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> No amount of just grinding out the digits and checking will ever prove it: there are always more digits to check. This guy doesn't know how mathematical proo

by 08-15 8y ago

> No amount of just grinding out the digits and checking will ever prove it: there are always more digits to check. This guy doesn't know how mathematical proofs work. If the above was close to reality, nobody could ever proof Fermat's major theorem, because there are "always more triples of numbers to check". > All Gödel did was find a clever way to construct a provably unprovable mathematical fact. That not what Gödel did, and certainly not all he did. Gödel demonstrated that number theory expressed in first order logic is incomplete, i.e. admits more than one model. He did that by constructing a statement that is true in the smallest model, but does not have a proof, because it is false in others. With these ignorant statements, Maudlin just reinforced my opinion that philosophers are simply professional bullshitters.

wwarner 8y ago
I don't know if it makes him ignorant, but I agree the statement sweeps the philosophical issues Gödel addressed under the rug. There were two major works of the 20th century that would never have been attempted if the authors had known of Gödel's proof. First, Whitehead and Russel's Prinicpia Mathematica, which attempted to "describe a set of axioms and inference rules in symbolic logic from which all mathematical truths could in principle be proven". The other was Wittgenstein's Tractatus, which was a similar attempt to provide a foundation for language. To be fair, Gödel's theorem didn't end scientific inquiry, and I'm sure that Maudlin knows about these titanic failures. I'd like to know what he thinks of them.
codeulike 8y ago
You're taking that bit out of context. In that sentence he's talking about a very specific thought experiment in which we constuct a theory that certain digits in the root of 17 and the 27th power of pi match. I think his arbitrary example is supposed to be an analogy of Godel's work. Example: let’s say that the decimal expressions of the square root of 17 and pi to the 27th power “match” just in case either they have the same digit in the tenths place, or the same two digits in the next two places, or the same three digits in the next three places, etc. The point of his example here is that the 'match' is defined in never-ending terms. If the 10th digit doesn't match, you check the next two. If they don't match, you check the next three. And so on. You can go on comparing digits forever, even though finding a 'match' becomes less and less likely.
- 08-15 8y ago
  Oh no, not at all. The context is the whole problem, because this is an awful analogy. Maudlin confuses "I think this proposition is false, but I don't know how to prove it." with "This proposition is neither true nor false and I can prove it.", and he does it because he doesn't know what Gödel's work is about. (Also, "I don't know a proof" is only equivalent to "There is no proof" if you're a pompous asshole that thinks you're smarter than everyone else. Learn some humility, Tim Maudlin.)

by 08-15 8y ago

wwarner 8y ago

I don't know if it makes him ignorant, but I agree the statement sweeps the philosophical issues Gödel addressed under the rug. There were two major works of the 20th century that would never have been attempted if the authors had known of Gödel's proof. First, Whitehead and Russel's Prinicpia Mathematica, which attempted to "describe a set of axioms and inference rules in symbolic logic from which all mathematical truths could in principle be proven". The other was Wittgenstein's Tractatus, which was a similar attempt to provide a foundation for language. To be fair, Gödel's theorem didn't end scientific inquiry, and I'm sure that Maudlin knows about these titanic failures. I'd like to know what he thinks of them.

codeulike 8y ago

You're taking that bit out of context. In that sentence he's talking about a very specific thought experiment in which we constuct a theory that certain digits in the root of 17 and the 27th power of pi match. I think his arbitrary example is supposed to be an analogy of Godel's work. Example: let’s say that the decimal expressions of the square root of 17 and pi to the 27th power “match” just in case either they have the same digit in the tenths place, or the same two digits in the next two places, or the same three digits in the next three places, etc. The point of his example here is that the 'match' is defined in never-ending terms. If the 10th digit doesn't match, you check the next two. If they don't match, you check the next three. And so on. You can go on comparing digits forever, even though finding a 'match' becomes less and less likely.

08-15 8y ago
Oh no, not at all. The context is the whole problem, because this is an awful analogy. Maudlin confuses "I think this proposition is false, but I don't know how to prove it." with "This proposition is neither true nor false and I can prove it.", and he does it because he doesn't know what Gödel's work is about. (Also, "I don't know a proof" is only equivalent to "There is no proof" if you're a pompous asshole that thinks you're smarter than everyone else. Learn some humility, Tim Maudlin.)