[esarbe]

I'm not drawing a hard line at all; yes, imagination is part of the same system. And of course it has the capacity to affect the world.

I'm just pointing that without arbitrarily dividing the world into separate parts, numbers don't arise.

[Radim]

But "world", "separate" and "parts" are all language concepts too. I feel the inconsistency in your (circular) argument is not getting through.

That divisions are arbitrary and "exist just in our imagination" doesn't line up with your admission that imagination is real, and using words to describe it. That line between "real" vs "arbitrary / imaginary" is not as clear cut as you (unconsciously, apparently) draw it.

[esarbe]

> I feel the inconsistency in your (circular) argument is not getting through.

I guess it's not, since I'm not convinced that mine is a circular argument.

My argument - to put is simply - is that we are all part of the same system and that there are no divisions. Without divisions, no numbers. I don't need any distinction between 'real' and 'arbitrary' for this to hold, that's a dichotomy you assume on your part.

[Radim]

Yes, we may be all part of the same whole. But there definitely are divisions – you are manifesting them with your own words. QED.

Let me try differently. Your premise seems to be that "base reality" (your words) is a single teeming interconnectedness, indivisibly unique, from which it follows "there are no discrete systems", no categories, from which it follows that counting discrete things is an "artifact of human cognition".

Correct? Did I get your position right?

I simply pointed out that human cognition / imagination, including language and categories and logic and numbers, is as much a part of the base reality (that same teeming interconnectedness) as anything else. You manifest your words = they capture a pattern, patently recognizable from other patterns, transmittable (e.g. to me), with a potential to affect me and others and our future.

The world being interconnected doesn't mean it's undifferentiated. All work is still ahead of you in showing that categories and words are somehow "not intrinsic" (again, your words). Yes they may be a teeming that refers to other teeming, but you haven't shown that's anything special, worthy of singling out as extrinsic.

[esarbe]

> Let me try differently. Your premise seems to be that "base reality" (your words) is a single teeming interconnectedness, indivisibly unique, from which it follows "there are no discrete systems", no categories, from which it follows that counting discrete things is an "artifact of human cognition".

Yes, I think you summarized it pretty good! Thanks for that.

> Yes, we may be all part of the same whole. But there definitely are divisions – you are manifesting them with your own words. QED.

Woah, not so fast, there! Where exactly do my words manifest divisions? The words you read on the screen, that manifest in your mind as meaning are not discrete things themselves. No word stands for itself, else we would not need dictionaries. They are fuzzy things that often change their meaning, depending on context, place and time, on the reader and what she ate in the morning. To claim that words are discrete things that exists

> The world being interconnected doesn't mean it's undifferentiated.

I agree. Just as there are patterns in stellar nebulae that swirl and dance but never quite separate, all the world manifests its decay in wonderful shapes and patterns.

But none of these patterns can be isolated from the others, for non of the patterns can there a definite line be drawn to say "your existence starts here and ends here". The boundary of every definition, of every category can be shifted and shifted and shifted some more. They are - as already mentioned - artifacts of cognition that allow us to form a mental model of the world that surrounds us. Replacing the unfathomable interconnectedness with a simple game of blocks and strings and forces that fit into the limited capabilities of the simulation we run in our heads.

> All work is still ahead of you in showing that categories and words are somehow "not intrinsic" (again, your words).

Categories and words, numbers and letters and the human mind are fleeting. How can they be intrinsic if they exist for only an eye blink?

[dalmo3]

In your world without numbers, do letters exist? Does the letter "n" exist? Is there any relation between "n" and "nn" and "nnn"? If so, how would you describe that relation?

[esarbe]

Do letters have an existence outside of our heads? I doubt it.

With regards to the relationship between repeating sequences; we (humans) invented funny games to describe these patterns as we perceive them. Some of these games have very strict and elaborate rules, although most of them are either inconsistent, incomplete or undecidable or trivial.

Even constructive mathematics offers no help here.

[trashtester]

> I'm just pointing that without arbitrarily dividing the world into separate parts, numbers don't arise.

I agree. Though I think a stronger statement is also true: Without "arbitrarily" dividing the world into separate parts, non-trivial thought is not possible.

Assuming by "parts", you mean "categories", I think my statement is still true. And, once we have categories, we can use numbers to compress information, which in terms allow us to perform more complex computation/though with our limited computational power.

As to how arbitrary our categories are, one could argue that some are hardwired to our DNA, as claimed by Chomsky(1).

[1]: https://en.wikipedia.org/wiki/Universal_grammar