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https://en.wikipedia.org/wiki/We_Have_Never_Been_Modern https://en.wikipedia.org/wiki/We_Have_Never_Been_Modern A book for those who are interested in this vie

https://en.wikipedia.org/wiki/We_Have_Never_Been_Modern https://en.wikipedia.org/wiki/We_Have_Never_Been_Modern A book for those who are interested in this viewpoint; though, its a bit technical, its audience is anthropologists. I agree and disagree, in that, the concept of the "other," which Brin subtly attributes to a crude reading of Hegel, is misused in contemporary academia, in contemporary culture, to create these what can't be said to be other than corruptive ideas like an infinite meakness in the face of what we cannot know about ourselves, but a meakness which is secretly all the more chauvinistic, as it claims, above all, that only we are superior who recognize our "mediocrity," in the face of all those animals, cultures, potentialities of otherness, that fail to do so themselves. But, of course, Hegel's concept of the "other" is not this way at all. As JN Findlay argued, there is no substantial difference between Godel and Hegel's logic in terms of incompleteness: it is likely that, although the only philosophy which Godel ever adopted was Phenomenology, he would himself not have had any issues with the comparison. It is the "identity of non-identity," its not that you "encounter" the other, its the recognition that the other is already contained in what is non-other; 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, and the discreteness of the world only comes when those elements come to a head, when people are forced to, for Hegel, fight in a conflict to resolve, at the level of the Idea itself, what they cannot be certain of: this is why, science, what you'd think is objective and independent, depends on massive political and social forces: and if the Israeli's, for instance, could not fight their wars, it would be the proof that ideology of faith is more powerful than the ideology of the world, of technological power. The "truth" of a missile only becomes apparent when it hits its target, just in the same way that one cannot know, here on HN especially, how others will think of their comment, until they post it.

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...

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...