I have rebutted great amounts of your confusions. You either skip the most crucial parts of those rebuttals or get them all mixed up in your mind. Any...
Do you mean this post?: Whatever "change of mind you had" in that pile of confusions, you said inter alia: (1) and (2) So there you are, still demandi...
No, it was as "planned", and consistent (without reguarity). Wrong. That kind of nesting is consistent (without regularity). And it does not mean that...
With Z set theory, there is no set that is a member of itself. With ZFC-R, it is not inconsistent that there is a set that is a member of itself. I ga...
Basically, it's just saying: Suppose we have a set U whose members are all only those that are not the Russell set. Let R be the subset of U such that...
Somewhere you asked about having a set of all sets except the Russell set. I didn't send a proof that that doesn't work, but I want to now, because it...
I can't do it some justice without some technicalities, but I will have to skip some defintions and to fudge some technicalities that would be handled...
It's merely an informal heuristic expression. If that is the case (I don't recall all of that paper now), then it supports my point. Anyway, his task ...
As far as I can tell, you don't understand the nature and motivation for formal languages. You would benefit from an introductory chapter in a book th...
A machine can check the second proof, But a machine cannot check the first proof (unless the machine had those English phrases programmed as fixed syn...
(1) That translation is different from the one in the van Heijenoort book, which, if I recall correctly is the only one approved by Godel. I don't men...
No, because you don't understand the very particular point of this particular enquiry. This is not about saying how we should regard the notion of pro...
In a conversational way, that's an okay summary. But it actually describes Tarski's result pursuant to incompleteness. To me, it's odd that Church's t...
I don't. Non sequitur. I am sympathetic to the idea of assuming frameworks for making sense our experience. And, indeed, the mathematical notion of or...
Metaphysician Undercover fails to distinguish between two facts: (1) For every set, there is a determined set of strict linear orderings of the set. (...
Not only cannot you tell us what "THE inherent order" is for ANY set, but you can't even define the rubric. You can't even say what is "THE inherent o...
It was pointed out to you that there are orderings that are not temporal-spatial. But you insisted, over and over, that temporal-spatial position is r...
I made no argument for a philosophy regarding truth. And I didn't argue that mathematics is a purveyor truth known a priori and that empirical concern...
And you chided ME for my interest in mathematics that you deem not empirically justified. Now you're resorting to a mystical "true order that inheres ...
As you dogmatically claim. You keep skipping the central challenge to your claim. That challenge will be repeated in this post. Petitio principii! You...
That's condescension coming from a person who can least afford it. I haven't argued a philosophy. It's dogmatic of you to preclude that interest in ab...
I don't seek accommodation from you. Cleaning up your notation would be a favor to yourself. My main point is that ExAy yex is inconsistent in set the...
I showed that the very first sentence is inconsistent with subsets. What? The underlined passage is not an axiom of set theory. And it's your claim, n...
(1) Pointing out that you have not proved something is not an insult. (2) You began the volley regarding 'dogmatism' as you claimed that mathematician...
It is not unreasonable to desire a set theory that upholds our everyday notion of 'set'. However, certain difficulties arise. For example, our everyda...
AGAIN, you have not shown that "there does not exist a set of which all sets are a member" is contradictory. Au contraire, I have shown a proof that "...
It is the unique object whose members are all and only those specified by the set's definition. {0 1} is the unique set whose members are all and only...
That is not a proof. There are a few problems with it, but most glaring: There is no set D such that for all y, y is a member of D if and only if y is...
Whatever the merits or demerits of Carnap's views on metaphysics, the quote I mentioned does have wisdom. And one may have one's own reasons for esche...
The crank claims that mathematics is wrong. Not just that he proposes different mathematical conventions and definitions, but that the more ordinary c...
You claim that quote is dogmatic. What is your non-dogmatic basis for that claim? The quote is not dogmatic, I say non-dogmatically. The quote describ...
I'm talking about sentences in the language of arithmetic. I don't know whether these matters bear upon your areas of mathematics. I am pretty rusty o...
Modulo any typos or formatting glitches from one forum to another, of course, I agree that the function is partial. And I take the poster's word about...
If you're referring to Russell's paradox, it is a matter of logic and is not peculiar to set theory, but rather applies to any 2-place relation R: For...
We're addressing one particular metric: length of of the sum of the lengths of the formulas. This is not meant in itself to imply anything about the t...
What "truth=provability" principle do you have in mind? What is its mathematical formulation? Meanwhile, the incompleteness theorem proves that the se...
A sentence (such as set existence assertion) is found to be contradictory with other sentences by being found to be a self-contradiction (logically fa...
Which logicians and what formulations do you have in mind? I later corrected my typo of omission there. It should be: If we have taking of subsets, bu...
https://thephilosophyforum.com/discussion/comment/546862 I had a typo of omission there. I fixed it now. And I said that even if the demon throws out ...
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