4 ms·
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 share
by 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 agoThat'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 agoI 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.