Wolfgang Schwarz

Experiments on Semantic Intuitions

A few more comments on why I think the setup of Weinberg, Nichols and Stich's experiments on intuitions is unfortunate. The problem seems particularly obvious in the experiments on semantic intuitions reported by Machery, Mallon, Nichols and Stich, but I think it carries over to many (though perhaps not all) of the experiments of Weinberg, Nichals and Stich. Here is one of the questions Machery, Mallon, Nichols and Stich asked:

Suppose that John has learned in college that Gödel is the man who proved an important mathematical theorem, called the incompleteness of arithmetic. John is quite good at mathematics and he can give an accurate statement of the incompleteness theorem, which he attributes to Gödel as the discoverer. But this is the only thing that he has heard about Gödel. Now suppose that Gödel was not the author of this theorem. A man called "Schmidt" whose body was found in Vienna under mysterious circumstances many years ago, actually did the work in question. His friend Gödel somehow got hold of the manuscript and claimed credit for the work, which was thereafter attributed to Gödel. Thus he has been known as the man who proved the incompleteness of arithmetic. Most people who have heard the name "Gödel" are like John; the claim that Gödel discovered the incompleteness theorem is the only thing they have ever heard about Gödel. When John uses the name "Gödel," is he talking about:

(A) the person who really discovered the incompleteness of arithmetic?

or

(B) the person who got hold of the manuscript and claimed credit for the work?

What would you answer?

What would you answer if instead of options (A) and (B) there was a text field in which you could enter your answer?

I would write something like "in one sense, John talks about the man who proved the incompleteness theorem. But there is also a sense in which he talked about the man really called 'Gödel'." Or maybe I would answer "it depends." I really don't have any strong intuitions about the case, in particular as the question is put in terms of "talking about". Even a proponent of the causal theory of reference could admit that there is a sense in which John, claiming that "Hilbert's programme was shattered when Gödel proved the incompleteness of arithmetic", talks about the man who proved the incompleteness of arithmetic.

If many people are like me, and would choose (A) or (B) more or less at random because they believe the answer isn't clear, the result of the experiment will look like there are important differences in intuition even if there are no such differences at all.

I suspect that if there was a free answer field, or more options like "both answers are ok" and "it depends", the results would be much less interesting.

PS: Notice that the presented text contains sentences like "Now suppose that Gödel was not the author of this theorem" which presuppose that "Gödel" doesn't denote the author of the incompleteness theorems. These sentence are taken more or less directly from Kripke. Now I agree with Lewis and Jackson that the intension of names is far less determinate than often assumed, so that if someone's utterances presuppose one resolution of the indeterminacy, we usually follow that resolution. If that is right, then philosophers generally agree with the judgments of Kripke (and Putnam) only because Kripke (and Putnam) never put their thought experiments in neutral terms.

This would be worth testing, and it suggests an even better setup than directly asking people about reference or aboutness. The idea would be to present subjects at random with one of two texts, presupposing different determinations of reference:

1) Read the following text carefully once, then answer the questions below it without looking back at the text.

In 1930, Kurt Gödel proved two important mathematical results, known as Gödel's incompleteness theorems. The first incompleteness theorem says that some truths of mathematics are not mathematically provable. According to the second theorem, one cannot prove mathematically that "0 = 1" is not mathematically provable. These results came as a big shock to many logicians and mathematicians, and their proof is so ingenious that Gödel has often been called the greatest logician since Aristotle. About himself very little is known, though. He lived in Vienna in the 1920s, where he was murdered by Soviet agents in 1930, shortly after finishing his manuscripts. His real name wasn't actually "Gödel", but "Schmidt". It is not entirely clear why his manuscripts were published under the name "Gödel". Recent evidence suggests that there was another logician in Vienna at the time called "Gödel", who published Gödel's theorems under his own name to help his careeer. However, the plan didn't work out: this other logician was himself murdered by fascists shortly afterwards in 1932.

Question 1: What does Gödel's second incompleteness theorem show?
Question 2: Kurt Gödel has been called the greatest logician since -- whom?
Question 3: Who murdered Gödel?

2) Read the following text carefully once, then answer the questions below it without looking back at the text.

Two of the most important theorems in modern logic are known as "Gödel's incompleteness theorems". The first incompleteness theorem says that some truths of mathematics are not mathematically provable. According to the second theorem, one cannot mathematically prove that "0 = 1" is not mathematically provable. These results came as a big shock to many logicians and mathematicians. Recent evidence shows that they weren't really proven by Kurt Gödel, an Austrian logician, but by one of his colleagues, Karl Schmidt, who was murdered by Russian agents in 1930, shortly after finishing the manuscripts. Apparently Kurt Gödel got hold of the manuscripts and published them under his own name to help his career. So Schmidt's results came to be known as "Gödel's incompleteness theorems", and Gödel, who wasn't such a good logician at all, was praised as the greatest logician since Aristotle. He didn't live long to enjoy his fame, though: he himself was murdered by fascists in 1932.

Question 1: What does the second incompleteness theorem show?
Question 2: Kurt Gödel has been called the greatest logician since -- whom?
Question 3: Who murdered Gödel?

If Lewis and Jackson are right about this case, people might give different answers to question 3 depending on which version of the story they read, showing that they take "Gödel" to refer to the man really called "Schmidt" in the first case, but to the man called "Gödel" in the second.