(A) Frege's theory is Russellian;
(B) Frege is inconsistent in attributing senses to empty singular terms.
A.
- Meaning, according to the later Frege, has two aspects: reference and sense.
- The meaning of a complex expression is a function of the meaning of its parts.
- The reference of a singular term is its referent; the reference of a
sentence is its truth-value. So a truth value is a referent (and, for Frege, a sentence is a species of name). - The sense of a singular term is the mode of presentation; the sense
of a sentence is the thought it expresses: a mode of presentation of a truth value. - A sentence expresses a thought only if the singular term it contains
has a referent. (p.12) [Not sure who thinks this or why. Do you regard it as a consequence of (4) plus the general idea that there is no mode of presentation without an object presented? If so, the argument could proceed more swiftly.] - A sentence has a truth-value only if it expresses a thought. (p.12)
- Hence, a sentence containing an empty singular term does not express
a thought, and it has no truth-value either. - That is, a sentence containing an empty singular term has neither a
sense nor a reference; it is meaningless. - 9. A theory of meaning is Russellian if it is a view that 'someone who
uttered a sentence containing an empty singular term would fail to say
anything, in the sense that he would fail to express a thought.' (p.12)
- Hence, Frege's theory of meaning is Russellian. [from 8,9]
B. - An empty singular term has a sense.
- The sense of a sentence is the thought it expresses.
- The sense of a sentence is a function from its parts.
- Hence, a sentence containing an empty singular term has a
sense. [from 11,12,13] - Hence, a sentence containing an empty singular term expresses a
thought. [from 12, 14] [[15 contradicts 7]] - A determinate thought has a truth-value. (p.24?) [Not sure where this comes from. As Frege says that a sentence containing an empty name expresses a thought but has no truth value, this seems an easy way to make Frege out to be inconsistent!]
- A sentence containing an empty singular term has a
truth-value. [from 15, 16] - A sentence containing an empty singular term has no truth-value.
[from 7]
- Hence, Frege is inconsistent in attributing senses to empty
singular terms. [[17 contradicts 18]]
Russellain: the view that someone who uttered a sentence containing an
empty singular term would fail to say anything, in the sense that he
would fail to express a thought. p.12
Russellain singular term: a singular term whose significance depends
upon its having a referent. p.12
Q:A singular term without a referent can still be significant-- it has
a sense.
A: An empty name with a sense is just inconsistent!
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