aletheist

More nonsense. You are the one who wants to define "countable" entirely on the basis of whether it is actually possible for a subject to finish "count...

Where did I say that? I was addressing your specific examples, which are indeed fallacious as deductive reasonings, but valid as retroductive or induc...

Yes, exactly. It is a retroductive hypothesis that provides a very plausible explanation for our experiences, which we can then deductively explicate ...

The issue is not defining properties independent of a person or group of people, it is things having properties independent of what any person or grou...

In my view (and Peirce's), they are either real (full stop), or they are not. Something is real if and only if has properties that do not depend on wh...

Why are you asking me? You and I agree that the real numbers are not countable. See, this appears like nonsense to me. One can be able to do something...

This right here is where we disagree. To count something is not the same as to finish counting it. Being able to count something is not the same as be...

I appreciate the sensibility that you have tried to bring to this discussion, but I still have to comment on this (again). I agree that neither you, n...

Apparently you are in such a big hurry to reply that you are not even bothering to pay attention to what I actually post. In this case, you are mixing...

Only if it were true that we must be able to finish counting something in order to call it "countable." Your definition requires this; mine does not. ...

I am inclined to subscribe to how Peirce addressed this.

And which number would that be? I asked you to identify it, not describe it. Look, we have been using at least three different definitions of "countab...

Just curious, on this basis do you reject nominalism - the view that reality consists entirely of singulars - in favor of realism? Peirce did; he even...

I am not familiar with Bergson, and Peirce (not Pierce) is notoriously difficult to get one's arms around, because he never managed to write a book on...

Agreed. This is what I have in mind when I cite the famous quote by George Box: "All models are wrong, but some are useful." In my own field of struct...

I agree with this; what I question is whether mathematics is totally reliant on the discrete. As I have indicated previously, I have in mind Peirce's ...

I am not convinced that this is true. Two of Peirce's major objectives for philosophy were to make it more mathematical (by which he meant diagrammati...

Here is what he actually said. He then added this, which is basically the same point that I made. So I would still like to see the alleged proof that ...

Of course mathematics can and does model a continuum. However, the accuracy and usefulness of such a model depend entirely on its purpose, and that is...

He certainly did not think so. Could you please point me to the proof? Note, I acknowledge that the real numbers serve as a useful mathematical model ...

Please identify a natural number or integer that is not capable of being counted. You are still conflating the notion of counting with the notion of b...

As he defined "continuum," yes. However, Peirce argued (and I agree) that the real numbers still do not conform to our common-sense notion of a true c...

I am not the one who took us down that road by repeatedly insisting that "countable" must always and only mean the same thing as "actually countable."...

If it helps you feel any better, it took me about two solid years of reading Peirce - including two complete passes through both volumes of The Essent...

I have acknowledged this repeatedly - the natural numbers (and integers) are not actually countable, in the sense that someone or something could ever...

Charles Sanders Peirce offered a similar argument for the reality of his universal categories of Firstness (quality/feeling/possibility), Secondness (...

Yes, we must always keep in mind that such equations are models - or in Peirce's terminology, diagrams - which embody only the parts and relations wit...

No, I get it, you just stated more accurately what I meant all along. :)

It sounds like we are on the same page here. As Charles Sanders Peirce put it, citing his father:

What exactly do you mean when you assert that "space is indivisible"? Are you merely saying (as I do) that space is continuous, rather than discrete -...

Again, incorrect. You evidently have a rather idiosyncratic personal definition of "infinite." My dictionary provides several widely accepted definiti...

Incorrect; "uncountable" and "infinite" are not synonyms in mathematics, since there are countable infinities and uncountable infinities. This is a fa...

Thanks for the excellent clarification/explanation. Right, this is all that I meant when I said that the natural numbers are countable by definition. ...

There are really two basic principles here: All counting is by means of the natural numbers; therefore, the natural numbers are countable. Any set tha...

Yes, and there is no contradiction at all in saying this - unless you insist on conflating "someone can actually count them" with "it is possible in p...

Show me one genuine contradiction in any of my previous posts, without conflating "countable" (as defined in mathematics) with "actually countable." T...

As you know, I recently tried starting a thread on "Extreme Nominalism vs. Extreme Realism," but it did not get very far. My hope was to identify some...

Exactly - it actually does mean that it is countable, but it does not mean that it is actually countable. See the difference? And I would rather have ...

It appears very obvious to me that you do not understand the accepted meaning of the word "countable" and, more fundamentally, the distinction between...

I guess you must deny, then, that the integers are countable, since nothing and no one can actually count them all. And yet it is a proven mathematica...

No one is talking about doing anything. To say that something is infinitely divisible does not mean that a human being is actually capable of infinite...

No, you are the one with that confusion, as I have stated before. Space only has to be discrete if it is infinitely divided, not merely infinitely div...

It can be, but it does not have to be. Your whole argument hinges on insisting that the very act of moving from one point to another must be considere...

You're still making the same mistake. It is false to say that space is potentially infinitely divisible only if it actually is. No, it indicates that ...

That which is physically actual must be logically possible; and so it is only your logic that is faulty here, because you insist on applying the logic...

The problem is that the logic of discrete motion is incoherent, hence motion isn't discrete. Like I said, we are at an impasse. Cheers.

We agree that it is not possible for us to plot actual coordinates at distances that correspond to all of the rational numbers. We thus agree that it ...

No. The motion from one potential location to the next is not a discrete event. Only the motion from one actual location (i.e., arbitrarily defined co...

This is a good example to show why we are at an impasse. Your claim is that all actual objects that actually move go from one Planck length coordinate...

Well, it does appear so to me. So we have contradictory intuitions, which just goes to show that intuitions are not infallible guides to truth. Edit: ...