aletheist

I agree with you on this. However, mathematics is not always and only a matter of numbers or other discrete entities. Geometry, especially topology, i...

Only if by "identify" you mean "distinguish." What I thought we were discussing was whether the relation of identity itself is absolute or contextual ...

Marking a point on a line, or breaking it into two lines that have points at their separated ends.

He does? Where? Please cite his writings to support this claim. Did Aristotle also employ this notion, since he likewise held that a continuum is (inf...

I continue to be skeptical of your claim that all mathematics is inevitably discrete. In the last several decades, category theory - as a more general...

This sentence makes no sense to me. Differences that do not matter enable us to treat two things that are not identical as if they were identical, for...

I am surprised that you would say this, considering that we started the thread with your comments to the effect that discrete mathematics cannot prope...

And yet the traditional/classical conception of God is that He is absolutely simple; His attributes are not discrete in the way that you seem to be su...

What matters to someone is always a function of that person's purposes. Surely you can agree that some differences matter to you more than others; and...

I think what you mean to suggest is that our experiences of mental and physical phenomena seem fundamentally different, so common sense says that that...

So the idea is that the context of x is not-x, and defining the identity of x as not-not-x recognizes this, rather than making it a contextless tautol...

Deriving conclusions from information that is already present in the premisses. Also known as deductive reasoning. Arithmetic is an obvious example, s...

Again, much to ponder. Thanks for taking the time. For the moment, I can offer just a few initial responses. Which is what, in your view? According to...

There is much to ponder here, but you still have not explained - at least, not in a way that "clicks" for me - what you mean when you say that the pri...

Peirce's definition of "real" is that which has characters regardless of what anyone thinks about it. He came to realize by about 1896 that all three ...

I agree, but I think that it will be helpful to clarify the distinctions that we are trying to draw if we can assign a term to 2ns that goes along wit...

But if something is uncountable, then by definition, counting it is impossible; and if counting it is impossible, then by definition, it is infinite; ...

The more I think about it, the more I really like "contextual" as a candidate for the 2ns counterpart to "vague" for 1ns and "general" for 3ns. If I a...

What you do is important in Protestantism, as well - it just does not contribute to salvation; rather, it is the natural outcome of salvation. In the ...

The law of identity expressed in what way, either verbally or formally (or both)? What exactly is this constraint with which 2ns "refuses" to comply? ...

It is perhaps more emphasized in this particular formulation by certain kinds of Protestants, but I honestly think that most Roman Catholics and Easte...

I explained this already, multiple times and in various ways. A continuous line has no ends, so by definition its parts also have no ends. You cannot ...

I see believing in God and being ethical as two different things. Ultimately it is not about anything that I do, it is only about what God has done fo...

Your obstinate dogmatism would be quite impressive if it were an admirable trait. You simply refuse to accept the established definitions - as quoted ...

I think I get what you mean when you say that the principle of identity does not apply to the actual - it is a limit that existing things can approach...

People can be - and are - ethical without believing in God. People can be - and are - unethical despite believing in God. I suspect that the vast majo...

Why is it so hard for you to understand that there are no points in a continuous line, only shorter lines? Positing points of division makes the line ...

That is why I asked for clarification of what falls within the scope of one's metaphysics for the purposes of the OP. Arguably, belief in God is a met...

"My" SEP article? I certainly did not write it, I just referenced it. I asked you for sources to justify your claim, "It is a well known metaphysical ...

You already acknowledged that this is not a true continuum, because it has points at the ends, which are discontinuities. When you add a third point, ...

Yes, you have - I just quoted one to you, verbatim, from Webster's Collegiate Dictionary, Fifth Edition (1936), which is what I happen to have on the ...

True in my case, although there are plenty of examples of atheists becoming theists later in life, and vice-versa.

Out of curiosity, I checked my dictionary to see how it defines "continuous." Here is what it says: "Having continuity of parts; without cessation or ...

Unless you can demonstrate that the concept of "part" necessarily involves separation, rather than just baldly asserting this over and over again as y...

One more time: By definition, infinitesimals are not separate. One more time: By definition, a continuum has parts, all of which have parts of the sam...

You mean as a rationalization? Probably so, in many cases. Arguably one's behavior/outlook is one's metaphyics; or more broadly, one's beliefs in gene...

What do you include in the scope of someone's metaphysics? For example, I am a theist, and my belief that God is real significantly affects my behavio...

Wrong. There is no separation (assumed or otherwise) between infinitesimals. Neighboring infinitesimals are indistinct; the principle of excluded midd...

I have no problem with measuring continuous things using discrete models; as I have acknowledged previously, they are very useful for that purpose. No...

You still have it exactly backwards. Space, time, and motion are all continuous; we only model them as being discrete. Prompted by some of the discuss...

Another possible clue from Timothy Herron's 1997 paper, "C. S. Peirce's Theory of Infinitesimals." Any thoughts on these passages, @"fishfry"?

Another possible clue in the SEP article on "Continuity and Infinitesimals."

I certainly cannot do that - at least, not yet - but I just came across one possible clue in the SEP article on "Category Theory." A continuum (such a...

Please see my (second) previous response. You can define and mark as many discrete locations between A and B as you like, but this does not in any way...

Said another way, the object's motion comes first from a logical standpoint. Drawing a line that traces the object's path, and then defining and marki...

It depends on exactly what you mean by "an actual half way point." As I said, there are no actual points at all, if by that we mean mathematical (i.e....

Points and lines do not actually exist; they are mathematical abstractions that we use to model things that do actually exist, like objects moving fro...

Here is a relevant quote, attributed to Stephen Covey, that I just came across.

Only if all of those points actually exist, which is precisely what I deny. The line does not consist of separate, discrete points; it can only be mod...

We agree that the phenomenal experience cannot be modeled adequately by mathematics, or even by other symbols like narratives; but various other aspec...