[Koshkin]

> Did we really know what “5” was then? What is five-ness really?

Ah, but we do, and it’s very simple: it is what five cows an five fingers have in common in the most obvious sense. There’s no mystery there.

Or, stated in another way, “fiveness is something you’ll be very sad not to see when you look at your hand.”

[orthonormal]

I lost one of my fingers when i was a child, so after getting used to it i don't experience sadness when i look at it. That statement also checks out for four, in this case.

[lazydud]

Ok

[esarbe]

This presumes the existence of a category like 'cow' or 'finger'. I'm pretty sure there's nothing intrinsic about 'cows' and 'fingers'; these are artifacts of human cognition.

I base reality, there are no such things as 'cows' and 'fingers'. Just systems with similar properties. And if you have to be very pedantic, there are not even discrete systems, since everything is linked by information. You cannot separate a river from the ocean - it's part of the same system.

So, given that there are no categories to put discrete things into - they just exist in our imagination - and there are probably not even discrete things - these also just exist in our imagination - the question of five-ness is not really answered.

[Radim]

> You cannot separate a river from the ocean - it's part of the same system.

> discrete things - these also just exist in our imagination

What leads you to separate "imagination" from "exists"? Isn't imagination also "part of the same system"?

Imagination definitely has the capacity to affect the world, so it's not obvious in what way it's "not real". Why do you draw a hard line there?

[Koshkin]

More to the point, the idea that "you cannot separate a river from the ocean" seems to be ostensibly wrong - otherwise we wouldn't have the (very useful in practice) notions of 'river' and 'ocean' in the first place. If you look at a map, the differences stand out pretty clearly - e.g., a river has a starkly different topology from that of the ocean. So, no, these differences are not just figments of our imagination, as, in particular, everyday practice shows.

In general, the failure to perceive emergent phenomena as something different from the particular substrate, and consider it separately - for instance, the failure to see how nature is not just a bunch of atoms moving around, has a name - reductionism. It is a form of intellectual blindness (not to be confused with the ability to think abstractly).

[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.

[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?

[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

[vageli]

> This presumes the existence of a category like 'cow' or 'finger'. I'm pretty sure there's nothing intrinsic about 'cows' and 'fingers'; these are artifacts of human cognition. I base reality, there are no such things as 'cows' and 'fingers'. Just systems with similar properties. And if you have to be very pedantic, there are not even discrete systems, since everything is linked by information. You cannot separate a river from the ocean - it's part of the same system.

When I cut my finger the cow does not share in my pain. When we kill the cow for its meat, we do not share in its pain. That the cow becomes part of us through its consumption does not seem to invalidate this point—discrete systems do exist in our experience.

Of course, if you zoom out far enough you might refer to the sum of those discrete parts as some singular, complex system, but it seems the human experience is fairly limited in exposing this subtlety (not to mention that it is often useful to discuss the parts themselves without considering their relationship to the entire universe).

[trashtester]

Also, the concepts "artifacts", "human", "human cognition" and "artifacts of human cognition" are all example artifacts of human cognition.

As is "circular", "reasoning" and "circular reasoning", as well as "irony".

[Koshkin]

I don't know about that. Reality is strongly suggestive. (Of course you can argue that "reality" also is a figment of our imagination or, for example, it's not a thing in the first place, but I personally wouldn't go that far.)