9 > 7, by substitutivity of identity, Quine says it follows:

Necessarily (the number of planets > 7)

But there are two ways the scope of the definite description can be interpreted:

Necessarily (Ex)(y)((y numbers the planets equ x = y) & x > 7)

Which is false – but that is not a problem.

(Ex)((y) (y numbers the planets equ x = y) & Necessarily (x > 7))

Which is true & is not a problem.

As both Quine and Russell thought names should be replaced by definite descriptions (although Russell allowed logically proper names).
It is not unfair to exclude names from consideration.

This is discussed (a little differently)by Haack – Philosophy of Logics, location 3991 in kindle)

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Quine is searching for a rabbit.

I remember (or seem to) that both Quine & Wittgenstein bringing up “searching” as problematic for analysis.
It cannot be analyzed as:
(Ex)Quine is searching for x & x is a rabbit.
Quine is not searching for any particular rabbit.

But I think.
Quine wishes that Quine finds x & x is a rabbit.
works.

It does involve a propositional attitude, so perhaps that is why Quine had difficulty with it.
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