Are numbers as real as rocks?

[Jonti]

Are numbers as real as rocks, but rather more certain?

Seems to me that Kronecker was onto something when he remarked

God* created the integers, all else is the work of man.​

* Using God here in the transcendent deist sense

Not that I'm unhappy with the mathematics of infinities in any way, which is what Kronecker was attacking. It's just that, well, there's nothing particularly or specifically human about numbers, is there? All cultures have had them. Arithmetical operations are the same, and give the same answers, in all times and places. A number if prime, is prime, wherever and whenever one is in the universe.

When we meet with aliens, they will have the same infinite set of prime numbers as we, and they may also understand the (joke?) that the prime numbers are all you have left when you take the patterns away.

Numbers are real, no less than the trees and the stars. They are just here.

 

[In Bloom]

I'm sorry, but that's a pile of shite.

Numbers only exist where there is a subject to percieve separate objects. For example, there are two mugs on my desk. It's only by me being here that there is any distinction between the two mugs, or the mugs and the desk.

Numbers are an abstract concept.

 

[englaender]

but the abstract concept of numbers and the rules that govern them exist as a given throughout the universe.

so if we found aliens as such and they perceived the world in a similar enough way to ourselves then their 'numbers' would be governed by exactly the same rules as ours.

or not?

 

[8ball]

I have a suspicion that the rocks are actually made of numbers.

So numbers are actually realer than rocks.

 

[lizzieloo]

you stoned?

 

[118118]

Yeah, I am dead against psychologism.

If In Bloom is saying that they are a product of the mind alone, then couldn't it be the case that an alien had different logic that worked as well in the propositions in their mind (bit of dualism their), but was different.

No-one condones psychologism, get with the program. Anyway, I haven't revised my Husserl yet; but I would guess that no-one here (bar PhilDwyer ) knows Marx's ontology - it was just critical, anyway, probably. I reckon that wasn't psychologistic, though.

 

[In Bloom]

but the abstract concept of numbers and the rules that govern them exist as a given throughout the universe.

so if we found aliens as such and they perceived the world in a similar enough way to ourselves then their 'numbers' would be governed by exactly the same rules as ours.

or not?

That doesn't make numbers any less abstract or any more "real" (whatever than means).

I mean think about what you're saying here, to all intents and purposes, you're saying "If aliens percieved things in the same way as us, they'd percieve things in the same way as us".

 

[118118]

Numbers are an abstract concept

After you've had your way with capitalism, will numbers no-longer exist

 

[In Bloom]

If In Bloom is saying that they are a product of the mind alone

I'm saying that they are a product of the way that we percieve the world around us, not quite the same thing.

 

[118118]

That doesn't make numbers any less abstract or any more "real" (whatever than means).

I mean think about what you're saying here, to all intents and purposes, you're saying "If aliens percieved things in the same way as us, they'd percieve things in the same way as us".

So, like, perception is just logic?

 

[In Bloom]

After you've had your way with capitalism, will numbers no-longer exist

Eh? What does capitalism have to do with anything?

 

[118118]

I'm saying that they are a product of the way that we percieve the world around us, not quite the same thing.

Would that not leave you free to blame either/both physical reality or the relection of it, for the fact that number work.

So you are saying very little at all?

 

[In Bloom]

Is there any chance you could go sober up somewhere until you're capable of communicating in coherent English again?

 

[Jonti]

I'm saying that they are a product of the way that we percieve the world around us, not quite the same thing.

Ah, I guess I'm saying we see the world with numbers

 

[Jonti]

After you've had your way with capitalism, will numbers no-longer exist

After the revolution, only my numbers will exist

 

[Jonti]

Hey, smartarse

whatever "real" means.

What's your theory?

 

[118118]

So no-one is sayiong that aritmetic is laws of thiought?

I would say that numbers are seen, and !+! would == 2 whether or not anyone thought to prove it. I mean, the fact that I think 1+1 = 3, does not mean that this is the case.

 

[Loki]

After the revolution, only my numbers will exist

*buries a stash of numbers in garden*

 

[118118]

I will read my notes omn Husserl tommorow. I diunno, anyone think that through the intution of !+!=2 we see, some kind of non platonic realm of inuitions, like ethics as well. Does anyone actually know what his theory of number was, my notes are crap. I thi9nk the difference may be that ithey are essemces that do not interact with anything but mind, but he was a solipsist, so

 

[Knotted]

In my view the most succinct form of this question is:
"Are numbers invented or discovered?"

A lot of people will reply one or the other with absolute certainty and very little thought. I think that this is because there are clear and apparent problems both with the realist and the nominalist approaches, and thats without going into the numerous and often radically different subcategories.

If numbers are real then they should have an observable effect. If numbers are invented then the extraodinary relevance of mathematics needs to be explained.

The quote by Kronecker is indeed profound and ahead of its time and that's without going into the philosophical arguments that he was engaging in, or for that matter arguments about God. Frege showed that mathematics can be reduced to set theory and from set theory we have the notion of cardinality and thus numbers but its really difficult to define a set without the notion of a number to start with and I think that those who have tried have merely disguised the notion of number.

By the way it should be understood that Kronecker was talking about whole numbers (probably positive/non-negative whole numbers). Rational numbers, real numbers etc. can be constructed from the natural numbers.

Anyway, to take sides I favour a soft platonic realism of some form or other - just because it feels right if for no other reason. Last time I looked at this question I felt warmly towards the pseudo-empirical realists. However, the question is just far too hard to get a truly convincing answer to in my opinion. It hasn't been resolved in 2000 years and it won't be resolved in the next 2000 years either.

