No recognition that you were just blowing smoke when you referenced a source that you didn't even read to see that it says the OPPOSITE of your claim?...
Clearly, you're not reading. I gave you a proof in the very post to which you have now replied: You need it spelled out for you again? Definition: x i...
Followup with the liar bot: I wrote: "That's wrong. soundness does not follow from completeness" - TonesInDeepFreeze ChatGPT replied: "You're correct....
"Godel’s completeness theorem, which he proved in 1930, shows that if a formula is semantically valid, then it is provable within the system, while th...
(1) It is possible that Godel first proved the soundness of the predicate calculus. I mentioned in my post that I don't know who first proved it. (2) ...
Of course, I never took you to be stating that it is your own view that Russell's paradox undermines the basis of all mathematics. My point is that if...
No, only in your own ridiculous words. Consider: The Pentastring is this sentence has five words That's gibberish. Consider: "The Pentastring is this ...
An example of Wikipedia promulgating sloppy misinformation. What is called 'game formalism' or 'extreme formalism' regards mathematics as merely execu...
That is not what Godel said nor what we take from Godel. To show a sentence is to prove the sentence from a set of axioms and rules of inference. But ...
I would want to see the paper or talk in which Turing said that. The quote itself does not mention the liar paradox, let alone Russell's paradox. In a...
Russell correctly saw that it undermined unrestricted comprehension (as underlying Frege’s system, even if not called ‘unrestricted comprehension’) as...
None of that supports your confused mixing up which is the inner and which is the outer sentence. First, Quine didn't assert that "This sentence is fa...
What?! Not only have I not said that many times, I've not said it even once. On the other hand, I have said many times that an expression is in the wo...
You should say that it's on the basis that your "infinite recursion" argument had been refuted at least three times but you choose to ignore the refut...
The passages from Quine: "'This sentence is false'. Here we seem to have the irreducible essence of antinomy: a sentence that is true if and only if i...
So I underestimated AmadeusD's willingness to not understand plain words. For his remedial benefit, a review is in order. So let's take a gentle strol...
Logic doesn't require that we don't accommodate for the non-literal. If "I can eat a horse" is meant to mean only that I am extremely hungry, then log...
(1) Russell's paradox is couched in terms of sets, but that is not necessary, as it is not necessary even to couch in terms of the relation of element...
In set theory, we prove the existence of a particular complete ordered field and that it is unique within isomorphism. I didn't adduce any reasons tha...
For a mathematics for the sciences, ordinarily we use a complete ordered field. That requires having a non-empty set, a 2-place relation (<) on the se...
If you would read what I posted, you would see that I said that I don't know what your "nine pages" remark was supposed to mean. I listed some obvious...
You wrote: You literally wrote that it was a response to a discussion between RussellA and me. I think my counting is pretty good when I count Russell...
Again you reply by ignoring what I wrote. I said exactly why it is dismissive, even with its ambiguity. You failed to address the previous specifics a...
You ought not put strikethrough across my words within a quote like that. I said "naturally" and I did not strike it. The typo of omission is yours no...
Which clarification? The facts I informed you of? The fact that I did not, as you falsely claimed, dismiss the other poster with an ad hominem but rat...
You haven't addressed the specifics of my argument about it. Saying "clearly" is nothing. Being sarcastic is, of course, fine in and of itself. But it...
What you said was ambiguous. It could have meant that it took RussellA nine pages too long to wake up (though later contradicted by the fact that you ...
The absence of indication is not "clear indication". Clear indication would be something like, "Not directed at anyone in particular". You replied dir...
As I said, it's fine that you clarify that the "I can only laugh" was not meant to be directed at me specifically, but rather to two posters at once (...
The comment you made was directly after two fairly chunky posts by me. You could have said that this thread in general makes you laugh (but why?), but...
You posted immediately after my post, so it was reasonable for me to think you were commenting on me. But now that you have disclaimed that you meant ...
And that is not analogous to "This sentence is false" in the context of this discussion. Again, there is no other sentence at issue. And one may stipu...
They are both referring to the sentence "This sentence has five words". Mary is not referring to some random, unrelated sentence that is not even pres...
As I said from the start, I am open to a finding that "This sentence has five words" is not meaningful, if there is a good argument that it's not. But...
Ways in what is the case? Ways in which "This sentence has five words" is not paradoxical? RussellA's claim is that "This sentence has five words" is ...
I haven't said the sentence refers to itself. I said that "This sentence" refers to "This sentence has five words". The noun phrase "This sentence" is...
So what? "This sentence" in "This sentence is false" is not referring to the sentence "The Eiffel Tower is a lattice tower on the Champ de Mars in Par...
That is just so very nuts! In "This ferry contains fifty people" we don't think this "this ferry" refers to the sentence "this very contains fifty peo...
We've been over the "grounded" argument about a dozen times already. Whatever RusellA's definition of 'grounded' is, if sentences such as "The cat is ...
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