Paradox of irreducibility

[bahman]

You can't 'know' this! This is a philosophy forum, dealing with "knowledge" above all things. There are things that humans cannot 'know' currently. If you spoke of probability that would have been acceptable.

This is a philosophical argument: Things cannot be divisible into infinitum because it takes forever to divide things into its constitute hence it takes forever to build things up based on constitute.

Infinitum and forever are synonyms so:

If things were divisible to infinity,
then it would take infinity to divide things into their constituents,
thus the converse would be true.

Yes, this sounds completely reasonable to me.

You see, you can't say that the above, in blue, can't be the case, because your ignorance precludes it.
Why? Because you don't know everything!

So you agree with me?

[prothero]

"bahman wrote So you agree with me?

It all seems like a version of Zeno’s paradoxes, the arrow in flight, the tortoise and the race.

Ironically in General Relativity, the mathematics is based on mathematical points (non dimensional) and on continuity of space and time. It is not clear how anything dimensional could be composed of dimensionless points or how anything could be continuously divisible.
In Quantum mechanics on the other hand, nature comes in quanta (which are not non dimensional) and the world is discrete not continuous (at least in some interpretations).

The argument about whether space and time are continuous or quantized is at the center of the attempt to derive quantum theories of gravity.
Personally I favor the quantum interpretations of space-time but it is just a philosophical preference because I favor the process philosophy version of reality where reality is composed of discrete events in space time over the materialist ontologies.

[SpheresOfBalance]

This is a philosophical argument: Things cannot be divisible into infinitum because it takes forever to divide things into its constitute hence it takes forever to build things up based on constitute.

Infinitum and forever are synonyms so:

If things were divisible to infinity,
then it would take infinity to divide things into their constituents,
thus the converse would be true.

Yes, this sounds completely reasonable to me.

You see, you can't say that the above, in blue, can't be the case, because your ignorance precludes it.
Why? Because you don't know everything!

So you agree with me?

NO! You didn't catch my funny little point, which is that it's perfectly reasonable, since we're not done yet, since we're not done yet, since we're not done yet. Get it yet? The universe is not done morphing yet, hopefully it remains doing so until I finish this message and send it to you. In other words infinity hasn't been reached yet, and of course if the universe is infinite, it never will be reached. So it makes perfect sense that since infinity, in it's strictest sense, is forever, unending, then size can equally go on forever, to infinity, as it never ends. Understand my little play with words.

In other words, when dealing with infinity, it says absolutely nothing to say that "it would take infinity to divide things into their constituents," juxtaposed by "it would take infinity to build things up from their constituents, as it's saying the exact same thing, the direction through time that you reference is always going to be the reciprocal of the opposite direction. One direction does not collide with the other, they are the same, simply the reverse. The idea of infinity, in it's strictest sense, actually ensures that size could go on forever in both directions.

[prothero]

Infinite divisibility like non dimensional mathematical points, is not something we encounter in the real world of experience only in the realm of mathematics.