Such books don't axiomatize the principles used. And those books make use of infinite sets. I think even constructivist and intuitionist set theories ...
That seems okay at face value. But since you've put the argument in a list, I'd make explicit all the premises. I'd like to read Benacerraf's paper th...
While you were posting, I revised my post to better explain about continuousness and density. That is not at issue. Rather, as I've said twice now, at...
The division of time mentioned in the thought experiment doesn't require continuousness of time; it only requires density time (via the density of the...
If you don't mean "Therefore, it is impossible for the first task to be performed at 11:00, the second at 11:30, the third at 11:45, and so on" then i...
As I mentioned, that is a premise that you don't include in your own argument. As I mentioned: "his argument includes the premise that there is a stat...
My mistake. Just now I put an edit note in the post. Right. I am using 'define' in the exact sense of making a mathematical definition. A definition i...
But in that example, his argument includes the premise that there is a state at 12:00 and that that state must be determined by an immediate predecess...
You give me link to some unidentified video so that I would have to take my time to watch through to find out, or guess, what it is you want me to kno...
I like to keep the word 'series' for sums per convergences, and the word 'sequences' for sequences. It is not the case that when we define an infinite...
I made no judgement on that. Again: Suppose there can be no completion of all the tasks. That does not entail that there is a finite upper bound to ho...
There are three ways we could approach for set theory: (1) Take '=' from identity theory, with the axioms of identity theory, and add the axiom of ext...
That was said to Metaphysician Undercover. Actually, I am the one who took up his misconception that sets have an inherent order. I don't consider tha...
The poster wrote: "you claim that the only relevant concept of "identity" is the mathematical one" That is false. I've said very much the opposite in ...
If Hegel rejects the law of identity, but the poster endorses it, then it makes no sense for the poster to invoke Hegel as vindicating violations of t...
It's not hot air that the poster's claim was (and is now back) that there is THE ordering of a set. Evidence includes the poster's penultimate post: "...
Stern-Brocot is interesting. But a while back, your improvisations on it came to confused handwaving. I'm not inclined to start all over again about i...
The conflation is just as I stated it. But your new argument is quite different from the previous argument, and, as far as I can tell, it does not suf...
The poster is very mixed up and adding lies to the ones he's already committed. This is revisionist: "the identity of a thing (by the law of identity)...
As far as I can tell, you're committing the very conflation that Thompson warns about and as you quoted my paraphrase of it. Think of the difference b...
(1) We may question P2. (2) C1 doesn't follow from P1 and P2. And it contradicts the point you quoted. Again, even if there is no completion of all of...
Here's how it looks abstracted to a dialogue: MU (many times a while back): The axiom of extensionality is wrong because sets have a certain order but...
So put in terms the poster just used: The set whose members are all and only the famous four bandmates in the Beatles. That set is identical with itse...
The question is exact. What is supposed to be THE order of the set whose members are all and only the famous four bandmates in the Beatles? And woah! ...
The principle of division does not indicate that a material object can be perfectly divided in two. Whether a pie can be perfectly divided so that the...
Thank you for the quote. His statement of his view that the notion of super-tasks is nonsense is wedged in a chain of reasoning, and somewhat hedged b...
Combined with another premise, it yields a paradox. Thomson outlines the paradox: Premise 1. To compete the main task requires completing infinitely m...
By the way, the poster, in his earlier remark about mathematics, has it exactly backwards, as usual with him, just as he has it backwards with me. Mat...
I didn't argue that dividing a pie in half proves anything about the thought experiments. And the poster again states his big fat stupid red herring a...
And then the poster cites that halving material object is merely an approximation, as if that has any bearing here. Oh please! Of course it is underst...
Where in the paper does Thompson say that? I had in mind not 'object' but that 'ways of dividing' is vague. Or maybe the poster just refers to the fac...
The puzzle supposes infinitely many segments. Of course, if you deny the supposition of the puzzle, then it may be easy to dispense the puzzle. But on...
Previously I wrote: "Thomson says there's no finite upper limit to the number of tasks that can be completed in finite time, but that not infinitely m...
An infinite series that has a sum (some might say the series is the sum) requires first having an infinite sequence (each entry in the sequence is a f...
Mathematics doesn't say there is no limit to the ways objects may be divided. Where does such a claim about mathematics even come from? What actual pi...
The only infinite number in the puzzle is the domain of the sequence. So it seems your analogy is between misuse of imaginary numbers and misuse of in...
A deep reading of American history reveals that the right to the arithmetic operations was to be enshrined in the Bill of Rights. But it failed to pas...
The lamp puzzle doesn't require anything to occur in an infinitely small amount of time. And I don't think the discussions about a switch being moved ...
Everyone knows that tea is taken at at the tea time hour and that one is not to dawdle still drinking it, not even hypothetically, not even gedankenis...
Meanwhile, still interested in knowing what the poster would claim to be the inherent ordering of the set whose members are the bandmates in the Beatl...
Underphysician Metacover as the Baker: Customer: I'd like a cherry pie, divided in two. I'm going to give one half to my niece and that other half to ...
If there is a greatest divisor, then there is a greatest natural number, call it 'g'. So then what is g+1? If one says addition is not allowed with g ...
I'd need to check Thomson's paper again to ascertain whether that properly describes the particulars of his view. But, yes: The infinite sequence of d...
Thomson says that there's a false premise, which is that infinitely many tasks cannot be completed in finite time. He says that there's no finite uppe...
Ordinarily, an argument is valid if and only if it is not possible for the premises to be true and the conclusion false. But a paradox has seemingly t...
An argument has been given that physics is impaired by an improper application of mathematics. So the question arises whether that argument extends to...
My question was about mathematics not physics. Suppose there is a smallest number usable for a given application of mathematics. Then, must mathematic...
If there is a maximum number of divisions, then what is that maximum number? That is, for what natural number n is it the case that 1/(2^n) is not a n...
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