Frege’s Argument: Part 1



Here is a very simple, but I hope helpful, way of reconstructing Frege’s overall argument in On Sense and Reference:

1. It seems that identity statements (a = a; a = b) are either relations between the signs or the referent (the thing the sign refers to). 

2. But it’s not plausible to think that identity statements are relations between the signs.
Much of the time, our interest in identity statements is not plausibly thought of as being an interest in the signs themselves. The signs are vehicles to get to objects (either abstract or concrete) in the world. When we realize that the morning star is the evening star we have realized something about the world. 

Furthermore, signs are different from language to language, speaker to speaker, time to time, place to place, etc. 

3. Nor is it plausible to think that identity statements are relations between the referent. 
If they are relations between the referent, then they cease to be informative and a posteriori. They cease to be informative because all they wind up saying is that the referent is the referent. In other words, all identity statement become equivalent to a = a. The cease to be a posteriori for the same reason. 

4. Hence, there must be some other thing that identity statements are relating. 

5. Whatever it is that identity statements are relating it must be intermediate between signs and referents. 

6. Senses are intermediate between signs and referents. 
They are not the signs, since senses are what different language users grasp when they grasp the same thing by using different signs. 

They are not the referent for a couple reasons. First, senses can be intelligible even in cases where there is no referent (e.g. the sense of ‘the first baby born in 2100’ or the sense of ‘the son of Zeus’). Second, multiple senses can pick out the same referent. 

7. Hence, identity statements are relations between senses.
More carefully, informative identity statements of the form a = b relate two different senses to the same object. They, in effect, state that these two different senses are really about the exact same object.

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