When they're [scientists] explaining their theories, sure. But they're also comparing their just-so stories with each other and providing experiments which support the stories in a way which is very appealing to the critical mind. Do metaphysicians have anything comparable? — coolazice

The theory of abstract objects is a metaphysical theory. Whereas physics attempts a systematic description of fundamental and complex concrete objects, metaphysics attempts a systematic description of fundamental and complex abstract objects.

Most important, then began the period when the relevance of philosophy declined in the face of the rising influence of science.

Instead, let us imagine an infinitely small piece of elastic, contracted, if that were possible, to a mathematical point. Let us draw it out gradually in such a way as to bring out of the point a line which will grow progressively longer. Let us fix our attention not on the line as line, but on the action which traces it. Let us consider that this action, in spite of its duration, is indivisible if one supposes that it goes on without stopping; that, if we intercalate a stop in it, we make two actions of it instead of one and that each of these actions will then be the indivisible of which we speak; that it is not the moving act itself which is never indivisible, but the motionless line it lays down beneath it like a track in space. Let us take our mind off the space subtending the movement and concentrate solely on the movement itself, on the act of tension or extension, in short, on pure mobility. This time we shall have a more exact image of our development in duration.

Your thought experiment read simply, but the instructions were not that clear to me — Watchmaker

Are you talking about perceiving red and yellow as one simultaneous unity? — Joshs

Is it possible to explain it simply? — Watchmaker

These are the folk who will explain the ineffable at great length, with no awareness of the irony involved. — Banno

Time is the activity of pure self-affecting — Joshs

It's almost like you were attacking John Cleese with a banana. — Vera Mont

↪jgill
What was the point of that post? — Bartricks

If God wants us to know what he is like, then he can do that. And he has, for we can know that God exists . . . — Bartricks

A point and any geometric extension are completely dissimilar from each other. It is strange that there is no thing in-between them — Gregory

Honestly, @apokrisis is the only guy I know around here who's comfortable with this sort of metaphysics, — Srap Tasmaner

In sum: You seem to want to investigate notions of infinity in non-mathematical senses or contexts. Fine. But then you'd do well to leave mathematics out of it if you don't know anything about the mathematics — TonesInDeepFreeze

Countable in the sense of: one infinite line and another infinite line make up two infinite lines.

Or: the infinity of real numbers and the infinity of natural numbers and the infinity of transfinite numbers make up three numerically distinct infinities. More technically, make up three numerically distinct infinite sets — javra

Okay. I certainly don't understand what your stance is on whether or not infinite lines are countable. — javra

In other words, “countable” can only hold the valid usage in its mathematical senses when addressing things such as lines. Therefore, the concept of there being “2 lines” is … invalid and nonsensical. — javra

I too wonder how a continuum makes up something discrete — Gregory

The definitions can of course be questioned — javra

The unit itself - which is a unit only because there are limits or boundaries which so delimit it - can however be counted. A geometric line does not have limiteless or unbounded width; its width holds a set limit or boundary, namely that of zero width. Because of this, one can quantify and thereby count geometric lines on a plane as individual units. — javra

↪jgill

You're a butthead, so we're even. — frank

Can not two points in a plane (with the plane itself determined by a multitude of points) determine a unique line, this as ↪Srap Tasmaner offered? In which case, the line here then has determinants and is thereby not indeterminate (i.e., undetermined) — javra

Is there any property in taxicab geometry analogous to curvature? — Srap Tasmaner

What makes them countable if they are completely devoid of any boundaries? — javra

If one can discern the quantity of lines specified, then lines as a whole are indeed countable. Or would you disagree with what I actually said? — javra

So for your question about the determinateness of mathematical infinities, you would say here that a line is I guess 'determinate enough' that we can pick it out as an object? — Srap Tasmaner

OP's question is one of whether mathematical infinity - your field I take it - is determinate, indeterminate, or neither? — javra

A mathematical infinity (in contrast to metaphysical infinity) is not limited or bounded in only certain respects and is thereby countable — javra

To exist is to be at the present. The pages in the past no longer exist, yet we have learned from them. And the important thing to note is that the pages of the future have no existence until the prior page is turned. The living being, existing at the present, is not the one turning the pages though. The page turning is being forced upon us, and if we do not move to the next page, (which has no existence until the previous is turned), by creating a place for ourselves on that page, or even better, creating a spectacle for others, on that page, then we get forced into the past. — Metaphysician Undercover

The Moving Finger writes; and, having writ,
Moves on: nor all thy Piety nor Wit
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it.

All boils down to the meaning of the concept of "real" and how useful our usage is to avoid fallacies of ambiguity. — Nickolasgaspar

You simply refuse to adhere to the rule, and insist on defending all those sinners who have gone before you — Metaphysician Undercover

What I am arguing is that mathematicians ought not accept such theorems, I am not trying to say that they don't accept them. So, you providing me evidence that they do accept them, just provides me with inspiration to produce a stronger argument that they ought not do what they do. — Metaphysician Undercover

What you'd prefer is to say that they do not have any apples . . . calling 0 a quantity is an abuse of the idea of quantity — Srap Tasmaner

No good. 0+ and 0− are used in limit notation to indicate one-sided limits but have nothing to do with opposites. — Real Gone Cat

A curious statement. All the years I've practiced math I can't recall using "opposite" in this way. But I suppose some do. — jgill

↪jgill

Major Edit : "Opposite" is perfectly fine when discussing positives and negatives — Real Gone Cat

This user has been deleted and all their posts removed. — Deleted User


That's an excellent username. And what better way to admit that you were wrong, then to delete all your posts. — Metaphysician Undercover

In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number) — Additive inverse - Wikipedia

I dunno, I don't really feel that way. I find pre-theoretical intuitions interesting and important. No math without 'em. — Srap Tasmaner

Recently I have taken an interest in testing remote viewing. — TiredThinker

Abstract, "pure mathematics" shows that we dream up universal principles (axioms) first, from the imagination, or they come to us intuitively, then we try to force the particulars of specific circumstances to be consistent with the universals. — Metaphysician Undercover

That's at least in the neighborhood of Sellars's argument and the impasse I expected to reach, that empiricism from a blank slate can't actually get started. — Srap Tasmaner

Psychologically, how can we confront this terminal historical moment we have all been thrust into? — hypericin