5 ms·

> which is to say, in a manner that Godel expressed far more clearly, that all logical systems, all systematic programs, contain elements that cannot be contain

by kbrkbr 2y ago

> which is to say, in a manner that Godel expressed far more clearly, that all logical systems, all systematic programs, contain elements that cannot be contained in the system Wikipedia [1] summarizes better than I could: "The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e. an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency." That's seems a bit different than what you stated, to me at least. [1] https://en.m.wikipedia.org/wiki/G%C3%B6del%2527s_incompleteness_theorems https://en.m.wikipedia.org/wiki/G%C3%B6del%2527s_incompleten...

moefh 2y ago
Indeed. Godel's theorem is very technical, and any use outside the very technical realm of its immediate application should be viewed with great suspicion. For example, if you take the statement you quoted from Wikipedia and replace "natural number" with "real number", it doesn't work anymore: it's been proven that the arithmetic of real numbers is decidable[1]. That means that the sentence you quoted from OP's comment is not true. Anyone inclined to use Godel's theorem in these philosophical contexts should maybe read the great little book "Gödel’s Theorem: An Incomplete Guide to Its Use and Abuse" by Torkel Franzén. I'll leave here a quote from a review[2]: In addition to obvious nonsense, there are among the nonmathematical ideas inspired by Gödel’s theorem many that by no means represent postmodernist excesses, but rather come to mind naturally to many people with very different backgrounds when they think about the theorem. It is especially such naturally occurring misunderstandings that Franzén intends to correct. [1] https://en.wikipedia.org/wiki/Decidability_of_first-order_theories_of_the_real_numbers https://en.wikipedia.org/wiki/Decidability_of_first-order_th... [2] https://www.ams.org/notices/200703/rev-raatikainen.pdf https://www.ams.org/notices/200703/rev-raatikainen.pdf
- DiscourseFan 2y ago
  It was Brin, not me, who makes the connection, and says that Godel refutes Hegel. The scholar I mentioned, JN Findlay, has a rigorous understanding of both authors, but I couldn't quickly find an article where he makes the argument. Nothing to do with "postmodernist excesses" or whatever. Also read my comment, see this article here[0] about how Godel adopted phenomenology, which is the philosophical backbone of much of "postmodernism," so it would be entirely fair to make a connection between Godel and, say, Derrida, for instance, since they both claim to be in the same philosophical tradition. But that's just what the scholarly evidence suggests. In any case, Godel's proof has little to do with "math" in the sense of calculation but rather is a refutation of Russel & Whiteheads attempts at a logical foundation of mathematics, which is a philosophical endeavour. The mathematical aspect is secondary and merely follows from the philosophical argument which it entails. It is the simply the case that, Russel & Whitehead were themselves engaging with "Hegel" in Principia Mathematica, who of course had his own system of logic (cf. the Science of Logic), but they failed insofar as Godel's critique is accepted, and insofar as you accept Godel's critique you could make the inference (though by no means on an entirely solid basis) that Godel's work constitutes, in a certain sense, a re-interpretation of Hegel, though not directly. [0]https://plato.stanford.edu/entries/goedel/goedel-phenomenology.html https://plato.stanford.edu/entries/goedel/goedel-phenomenolo...
  - moefh 2y ago
    > Nothing to do with "postmodernist excesses" or whatever. To clarify, I wasn't implying you or Brin were commiting "postmodernist excesses". The part of the review I quoted was explicitly saying that the book aims to correct misunderstandings that "by no means represent postmodernist excesses, but rather come to mind naturally to many people with very different backgrounds".
  - PaulHoule 2y ago
    Then there is Badiou, who perfected deconstructionism in his works like https://www.amazon.com/Being-Event-Alain-Badiou/dp/0826458319 https://www.amazon.com/Being-Event-Alain-Badiou/dp/082645831... It's easy to see Derrida as a bullshitter who doesn't understand the texts that he abuses but hard to make the criticism stick because Derrida himself is unclear and hard to read. Badiou clearly does understand the math that he's abusing and you can't find anything really wrong with it except for the idea that anyone would care about Marxism when we know so much more about the science of civilization now. Many people come to the conclusion that Badiou is a bullshitter, but if he is a bullshitter he's much more rigorous in terms of working within the systems he works with and also much more clear in his exposition in that you really can follow what he says.

