Whether or not the mathematics mentioned here properly applies to the paradoxes mentioned, at least we should be clear about that mathematics. Adding ...
On may reasonably propose an alternative formalized logic, but a formalized logic requires that we have a purely mechanical method by which to determi...
The context I am using is ordinary mathematical logic applied to classical logic: For a given language, we have different models. A model is an interp...
To the point about paradox: 'paradox' may be defined in different ways. I'll use this definiens: a contradiction derived from seemingly acceptable pre...
An example of intellectually dishonest posting is a poster evading 1000 times that being inspired by an analogy between ideas does not entail that the...
Meanwhile, just for sake of keeping the eye on the ball: Godel proves incompleteness/undecidability, and the liar sentence is not in that proof. Tarsk...
Now that the poster cannot support his dogmatically ignorant and confused claim (that the liar sentence appears in Tarski's proof of undecidabilty) th...
I have no false assumptions in this context. But one of the many ridiculously dogmatic and ignorant false assumptions of the poster is that "This sent...
The proof on pages 275-276 is a proof of the undecidability of certain sound systems (a system is sound if and only if all its theorems are true). It ...
I did err in my previous post by overlooking the negation sign. And I should have emphasized again, for the 100th time, that 'unprovable' and 'untrue'...
Line 1 is: ~x e Pr if and only if p. That is to say, "x is not provable if and only if p." As has been pointed out over and over, that is not the liar...
This deserves an award for being one of the most goofball comments ever posted: "I have spent hundreds of hours on those four pages over the last seve...
It has been fully addressed that the proof of undecidability on pages 275-276 does not use the liar sentence at any step. / I am not opining about a n...
x e T if and only if p is not the liar sentence. Rather, it is the general truth scheme. For formal languages, the particulars of p are filled in per ...
First, as has been pointed out to the poster at least a dozen times, this is not a proof of undefinability. It is a proof of undecidability. In that p...
The easily verifiable fact is that in the undecidability proof, pages 275-276 of the paper, Tarski does not use the liar sentence in any step in that ...
Regarding the definition of 'antinomy', the point stands that, contrary to the poster's misconception, the definition is not merely 'self-contradictio...
One can look in a dictionary or in books and articles to see that there is more to being an antinomy than merely being a self-contradiction, especiall...
In sum: (1) In the Tarski proof of undecidability lately discussed here, Tarski did not use the liar sentence, but rather he used a different formulat...
It could only be a mistake if the footnote didn't pertain to the passages that begin with "The analogy ". So if one concedes, by actually reading the ...
I guess the poster won't concede that footnote 14 is to the passages that begin by saying that the antinomies are analogous to the Godel argument. Rat...
In another thread, I showed exactly that Tarski did not use the liar sentence in the proof discussed there. For the 100th time, Tarski himself said th...
(1) The footnote pertains to the sense of using the antinomy analogously to a certain argument. That argument does not itself use the antinomy, but ra...
The context in which they are not mistaken is the context in which he wrote them. The poster seems to have a problem: Posting the quote from the footn...
Godel is not wrong. What is wrong is brazenly, dishonestly attributing to him out of context, and then doing it yet again even after the context was r...
I am looking at the only Godel-approved translation right now. Page 598 of 'From Frege To Godel'. "The ANALOGY of this argument " which is the context...
We can read the many posts in which the poster claimed that Godel used the liar sentence (i.e. the epistemological antinomy) in the proof. And the quo...
Saying again that Godel used the liar sentence in the incompleteness/undecidability proofs is to yet again ignore the plain hard fact that he did not....
It has been pointed out at least half a dozen times in other threads: Godel is referring to using the general idea of such paradoxes to spring the ide...
Godel didn't hide steps regarding Godel numbering or diaganolization. Rather they are treated in exact detail. "x is true if and only p" is not, accor...
It was explained exactly why your versions are not paradoxes. Clear versions are available on the Internet. Moreover, I stated clear versions in this ...
Of course there are many kinds of paradoxes ranging formal to informal. But you referred to Russell's barber paradox, which is an informal illustratio...
The video about the liar paradox and incompleteness is atrocious, ignorant, lying disinformation. (1) The video, in its juvenile way, dishonestly mock...
(1) Higher order logics are usually 2-valued, especially the most famous and most studied ones. One may devise other valuations, but ordinary higher o...
Such utterly incidental questions as to the meaning of 'barber' can't seriously be considered part of the subject of paradox. Anyway, looking in sever...
(1) The proof on pages 275-276 of the Tarski paper is not a proof of undefinability, but rather it is a proof of undecidability, specifically that the...
To reiterate, the paradox doesn't even need any mention of maleness, barbers, towns or even humans. It is best seen in its starkest form: Something sh...
'the barber of Seville' is a definite description. There are different ways of handling definite descriptions, including, at least, both the Fregean a...
(1) If one insists on the premise that it makes no sense to speak of mathematical objects, then one may hold that it makes no sense to speak of the la...
We could add that men of Seville are shaved only by men of Seville and that every man of Seville is shaved, and still we would not have a paradox in e...
You could study the subject more to learn how to express your idea in an understandable way. But, of course, that would be a matter of how you spend y...
In this context, to claim that there is a paradox is to show how a contradiction is drawn. But there is no contradiction drawn from "The Barber of Sev...
I understood from your first post that you are not well versed in logic. So I have offered information that would help you, have pointed out where you...
As I said, an isomorphism is a 1-1 structure preserving function. What is the domain and range of the function you wish to adduce. What is the relatio...
Perhaps there are other people who understand what you're saying or asking, but I don't. It would help if you specified in already understood mathemat...
Symbolize: Sy <-> y lives in Seville My <-> y is a man Hxy <-> x shaves y Premises: Sb & Mb Ay((Sy & My & ~y=b) -> Hby) ~Hbb Consistent with those pre...
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