It has nothing to do with how I consider it. The movement does not actually consist of an infinite series of separate, discrete steps. It is simply a ...
I still think that this is an overreaction. We can still use mathematics for describing certain life experiences, depending on our purpose in doing so...
Yes, you pass each of those arbitrarily identified "points"; but each instance of doing so is not a separate, discrete step in the continuous motion o...
We do not have to treat every halfway point as a discrete step in the motion from the start of that 100-m line to its end. We can traverse the one ful...
Yes, I agree. What remains unclear to me is what it means to say that the principle of identity does not apply to something. Zalamea helpfully formali...
This is probably good advice, and I will try to heed it going forward. Sorry to nitpick, but is "contradiction" the right word here? In accordance wit...
He never said that you were wrong. He merely said that Zalamea said the opposite of what you said. What gave you that idea? I thought that was also un...
Really? That was not my intention at all. I was just trying to moderate a dispute between two of my favorite PF participants. What? Why would that be ...
I see nothing insulting about pointing out a discrepancy between what you wrote here and what is claimed in a paper that you recommended. I have alrea...
The actual is that which is neither vague nor general by these definitions - both principles apply to it. The tricky part is that this notion of absol...
Again, @"fishfry" simply pointed out something that Zalamea claims in the paper that you recommended, which is contrary to your own comments. I took h...
Come now - this is not @"fishfry"'s own claim, but Zalamea's, in the very paper that you recommended. The later discussion linking category theory wit...
Would you mind clarifying exactly what you mean by "analytic" and "synthetic" in this context? That is not how I understand it, unless by "constrained...
Ah, okay; it was (obviously) not obvious to me, since I generally assume - unless there is a clear indication otherwise - that a reply to one of my co...
What exactly is it that you think I am not comprehending? Sincere question, I am eager to learn. If it is a theorem that has been proved, then it foll...
It is a mistake to treat accuracy and success in the actual world as the only legitimate objectives of inquiry. For one thing, it is inconsistent with...
This right here is precisely the reason why we have been at such loggerheads throughout this discussion (and others). As I keep saying over and over, ...
Not when "cardinality" is defined as a specific property of infinite sets. There are no inconsistencies or contradictions within the hypothetical real...
My only exposure to category theory (so far) is Zalamea's paper, which I am in the process of rereading because I suspect that it will make even more ...
He might very well understand it, he just refuses to accept it. He is committed to the presupposition that only the actual is real, so if something is...
No, it is a deductive conclusion that is necessarily true, given the standard mathematical/set-theoretic definition of countable/denumerable/enumerabl...
No, I understand his 1ns in itself to be quality as possibility, or unembodied quality; medad rather than monadic predicate. Anything brute and/or act...
I was delighted to learn this evening that Zalamea has agreed to a "slow read" of this very paper via the Peirce-L e-mail list in the near future. If ...
Peirce: "If we are to explain the universe, we must assume that there was in the beginning a state of things in which there was nothing, no reaction a...
In this context, do you basically see continuity as 3ns, discreteness as 2ns, and possibility as 1ns? Given that existence is 2ns, do you generally pr...
I have no reason to doubt that you are correct about this. Thanks for another helpful clarification, especially since @"tom" chose for some reason not...
I am neither a mathematician nor a philosopher, but that statement seems consistent with the claim that the real numbers do not qualify as a true cont...
I doubt it, since I have been clearly saying all along that a true continuum is not made up of "individual points or their aggregates." I might even a...
We typically treat the two values as equal, but arguably there is an infinitesimal (non-zero) difference between them. As you might have guessed, the ...
It obviously does not yield an unbroken continuum. More real numbers, all of which are distinct; again, it obviously does not yield an unbroken contin...
Right - the real numbers constitute an analytic continuum, but not a synthetic continuum; i.e., a true continuum in the Peircean sense, which cannot b...
It is trivially true that no representation reproduces its object in every respect, and the purpose of musical notes - and mathematical symbols/equati...
But without that representation, you would not be able to play that particular piece of music at all, unless it happened to be one that you composed y...
Indeed, but @"Metaphysician Undercover" only accepts this definition if we divorce it from the colloquial meaning of "countable," which according to h...
Agreed, and likewise. I certainly do not believe that one must share all of a thinker's presuppositions and commitments in order to understand his/her...
But this is an online forum, not an academic debate. Oops, putting it that way is likely to have the opposite effect of what I intend ... :s Look, you...
Perhaps, but it seems to me that we have then already conceded that the real numbers do not and cannot constitute a true continuum. They are now just ...
Right, and a continuum is "that of which every part has parts of the same kind," so obviously a continuous line cannot contain any points. When we mar...
That is indeed a terrific paper, but it gets pretty technical and might be tough to follow for someone not already acquainted with Peirce's thought. T...
That is really what my first question is asking. @"Rich" seems pretty convinced, but I am still trying to make up my own mind, especially since I adhe...
Is there an a posteriori way of determining whether there are any real continua vs. everything (including space and time) being discrete? As I stated ...
As I asked in the OP, is it possible to determine whether there are any real continua vs. everything (including space and time) being discrete? If so,...
Comments