 

[Knotted]

No-one condones psychologism, get with the program. Anyway, I haven't revised my Husserl yet; but I would guess that no-one here (bar PhilDwyer ) knows Marx's ontology - it was just critical, anyway, probably. I reckon that wasn't psychologistic, though.

I think you are talking about nominalism rather than psychologism. The latter is an example of the former.

But yes, I think that Marx was not a nominalist with respect to abstractions in general. I see him as following Aristotle. Roughly, abstractions are real but not seperable from the concrete (if I remember correctly). His political economy relies on this, I think. Concepts like exchange value and surplus value do not have a direct empirical existance, but are not supposed to be considered seperatly from the (real material) totatlity of social relations.

Engels claimed that mathematics is discovered through the study of nature rather than the other way round. I would categorise that as an empiricist/realist outlook perhaps similar to John Stuart Mill's.

No idea about Husserl though.

 

[Bob_the_lost]

Numbers are an invention rather than a fundamental thing. The more you spend studying maths the more you realise just how contrived it can be at times.

You can't count - 5 pigs, it's compared to debt as a thought process but it's not physically possible to get hold of -5 pigs the entire idea is stupid. It only gets really confusing when you start getting to complex numbers (the second axis on the number line) and start wondering just how many dimensions this mathematical system wants to develop.

 

[weltweit]

Are numbers as real as rocks?

No of course not, run flat out into some rocks and you will bleed and hurt, numbers do not have physical presence they are an idea, a thought, a description of quantity, a simple logic that I think we come to understand innately initially.

There must be something innate about numbers because we are not the only animals to understand them.

Consider a rabbit with 6 babies, how does it know it has all 6 of its babies back in its hole after having come in from eating green green grass.

Answer: the rabbit must *somehow* count them, realise they are all there before relaxing.

Even if it does not count as humans do I am sure the rabbit with 6 babies knows that it has a greater quantity than 2 or 1 or 0 .. it certainly knows all of its babies and will defend them all.

Does a human child with two toys realise that they have more than 1, try taking the other toy away, I bet the child will say “hey that is mine”, so it knows at an early age that it can have more than one toy.

Try taking both toys away and it will have “the absence of toys” = 0 toys

Therefore numbers or some kind of appreciation of quantity is present in human children and in animals.

Does that make any sense?

At its most basic level zero of anything is the absence of 1 or more of that thing.

I have no baby rabbits = I have zero = I do not even have 1

Then I have a baby rabbit = I have some / 1 = the presence of something

Of course rabbits can confuse maths because once you have a male and a female they self multiply like rabbits - another mathematical issue

Two humans coming together intimately m/f can also manufacture a third, so in that sense of it 1+1=3 ..

I expect though that will not make any sense

Just a few thoughts, I am not a philosopher.

 

[Bob_the_lost]

Answer: the rabbit must *somehow* count them, realise they are all there before relaxing.

Nice idea, but it's along the same lines as someone who can see saying that it's not possible for a blind person to be able to climb stairs, thus anyone who can climb stairs can't be blind

Rabits will probably work upon smell (?), so it'd be like walking into your room and noticing that the smell is somehow wrong.

 

[weltweit]

Rabits will probably work upon smell (?), so it'd be like walking into your room and noticing that the smell is somehow wrong.

That is surely just a nice idea, why are you so sure that rabbits cannot tell that the absence of an absence is a presence

Or I can smell all 6 of my babies therefore they are all there.

Me I do not buy the idea that human minds are so superior .. granted it can be claimed in some aspects .. but polar bears bring up their kids for years .. what is it that they are teaching their children if it is not *the knowledge* in polar bear terms.

 

[Aldebaran]

It's just that, well, there's nothing particularly or specifically human about numbers, is there? All cultures have had them. Arithmetical operations are the same, and give the same answers, in all times and places. A number if prime, is prime, wherever and whenever one is in the universe.

It is particularly and specifically human because for humans it can only become a reality within its human invented form and frame. I don't think what you call "answers" are bound to be the same everywhere in the universe. Would an other lifeform not have other answers because using other systems?

Numbers are real, no less than the trees and the stars. They are just here.

They are real for those who take them as real.
When I look at a serial of numbers a bit more complex then 1+1=2, I see something very different then you do.
Maybe I am an alien or maybe an alien would see them like I do and maybe its whole culture does. That would make your outcome, which for you is normal because inevitable, alien to them.
Of course I see the core of the problem you discuss, but I think you are premature to conclude that "the universe" as we perceive it would be perceived the same way all over the universe.

salaam.

 

[Knotted]

Numbers are an invention rather than a fundamental thing. The more you spend studying maths the more you realise just how contrived it can be at times.

You can't count - 5 pigs, it's compared to debt as a thought process but it's not physically possible to get hold of -5 pigs the entire idea is stupid. It only gets really confusing when you start getting to complex numbers (the second axis on the number line) and start wondering just how many dimensions this mathematical system wants to develop.

This is what I think that Kronecker was talking about though. Negative numbers, rational numbers, real numbers, complex numbers, solvable groups, lebesque measures, complete semilattices etc. etc. are mathematical constructs. (We should bare in mind that Kronecker's main target was Cantor's transfinite set theory though). However ordinary natural numbers seem to be 'God given'. I'm not in the habit of saying things are God given but it gets a point across.

If the notion of 5 pigs is just pure mathematical idealism, why does it seem to make sense?

 

[Jonti]

You can't have any thing, except by having a number of those things. So objects themselves imply number. If there's a real world of objects (!) integers are real.

They're as real as the rocks they count. More "real", because messing with numbers gives more certain results than banging the rocks together.

 

[Jazzz]

numbers are possible realer than rocks.

Mind you, I'd rather hit my head on a number.

 

[danny la rouge]

Mind you, I'd rather hit my head on a number.

Very true.

I'd also rather smoke a number.