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But the Liar's Paradox leads to the essence of Godel Incompleteness (Hofstadter starts off with that paradox in GEB as well, to build up a repertoire of modes o

by Phemist 10y ago

But the Liar's Paradox leads to the essence of Godel Incompleteness (Hofstadter starts off with that paradox in GEB as well, to build up a repertoire of modes of thought in the reader). I think the oversalted and undersalted paradox should be seen in the same light, because the point about dishes does seem beautifully isomorphic to godel sentences. The interesting dishes are their own dish, but also a different dish, depending on the system (the taster) in which they are interpreted.

chubot 10y ago
The essence of the Liar's paradox ("this sentence is false") is that the sentence refers to itself -- it's a "strange loop". Godel's incompleteness proof shares this property of self-reference. There is no self-reference in the paradox of something having 2 properties at once (e.g. undersalted and oversalted). It is a paradox, but it's not a Liar's paradox or a strange loop. In other words, not all paradoxes are the Liar's paradox.
- Phemist 10y ago
  That's fair, I'll have to clarify myself a bit further. I didn't think of the undersalted/oversalted thing as having two properties at the same time (basically means it is inconsistent, the dish might be both, but you can't taste both). I think it can be likened to the Shepard Tone[1], in the sense that the means a dish can be feeling to get saltier and saltier, and suddenly it's undersalted, without a very strong negative delta. [1] https://en.m.wikipedia.org/wiki/Shepard_tone https://en.m.wikipedia.org/wiki/Shepard_tone
- beat 10y ago
  I don't think it has to be a fully-qualified Strange Loop to be influenced by Hofstadter's thinking. In order to grok strange loops, one must learn to accept rather than reject paradox. "Logic" doesn't like paradox, and tries to get rid of them when they are encountered. But once you've read GEB, you're sensitized to accept paradox. I agree that all strange loops are paradoxical, but not all paradoxes are strange loops. Where I don't agree is that just because an idea isn't a strange loop doesn't mean it wasn't inspired by an awareness of strange loops. Without Hofstadter's idea, Chang would never have had this breakthrough on his own.

by Phemist 10y ago

chubot 10y ago

The essence of the Liar's paradox ("this sentence is false") is that the sentence refers to itself -- it's a "strange loop". Godel's incompleteness proof shares this property of self-reference. There is no self-reference in the paradox of something having 2 properties at once (e.g. undersalted and oversalted). It is a paradox, but it's not a Liar's paradox or a strange loop. In other words, not all paradoxes are the Liar's paradox.

Phemist 10y ago
That's fair, I'll have to clarify myself a bit further. I didn't think of the undersalted/oversalted thing as having two properties at the same time (basically means it is inconsistent, the dish might be both, but you can't taste both). I think it can be likened to the Shepard Tone[1], in the sense that the means a dish can be feeling to get saltier and saltier, and suddenly it's undersalted, without a very strong negative delta. [1] https://en.m.wikipedia.org/wiki/Shepard_tone https://en.m.wikipedia.org/wiki/Shepard_tone
beat 10y ago
I don't think it has to be a fully-qualified Strange Loop to be influenced by Hofstadter's thinking. In order to grok strange loops, one must learn to accept rather than reject paradox. "Logic" doesn't like paradox, and tries to get rid of them when they are encountered. But once you've read GEB, you're sensitized to accept paradox. I agree that all strange loops are paradoxical, but not all paradoxes are strange loops. Where I don't agree is that just because an idea isn't a strange loop doesn't mean it wasn't inspired by an awareness of strange loops. Without Hofstadter's idea, Chang would never have had this breakthrough on his own.