All I can suggest at this point is looking into the standard mathematics of infinity. — aletheist

I've looked at it; its rubbish. They declare in the axiom of infinity that actual infinity exists and prove absolutely nothing. They then move on to patch up all the paradoxes that creates with further illogical axioms.

Between any two points that we mark on a line, there is an inexhaustible continuum of other potential points; — aletheist

A point has length 0. How many points on a line segment length 1? 1/0=UNDEFINED.

I've looked at it; its rubbish. — Devans99

No doubt they would say the same about your arguments here.

A point has length 0. How many points on a line segment length 1? 1/0=UNDEFINED. — Devans99

You remain wedded to the mathematics of discrete quantity. Again, there are no points on a continuous line, unless and until we mark them as discontinuities.

No doubt they would say the same about your arguments here — aletheist

My arguments are not shot through with paradoxes. Cantor's, Galileo's, Hilbert's Hotel, Zeno's... what a mess actual infinity has made of maths and science.

Paradoxes indicate an underlying logic error (actual infinity exists).

Paradoxes indicate an underlying logic error (actual infinity exists). — Devans99

Contradictions indicate an underlying logic error; paradoxes indicate a need to think more carefully.

How many times must I repeat that I am arguing for real continuity, not actual infinity, and that these are two distinct concepts? that motion (space-time) is more fundamental than position (space) or duration (time) treated separately? that a line does not consist of points, and that a temporal interval does not consist of instants?

How many times must I repeat that I am arguing for real continuity, not actual infinity, and that these are two distinct concepts? — aletheist

I see no model of continuity that does not need actual infinity. If you point me to such a model, I stand corrected, but they all seem to use actual infinity.

Any real continuum can be subdivided infinity so it it exists in the present or the past, it must support an actually infinite number of sub-divisions.

I see no model of continuity that does not need actual infinity. If you point me to such a model, I stand corrected, but they all seem to use actual infinity. — Devans99

In Peirce's model of a true continuum, the infinity is potential rather than actual. The real is not coextensive with the actual (existence); there are also real possibilities and real (conditional) necessities.

Any real continuum can be subdivided infinity so it it exists in the present or the past, it must support an actually infinite number of sub-divisions. — Devans99

No, any real continuum could potentially be subdivided infinitely; it can never actually be subdivided infinitely. See the difference?

Actual infinity, if it existed, would be a quantity greater than all other quantities, but:

There is no quantity X such that X > all other quantities because X +1 > X

Now you could define:

∞ + 1 = ∞
But that implies:
1 = 0 — Devans99

Didn't you know that the mathematics of infinity is a kludge put there to force it into the arithmetic we use on finite numbers? :chin:

Didn't you know that the mathematics of infinity is a kludge put there to force it into the arithmetic we use on finite numbers? — Pattern-chaser

Yes I think so. It was all motivated by misplaced belief I think: Cantor an Co thought God was infinite so infinity was shoe-horned into mathematics for that reason.

Nothing wrong with having a finite-sized God IMO.

No, any real continuum could potentially be subdivided infinitely; it can never actually be subdivided infinitely. See the difference? — aletheist

I would argue that our progress through time is progress through the continuum at the most fundamental level so it requires actual infinity. As does our progress through space when we move. So in both cases our progress through time and space subdivides the continuum to an actual infinity.

How on earth could you construct a continuum? It requires us to construct an actual infinity of possible positions for particles to occupy. — Devans99

I'd say that the mistake you're making here is that you're thinking of spatial extension as a "construction consisting of possible positions for particles to occupy," You're reifying mathematical ideas.

So in both cases our progress through time and space subdivides the continuum to an actual infinity. — Devans99

No, that progress itself through the space-time continuum (i.e., motion) is the fundamental reality; any discrete subdivisions of space and time are our arbitrary constructions.

No, that progress itself through the space-time continuum (i.e., motion) is the fundamental reality; any discrete subdivisions of space and time are our arbitrary constructions. — aletheist

I don't think we will ever agree on this point.

You did not answer my argument that the information content of a larger region of space-time must be larger than a smaller region of space-time? It rules out all forms of continuum with a very reasonable axiom?

You did not answer my argument that the information content of a larger region of space-time must be larger than a smaller region of space-time? — Devans99

Yes, I did.

