= 27d567bc2d48d9f40e9ccc20ea370b15)
dclayh comments on Deleting paradoxes with fuzzy logic - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (70)
This makes it sound like you have indeed just reintroduced types under another name, patching "this statement is false" by forbidding "this statement has truth value 0.0".
I think "this statement has truth value 0" is allowed.
ADDED: It has no discontinuity. It is the iterated system f(S) = 1 - S, and its fixed point is at S = .5.
But it manifestly has a discontinuity. Would you prefer the equivalent "this statement's truth value is less than epsilon (epsilon some infinitesimal)"?
Why does it have a discontinuity?
Folks, you shouldn't vote down legitimate questions.
Relevantly, because it's structurally identical to Warrigal's sample sentence, so whatever definition Warrigal is using (a perfectly standard one, it seems to me) must apply to both.
It's structurally identical to a sample sentence that Warrigal used in describing a different approach, not the one he/she is taking.
If it manifestly has a discontinuity, you should be able to say where it is.
(In fact, it does not have a discontinuity. For not(S) = 1-S, it is completely linear: it is the iterated system f(S) = 1-f(S), having a fixed point at .5. )
Okay, this is getting silly. Warrigal says "The sentence 'this sentence's truth value is less than 0.5' has a sharp jump in truth value at 0.5, but the sentence 'this sentence's truth value is significantly less than 0.5' does not [and we will ban the first form]". In the same way, my sentence "This sentence's truth value is less than epsilon" has a discontinuity at epsilon. Both sentences make discontinuous claims about their truth values.
What is the "different approach" that you claim this sentence is in reference to?
(Incidentally, I agree with you that my sentence has a fixed point at 0.5 under Warrigal's system. That's why my original comment was criticizing the presentation and not necessarily the content of the theory.)
The sentence we were discussing was "This statement has truth value 0". I assumed that when you said it was structurally identical to Warrigal's sample sentence, you were referring to this passage:
That sentence refers to the traditional ways around Russell's paradox.
You seem to say discontinuity when you mean a noncontinuous first derivative.