# Frege proof.

1. Jun 3, 2006

### MathematicalPhysicist

im searching for the philosophical proof of the next statement (according to my text the source is from frege):
if:
1)propsitons aren't complex singular terms (definite descriptions) and they are domain indicators for definite descriptions.
2)for equivalent singular terms there's the same domain indicator.
3) a singular term doesnt change its indicator. if a singular term is contained in/substituted by another with the same indicator;
then:
4) for all the propsitions with the same truth value there's the same indicator.

2. Jul 23, 2006

### NickJ

First, the use of "singular term" and "definite description" strikes me as odd: these are properties that terms can have (like nouns or pronouns).

Better to say (1) as: "Propositions are not sentences; but they are domain indicators for sentences".

This captures the fact that the same proposition can be expressed by different sentences (e.g., by an English sentence and a French one). The domain of what is talked about by a sentence is captured by teh proposition the sentence expresses.

Then (2) becomes: sentences that "are equivalent" express the same proposition.

Of course, this claim about equivalence needs to be made more precise. But let's ignore complications that might arise for sentences that contain indexicals and non-rigid designators and so on.

(3) is more clearly written as: if one sentence is replaced by a sentence that expresses the same proposition, then:

(4) the proposition retains its truth-value.

Now on to the main question: how to show that (4) follows from (1)-(3)?

a. Consider a sentence token "s". Suppose that "s" expresses the proposition "S", and suppose that "p" is a sentence-token that is "equivalent" to "s". (Example: let "s" = "Snow is white", "p" = (however one says "snow is white" in some other language", and "S" is the proposition that snow is white.

b. Suppose, for the sake of argument, that "s" is true. (We could give a parallel argument for the case in which "s" is false.)

c. Then "S" is true, since "s" expresses the proposition "S". (I take this to follow from the idea that (1) is trying to capture.)

d. Since "p" is equivalent to "s", "p" also expresses "S" (via (2)).

e. Since "p" is equivalent to "s", "p" is also true. (from whatever "equivalence" is supposed to mean?)

f. Hence, "S" is true, since "p" expresses the proposition "S". (I take this to follow from the idea that (1) is trying to capture.)

g. Thus, whenever "s" is replaced by "p" (as supposed by (3)), the proposition expressed by "s" retains its truth-value. (Follows from the above argument.) QED.

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Perhaps you are trying to show something different, namely, that whenever one term in a sentence is replaced by a term that refers to the same thing, the sentence retains its truth value.

This thesis is false. Example: It is true that Lois Lane knows that Clark Kent is Clark Kent, because (we can suppose that) she knows that everything is identical to itself. But Lois Lane does not know that Clark Kent is identical to Superman. Yet "Superman" and "Clark Kent" refer to the same person. QED.

Example 2: It is necessarily true that nine is greater than seven. But it is not necessarily true that the number of planets is greater than seven -- the number of planets might have only been three or six or one. But "nine" and "the number of planets" refer to the same thing, namely, how many planets there are in our actual solar system. QED.

Hope this helps!