It begs the question to presuppose discrete units of "information" (i.e., points or finite segments) that comprise a "real line." — aletheist

... or in this case, a "region of space-time."

Ah sorry. The information can be in analog form; number of bits is merely a way to quantify it. Indeed that is the problem; the fact that position is given to infinite precision by the continuum means it is contradictory; all volumes of space-time contain the same amount of information no matter what size is clearly contradictory.

1. A point in space cannot have size=0 because it would only exist in our minds and not reality (no width; insubstantial) — Devans99

And yet we can calculate instantaneous velocity.

I do not see how your argument can survive that.

Not sure I see what you mean. A calculation is just purely in our heads; that does not mean an object actually has instantaneous velocity. Discrete space-time would make instantaneous impossible.

What about the analogy of filming someone for zero seconds? No film would exist. Film is a good analogy for time.

A calculation is just purely in our heads... — Devans99

And yet the car is moving at 50km/h.

So, from "A calculation is just purely in our heads" it does not follow that "A velocity is purely in our heads..."

A film zero seconds long is called a Photo.

But the car can only be said to have instantaneous in a continuum; in a discrete world it would have velocity over a discrete interval rather than an 'instant'

Photo's require a non-zero length to exist (exposure time).

I think I will maybe adopt 'things need a non-zero length to exist' as an axiom.

The information can be in analog form; number of bits is merely a way to quantify it ... all volumes of space-time contain the same amount of information no matter what size is clearly contradictory. — Devans99

As soon as you talk about comparing the "amount" of something, you are quantifying it, and thereby treating it as discrete--i.e., begging the question.

the fact that position is given to infinite precision by the continuum means it is contradictory — Devans99

What part of "motion is more fundamental than position" do you still not understand? Giving the position of something to any degree of precision requires measuring its distance from an arbitrary reference point at an arbitrary instant using an arbitrary unit.

Film is a good analogy for time. — Devans99

Only if you presuppose that time is discrete, like the film in a motion picture.

As soon as you talk about comparing the "amount" of something, you are quantifying it, and thereby treating it as discrete — aletheist

We can compare analog quantities perfectly well.

What part of "motion is more fundamental than position" do you still not understand? Giving the position of something to any degree of precision requires measuring its distance from an arbitrary reference point at an arbitrary instant using an arbitrary unit. — aletheist

You are clearly on a different planet to me. There is just no way a light year has identical granularity and structure to a centimetre; I think I will have to bail out! Thanks for the conversation though. Happy Xmas.

There is just no way a light year has identical granularity and structure to a centimetre — Devans99

The mistake is assuming that, in itself, any arbitrary portion of space-time has any granularity--i.e., discreteness--at all.

Thanks for the conversation though. Happy Xmas. — Devans99

Likewise!

But the car can only be said to have instantaneous in a continuum; in a discrete world it would have velocity over a discrete interval rather than an 'instant' — Devans99

SO if you assume a discrete world, you find that the world is discreet.

(??)

a) Imagine a second and a year
b) By the definition of continuous, both time period are graduated identically (to infinite precision).
c) So there must be the same information content in both (same number of time frames: ∞)
d) But a year should contain more information than a second
e) Reductio ad absurdum, time must be discrete — Devans99

This is pretty directly erroneous.

a) Imagine 2 and 4
b) By the definition of continuous, both numbers are graduated identically (to infinite precision).
c) So there must be the same information content in both
d) But 4 should contain more information than 2...

It's just bad maths.

Imagine an interval of 2 and 4 I mean...

SO an interval of 4 has twice as much information as an interval of 2?

What does that mean?

That makes sense. What does not make sense is that they both contain an actually infinite and therefore equal amount of information. One is larger than the other.

Only in our minds does the actually infinite exist; its not a real world concept.

That makes sense. — Devans99

No, it doesn't. 4 might be twice two, but what could it mean to say it has twice the information?

What sort of thing is information?

Only in our minds does the actually infinite exist; its not a real world concept. — Devans99

So your mind is not in the real world? Infinity is not a thing like my cat or last Tuesday? What's going on here? Is infinity a thing like my mortgage? Like a unicorn?

What sort of thing is information? — Banno

What is it?

Yes, that's right.