by kbrkbr 2y ago

moefh 2y ago

Indeed. Godel's theorem is very technical, and any use outside the very technical realm of its immediate application should be viewed with great suspicion. For example, if you take the statement you quoted from Wikipedia and replace "natural number" with "real number", it doesn't work anymore: it's been proven that the arithmetic of real numbers is decidable[1]. That means that the sentence you quoted from OP's comment is not true. Anyone inclined to use Godel's theorem in these philosophical contexts should maybe read the great little book "Gödel’s Theorem: An Incomplete Guide to Its Use and Abuse" by Torkel Franzén. I'll leave here a quote from a review[2]: In addition to obvious nonsense, there are among the nonmathematical ideas inspired by Gödel’s theorem many that by no means represent postmodernist excesses, but rather come to mind naturally to many people with very different backgrounds when they think about the theorem. It is especially such naturally occurring misunderstandings that Franzén intends to correct. [1] https://en.wikipedia.org/wiki/Decidability_of_first-order_theories_of_the_real_numbers https://en.wikipedia.org/wiki/Decidability_of_first-order_th... [2] https://www.ams.org/notices/200703/rev-raatikainen.pdf https://www.ams.org/notices/200703/rev-raatikainen.pdf

DiscourseFan 2y ago
It was Brin, not me, who makes the connection, and says that Godel refutes Hegel. The scholar I mentioned, JN Findlay, has a rigorous understanding of both authors, but I couldn't quickly find an article where he makes the argument. Nothing to do with "postmodernist excesses" or whatever. Also read my comment, see this article here[0] about how Godel adopted phenomenology, which is the philosophical backbone of much of "postmodernism," so it would be entirely fair to make a connection between Godel and, say, Derrida, for instance, since they both claim to be in the same philosophical tradition. But that's just what the scholarly evidence suggests. In any case, Godel's proof has little to do with "math" in the sense of calculation but rather is a refutation of Russel & Whiteheads attempts at a logical foundation of mathematics, which is a philosophical endeavour. The mathematical aspect is secondary and merely follows from the philosophical argument which it entails. It is the simply the case that, Russel & Whitehead were themselves engaging with "Hegel" in Principia Mathematica, who of course had his own system of logic (cf. the Science of Logic), but they failed insofar as Godel's critique is accepted, and insofar as you accept Godel's critique you could make the inference (though by no means on an entirely solid basis) that Godel's work constitutes, in a certain sense, a re-interpretation of Hegel, though not directly. [0]https://plato.stanford.edu/entries/goedel/goedel-phenomenology.html https://plato.stanford.edu/entries/goedel/goedel-phenomenolo...
- moefh 2y ago
  > Nothing to do with "postmodernist excesses" or whatever. To clarify, I wasn't implying you or Brin were commiting "postmodernist excesses". The part of the review I quoted was explicitly saying that the book aims to correct misunderstandings that "by no means represent postmodernist excesses, but rather come to mind naturally to many people with very different backgrounds".
- PaulHoule 2y ago
  Then there is Badiou, who perfected deconstructionism in his works like https://www.amazon.com/Being-Event-Alain-Badiou/dp/0826458319 https://www.amazon.com/Being-Event-Alain-Badiou/dp/082645831... It's easy to see Derrida as a bullshitter who doesn't understand the texts that he abuses but hard to make the criticism stick because Derrida himself is unclear and hard to read. Badiou clearly does understand the math that he's abusing and you can't find anything really wrong with it except for the idea that anyone would care about Marxism when we know so much more about the science of civilization now. Many people come to the conclusion that Badiou is a bullshitter, but if he is a bullshitter he's much more rigorous in terms of working within the systems he works with and also much more clear in his exposition in that you really can follow what he says.