Mathematics does not need philosophy, since pure mathematics is the science of drawing necessary conclusions about strictly hypothetical states of aff...
The existence of evil is insufficient to disprove the reality of an omnipotent, omniscient, and omnibenevolent God. However, by itself, this does not ...
I must confess that I am not very familiar with Kant or that particular terminological distinction. Peirce, on the other hand, was very familiar with ...
Rather than a deductive conclusion, Peirce's take was that the initial recognition of one's own existence as a subject of experience is a retroductive...
I am only talking about mathematics in this thread, not ontology; maybe you should start your own thread on "Continuity and Ontology." I am only talki...
That would be news to mathematicians. Not at the same time and in the same respect, hence no contradiction. It is not possible to divide it and still ...
The first four questions that I posed in the OP were as follows. Is contemporary mathematics inherently discrete, such that it is incapable of accurat...
I still suspect that this right here is what you are perceiving as contradictory, perhaps because you are locked into the standard rules of classical ...
As I have repeatedly made clear, I am discussing mathematics here, which has to do with ideal states of affairs; I am not saying anything whatsoever a...
That which cannot be divided at all is an individual, not a continuum - e.g., a point rather than a line. There has to be a way to distinguish these t...
Not really. To say that a continuum has no definite parts just means that it does not have any distinct, discrete, or indivisible parts. With this qua...
The "original ship of Theseus" is the one made up of the original planks. The "current ship of Theseus" is the one that has had all of its planks repl...
In reviewing Fernando Zalamea's paper, "Peirce's Continuum: A Methodological and Mathematical Approach," I came across his explanation of what we have...
No, consisting of members - no matter how many of them there are - means being discrete, not continuous. There are infinitely many natural numbers, in...
Your failure to understand it does not render it incoherent. I understand it, I just seem to be unable (so far) to explain it in a way that you will a...
Apparently not, given your subsequent comments. He understood all of that extremely well. His point was that consisting of members - whether finite or...
A true continuum is not a set or collection at all; it does not consist of discrete members. Who is Pierce? If you mean Peirce, it is clear from your ...
If and when you ever come to understand this, you will then finally understand what Peirce and I mean by a true continuum. You are now equivocating on...
As stated in the OP and several times since then, the real number line is not a true continuum as defined by Peirce, nor is anything else that consist...
Remember, I pointed out that this is false, because the concept of separate/broken/discontinuous is not necessary to the concept of parts. In any case...
Of course not, but it is another matter to claim that this is the only or primary reason why we are seeing detrimental changes to the global climate. ...
This is a very important point. Identity is only possible within a context, where we can distinguish one "thing" from all of the other "things" that a...
Why are you so adamant about imposing your terminology on any discussion here? I was just trying to improve clarity by distinguishing "continuity" as ...
I think one reason for the shift in terminology from "global warming" to "climate change" is that the latter is less controversial; of course the clim...
Just to add another option to the table, Peirce's version of objective idealism understands mind as living and active, and matter as "effete mind, inv...
This "paradox" simply illustrates how identity is not an intrinsic aspect of macro-scale objects; it is something that we assign to them in accordance...
First of all, you keep referring to "a continuity" as if it were a thing. Continuity is a property, not a thing; a continuum is a thing that has the p...
My mistake, I did not follow the link to check your source; everything that you wrote right before the quote implied that it was directly from Peirce ...
Are you now taking up the argument that MU always insists on making? Pure mathematics has nothing to do with what is actual, physical, or computable. ...
That is fine, I was just playing around with another angle. I like how you stated this. I finally found where Peirce did make a trichotomy with vaguen...
There is no first real number after 0 with the standard order; there is an uncountable infinity of real numbers between 0 and any arbitrarily small bu...
Please just make your point, if you have one. The real numbers constitute an analytic continuum, not a true continuum as defined by Peirce (and others...
Right, there are no "missing" numbers; but that still means that the set of real numbers consists of individual numbers. A true continuum does not con...
Another thought. Vagueness: ¬(?x)(Px ? ¬Px) does not entail ¬ Generality: (?x)(Px ? ¬Px) does not entail (?x)(Px) ? (?x)(¬Px) Contingency: (?x)(Px ? ¬...
Numbers are intrinsically discrete; and it is not a matter of whether this discrete thing adequately represents the real numbers, but whether it adequ...
Kudos for quoting Peirce, but I still think that you do not properly understand him. That would be the same Book VI of Aristotle's Physics that I quot...
It took me a while, but I finally figured out Zalamea's notation, and thus his point about "failures of distribution": the concepts of vagueness and g...
Even while driving? Seems dangerous. :D I am not looking for a pat on the back; just saying that I am not blithely neglecting the kinds of concerns be...
I worry about anything that is characterized as "unquestionable," especially in the realm of public policy. But I also drive a hybrid vehicle, and bel...
Developments such as category theory, nonstandard analysis, and synthetic differential geometry or smooth infinitesimal analysis reflect dissatisfacti...
This is really the only point that I wanted to make. We do not (yet) know the global effects of widespread implementation of various "alternative" ene...
The point is that "clean" and "renewable" are buzzwords implying that anything that avoids burning fossil fuels is inherently and unquestionably less ...
If that were true, then you would not be arguing with me, because it is simply a fact that - going back at least to Aristotle - "continuous" means bei...
This brings up a question that I have long had about allegedly "clean" or "renewable" energy sources. There is no free lunch, so we are always redirec...
Thanks for the link. I knew that you did not invent it; you are just the one who introduced it to this thread. MU wrongly attributed it directly to Pe...
The continuum was not discovered via set theory, it was (and still is) modeled using set theory. Real numbers merely constitute an analytic continuum;...
As I keep telling you, mathematics does not rely totally on manipulation of the discrete; or at least, mathematics need not rely totally on manipulati...
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