The Gödel-Schmidt Case
If 'Gödel' just means 'the man who proved incompleteness,' and someone else did the proof, does 'Gödel' refer to that someone else?
Saul Kripke introduced this case in his 1970 lectures, published as Naming and Necessity in 1980, to demolish the description theory of proper names. It shows that names do not work like abbreviations for descriptions, and that reference is fixed through causal history, not through what speakers believe.
Kripke, S. (1980). Naming and Necessity. Harvard University Press.
The scenario
Most people who use the name "Gödel" cannot prove his incompleteness theorems. What they associate with the name is something like "the man who proved the incompleteness of arithmetic." On the description theory of names, associated with Frege and Russell, this description is what the name means: "Gödel" refers to whoever uniquely satisfies it.
Now suppose historians discover that the incompleteness proof was actually stolen from an unknown mathematician named Schmidt, who died without recognition. Schmidt did the proof. Gödel published it under his own name. On the description theory, "Gödel" should now refer to Schmidt, since Schmidt is the man who actually proved incompleteness. The sentence "Gödel proved incompleteness" would turn out to be trivially true and the sentence "Gödel was Austrian" would be a sentence about Schmidt.
This is the wrong result. We want to say that Gödel is Gödel regardless of what he did or didn't prove.
Why this refutes description theory
The description theory fails because names do not behave like disguised descriptions. When we say "Gödel proved incompleteness," we are talking about a particular person, the one baptized Gödel, the one whose name passed through a historical chain of use to us. We are not talking about whoever happens to satisfy a description we associate with that name.
The case generalizes. Most people associate "Einstein" with the theory of relativity, "Darwin" with natural selection, "Shakespeare" with Hamlet. If those associations could be wrong, the description theory would redirect these names to whoever actually did the relevant work. That strikes nearly everyone as absurd. The absurdity reveals that reference is not carried by descriptions in the speaker's head.
Rigid designation and causal chains
Kripke's alternative is that names are rigid designators: expressions that refer to the same individual in every possible world. "Gödel" picks out Gödel in every possible scenario, including ones where he never studied logic.
Reference is fixed through a causal-historical chain. Someone used the name in an original act of naming, either a baptism or a stipulation. Subsequent speakers picked up the name through their contact with that chain, through books, conversations, and documents. Each use inherits its reference from prior uses, tracing back to the original. The speaker does not need to know anything special about the referent; they just need to be connected to the right chain.
This picture shifts meaning from the inside of the mind to the history of use in the world, echoing the externalism of Putnam's Twin Earth, but through a different route.
Discussion questions
- When you use a historical name, what are you actually referring to?
- If you discovered that the historical figure you were thinking of was actually a different person than you thought, would your reference change?
- Does meaning depend on the speaker's intentions or on the actual history of how a word was used?
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