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.”
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.
> 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?
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).
I'm just pointing that without arbitrarily dividing the world into separate parts, numbers don't arise.
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.
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.
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.
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?
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.
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).
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).
As is "circular", "reasoning" and "circular reasoning", as well as "irony".
Using different bases, to me, is just about storing information. How many symbols do you want to create before you increase the length of your number and start re-using them.
It is everything that has some relation to something that has that same relation to something that has that same relation to something that has that same relation to something that has that same relation to some unique thing that does NOT have that same relation to anything.
I would say I knew what 5 was even before I learned any notation or written language whatsoever.
The reason it seems mushy is because there are two related concepts at play: a numeral vs. a number.
A numeral is the symbol: 5 in Arabic numerals in Latin script or ٥ in Arabic script; V in Roman numerals etc.
A number is the quantity, the amount being expressed: five (English), ḫamsa (Arabic), cinq (French) etc.
But for us humans, the tokens and concepts blend to some degree: maybe not so much with regards to numerals (although there seem to be exceptions ...). So even if 'Amour', 'Love' and 'Liebe' essentially point to the same concept, we might conceive of them differently, ever so slightly, depending on the language we chose to use.
Which gives an inkling of the vast difference between computers and humans, at the current stage.
(My inner Asberger's could not resist.)
Every interaction our human minds have with fiveness is with a representation or encoding of 5. With each new representation, I’ve experienced fiveness slightly differently.
But I like computers and math. For me, the best to experience oneness with the fiveness is through computation with Lambda Calculus and Church Numerals. Very fond of that encoding.