Notes on Frege
Pete Mandik
(Much of the following is quote and paraphrase from A.W. Moore ed. Meaning and Reference)
Frege draws a distinction between sense and reference.
He introduces the distinction in terms of names: singular noun-phrases that are used to refer to particular things. A name's reference is whatever the name refers to. "The positive square root of 16" refers to 4. "Plato" refers to a particular human being, who, happened to be a student of Socrates and a teacher of Aristotle.
When you know what the reference of a name is, you know as much about the name as is directly relevant to the truth or falsity of any declarative sentence in which the name occurs. (Note, then, the close connection between the notions of reference and truth value (truth or falsity).)
Declarative sentences are the sorts of sentences that can be true or false. An example would be "George has a towel". An example of something that would not be a declarative sentence would be the command "George, bring me a towel".
To sum up Frege's position on reference of names
The reference of a name is
Frege argues that knowing the reference of a name is not the same as understanding the name. To understand a name, more is needed: one must grasp its sense.
One of the key arguments for the thesis that understanding a name involves something more than knowing its reference hinges on the informativeness of some identity statements. Identity statements take the general form common to the following examples;
Note that of the example 1-5 only 2-4 are informative identity statements: learning the truth of anyone of them could count as learning something new, gaining a new piece of information.
Part of the argument for sense involves pointing out that if knowing a name's reference was all there was to understanding a name, then we would have no explanation of why identity statements like 4 can be informative while identity statements like 5 cannot.
Note, however, that thus far all the argument shows is that something beyond reference of a name is needed. It has not yet been established that the something more is Fregean sense.
Nonetheless, this seems to be Frege's main motive for introducing senses.
So, first and formost, senses are supposed to help explain the informativenes of identity statements. What else, according to Frege, are senses supposed to be?
To sum up Frege's position on senses of names
a sense of a name
re: 3) the sense of a name determines its reference. That is, two names with the same reference can have different senses, but two names with the same senses cannot have different references. (Is this true? Can you think of any counter examples? Later in the semester we will see Putnam attempt to provide counter examples.)
re: 4) Frege gives as examples of different modes of presentation thinking of one and the same point as either 'point of interesection of a and b' and 'point of intersection b and c'. Why couldn't these differences be cashed out in terms of the differences of the references of the names (and other terms) used in the different descriptions? Note that the name 'a' appears in the first but not the second and 'c' in the second but not the first.
[Note the problem, raised in class by Warren MacDonald, that arises when considering 4 and 5: it is not entirely clear that they are cinsistent with eachother.]
Frege on Senses and References of entire sentences.
Starting on p. 28 is Frege's discussion of the senses and references of entire (declarative) sentences
Frege begins by asserting that sentences contain thoughts. He begins his arguments by wondering whether the contained thought should be regarded as sense or reference. He argues that the thought is the sense of the sentence. The argument goes like this (p. 28):
Assume that a sentence has a referent. Change one of the names for another with the same reference (eg. Switch Mark Twain with Sam Clemmons). This does not result in changing the referents of ay part of the sentence, thus it cannot, says Frege, change the referent of the sentence of the whole. But obviously the thought has changed. So therefore what has changed is sense. So the thought contained by a sentence is identical to the sense of an entire sentence.
(Note how the form of Frege's argument is similar to the one concerning the informativeness of identity statements: Something more than reference is needed, therefore that something is sense)
After having argued that the senses of sentences are thoughts, Frege turns to the question of what, if anything, the referent of an entire sentence might be. First off, Frege argues that there has to be more to the sentence than its sense. Then he goes on to conclude that the something more must be its reference. That's what seems to be going on on pp28-29. Further, Frege argues, this questing for something more arises "when and only when we are inquiring after the truth value of the sentence." Then, Frege makes the leap to saying "we are therefore driven into accepting the truth value of a sentence as constituting its reference".
Part of the argument for this last statement is by eliminating other possibilities. For instance, on p. 30, Frege argues against treating the relation of the thought to theTrue as the relation of subject to predicate.
One of the implications of treating the truth value of a sentence as its reference is what I will call "principle P"
Principle P: changes of reference of parts of the sentences should not affect the reference of the whole.
On p. 30 Frege says that this is indeed the case when the parts in question are names. On p. 31 he turns to consider the case in which the parts in question are themselves sentences. Will these cases be sources of counterexamples to Frege's claim? Frege will say "no". He starts off by noting that trouble is to be expected when the embedded sentences in question are involved in quotation (both direct and indirect).
This is obvious. Consider:
1 may be true while 2 false even though George both stinks and smells. Likewise for indirect quotation as in
These are not genuine violations of principle P since "the words do not have their customary reference. . . .In direct quotation, a sentence designates another sentence, and in indirect quotation a thought" p. 31
From here to p. 34 Frege examines cases in which "the words of the subordinate clauses had their indirect reference, and this made it clear that the reference of the subordinate clause itself was indirect, i.e. not a truth value but a thought, a command, a request, a question. The subordinate clause could be regarded as a noun, indeed one could say: as a proper name of that thought, that command, etc., which it represented in the context of the sentence structure."
And then on p. 34, Frege turns to consider "other subordinate clauses, in which the words do have their customary reference without however a thought occurring as sense and a truth value as reference."
P: 35 ". . .languages have the fault of containing expressions which fail to designate an object . . .because the truth of some sentences is a prerequisite"
On p. 36, Frege considers adjective and adverbial clauses that are logically similar to the noun clauses previously discussed. . .
On p. 39, Frege sums up:
"The subordinate clause. . .no grammatical obstacles."
Then, on 39, Frege turns to clauses that "do not fit well into these categories. The reason, so far as I can see, is that these subordinate clauses have no such simple sense." This is due to our subjective reactions seeming to be part of the sense of the sentence.
P. 42 frege sums up his discussion of the clauses: "It is hard to exhaust all the possibilities given by language; but I hope to have brought to light at least the essential reasons why a subordinate clause may not always be replaced by another of equal truth value without harm to the truth of the whole sentence structure. These reasons arise. . ."
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Summing up. . .
Senses of sentences
1) The sense of a sentence is the thought contained in the sentence
2) A thought is not the subjective performance of thinking but its objective content, which is capable of being the common property of several thinkers p. 28 fn 7
Referents of sentences
1) The reference of a true sentence is the True. The reference of a false sentence is The False.