Gottlob Frege · Mathematics
In ‘Über Sinn und Bedeutung’ (1892) Frege solved a puzzle about identity - how ‘the morning star is the evening star’ can be informative though both name Venus - by distinguishing the <em>reference</em> of an expression (the object it stands for) from its <em>sense</em> (the mode of presentation, the way the object is given). It founded the philosophy of language.
Frege begins his most famous essay with a small puzzle that turns out to be bottomless. Compare two identity statements. ‘The morning star is the morning star’ is trivial, knowable with your eyes shut, an empty tautology of the form ‘a = a.’ But ‘the morning star is the evening star’ - the bright body seen at dawn is the same body seen at dusk - was a genuine astronomical discovery, hard-won and informative, of the form ‘a = b.’ Yet both statements are about the very same object: the planet Venus. If a name simply stands for its object, and both names stand for Venus, the two statements ought to say the same trivial thing. They plainly do not. One is empty; the other extends our knowledge. How can two true identity statements about the same object differ so completely in cognitive value? Solving this, Frege saw, required a new distinction at the heart of meaning itself.
The relation between the two notions is orderly. The sense is a route to the object; the reference is the object the route arrives at. Grasp the sense and, if all goes well, you are led to the reference. Frege gives a lovely image: think of a telescope trained on the Moon. The Moon itself is the reference. The real optical image cast inside the telescope - objective, the same for every observer who looks through that instrument - is like the sense. And the fleeting picture on your own retina is like a private idea, which differs from person to person. The crucial point is that sense is not private. It is objective and shareable: everyone who understands ‘the evening star’ grasps the same sense, just as everyone using the telescope sees the same optical image. Different senses can lead to the same reference (two telescopes trained on one Moon), which is exactly what happens with the morning and evening star. And a sense may even be perfectly clear while failing to reach any reference at all - as we are about to see.
Frege pressed the distinction to a startling conclusion about whole sentences. If a name has both a sense and a reference, what are the sense and reference of a complete declarative sentence? Its sense, Frege said, is the thought it expresses - the objective content, the same thought whether stated in German or English, that we grasp when we understand it. But what does a sentence refer to? Frege’s answer is famous and bold: a sentence refers to its truth-value - to one of two objects, the True or the False. His argument is elegant. If reference is what we care about when we care about truth, then swapping any part of a sentence for something with the same reference should leave the sentence’s reference unchanged. Replace ‘the morning star’ with ‘the evening star’ in a true sentence about Venus, and it stays true; the thought changes (the sense differs), but the truth-value is preserved. What every true sentence has in common, and shares with no false one, is precisely its reference: the True. Sentences, on this view, are names of truth-values, and thoughts are their senses.
This is the opening of the lesson. The rest — the dialogue, the primary source, and the recall — is in the app.
You learned that Frege distinguished the Bedeutung (reference, the object named) from the Sinn (sense, the mode of presentation), explaining how identity statements like ‘the morning star is the evening star’ can be informative, and that a sentence’s reference is its truth-value while its sense is the thought it expre…
Leads to Gottfried Leibniz.
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