Do Mathematical Entities Really Exist?

[athon]

I guess it depends on how one feels about a Platonic 'realm' or facet to the universe.

It's impossible for us to grasp something existing without a set of mechanics behind it. Where are the laws of the universe kept? What is the nature of information? Are numbers actual entities? All of these things require us to see reality as having an extra layer, where rules are kept. We can try to imagine it like a computer game - your 3D avatar runs through a constructed world that exists only in a set of rules that conduct how the pixels will arrange on a screen. We're content in knowing that the rules are binary codes contained in logic gates and electron movements. As if that answers anything about where the laws are kept.

In short, we don't even know if there is an answer, let alone where it is. As I've got in my sig', we're looking for the ghost in the machine; when we find it, we'll only start looking for the machine in the ghost. For now, information can only be a commentary on what we observe and we can't say much about the nature of it in itself.

Athon

 

[Merko]

I believe that numbers 'exist' as relations. Eg, '2' is comparable to 'in front of'.

They have no meaning on their own, only in expressions dealing with other entities.


Incidentally, I think the answer to 'do humans have a soul?' is the same. Sure, if we define the 'soul' as the pattern that shapes our personality.

 

[nimzov]

I guess it depends on how one feels about a Platonic 'realm' or facet to the universe.

It's impossible for us to grasp something existing without a set of mechanics behind it. Where are the laws of the universe kept? What is the nature of information? Are numbers actual entities? All of these things require us to see reality as having an extra layer, where rules are kept. We can try to imagine it like a computer game - your 3D avatar runs through a constructed world that exists only in a set of rules that conduct how the pixels will arrange on a screen. We're content in knowing that the rules are binary codes contained in logic gates and electron movements. As if that answers anything about where the laws are kept.

In short, we don't even know if there is an answer, let alone where it is. As I've got in my sig', we're looking for the ghost in the machine; when we find it, we'll only start looking for the machine in the ghost. For now, information can only be a commentary on what we observe and we can't say much about the nature of it in itself.

Athon

Nominated.

Very interesting thanks.

We may also ask ourselves what would be the "reality" of fractals if we did not have computer to calculate and visualize them. I guess that fractals were discovered.

Will the question of discovery versus invention in mathematics ever have an answer ?

nimzo

 

[69dodge]

Will the question of discovery versus invention in mathematics ever have an answer ?

We invent axioms. We discover their consequences.

(And we hope they're consistent. )

 

[Wowbagger]

I am honored to have inspired this thread. But, I think it treads into philosophical realms, where multiple people could come up with different reasonable definitions of "exists", and although some of those definitions might conflict with each other, they would still be correct, from a particular point of view. I think Daniel C. Dennett wrote a book about such things, he refers to as the "intentional stance". You could claim that Santa Claus exists, if by "Santa Claus" you were referring to some particular guy walking on the street, even if said person does not look anything like "Santa Claus" as most others would define him.

Does that make sense, or is that another example of rambling?

In my humble view, it seems mathematics evolved as a very concrete method of defining things, and solving problems. Mathematics may not be very real, as far as the rest of the natural Universe is concerned, but for us, it is an undeniably useful tool for examining the world.

In my pi thread, someone brought up the idea that numbers are like adjectives, used to describe things, like "ugly" is a verb, and thus numbers do not really exist as physical entities, but rather descriptions of entities. I think the biggest difference between "ugly" and, say, the number 2, is that "ugliness" is subjective: Two people can disagree on what is ugly, and both be right. Yet, the number 2 is objective: If two different people disagree on how many things is 2, then one of them is probably crazy.

So, to summarize, mathematics is about the most realistic method we have for modeling our Universe, but the numbers, themselves, do not exist as entities: They are merely convenient states of thinking we evolved to help us live.

 

[Dave1001]

interesting question.....

my own opinion would be that mathematics is the underlying reality of the universe.
If the universe is completely deterministic then i think that the all encompassing theory of everything would be that which really exists - the universe as we percieve it exists as a representation of that underlying reality - a bit like how the underlying reality of this website is its source code and that which we perceive as existing is just a manifestation of that code.

lol
although i'll admit i'm way out of my depth on this one (not that it usually stops me giving an opinion )

How do you think the limits of our brains play into that? The question of whether it's underlying reality we're discovering, or the fundamental limiting structures of our brains.

 

[tsg]

What would be a mathematically impossible amount of beef?

-1 beef.

 

[Merko]

wowbagger: I believe 'ugly' is an adjective. But although 'ugly' is subjective, there are definitely adjectives that are just as objective as math. An obvious example would be 'double'. Like I already wrote above, I think mathematical concepts exist exactly in this way.

 

[hammegk]

The question of whether it's underlying reality we're discovering, or the fundamental limiting structures of our brains.

mu

 

[Squishua]

What would be a mathematically impossible amount of beef?

Maybe 1/2 lb of beef in a patty that weighs 1/4 lb?

Nobody beats ad-men when it comes to nonsense statements.

-Squish

 

[Pidge]

<Insert Gary Larson cartoon of "Please sir, may I leave the room? My brain is full.">

 

[Wowbagger]

wowbagger: I believe 'ugly' is an adjective.

I knew that! Stupid mistake! Stupid, stupid, stupid...

Anyway, I corrected the thread, so no one else will know.

But although 'ugly' is subjective, there are definitely adjectives that are just as objective as math. An obvious example would be 'double'. Like I already wrote above, I think mathematical concepts exist exactly in this way.

True, but 'double' is not so different from the concept of 'two of them'.

 

[l0rca]

I suppose we don't have any hardcore mathematicians here?

Not that I enjoy math much. But I'll describe here, as simple logic compounded, and eventually in its use morphed, morphed enough to draw the line.

Math originally was, and in real number systems, still is a game of being specific. This math in theory takes quantities in supposed equal sums and computes them. Symbols see. These symbols perfectly represent reality, again in theory, because they carry no meaning beyond quantity, and the theory assumes quantities do not randomly change, so long as they are initially accurate.

So this sort of math is a subjectional reference point for real quantities. It's subjectional because this human invention of math has its own individual connotations of emotion and history with its users.

So far as math as an entity, no, it does not exist at all. The universe does not operate according to mathematical principles. It can be described in math as it can in the best of words, though perhaps better, since math relays concrete quantities quite bare to mind, though our minds do dress them so. Still, the workings of the universe are unknown.

Now if we were to redefine math not as a computational ideal, but as an ambiguous, simple set of underpinnings for which things seem to operate, inversely identifiable by complex algorithms and the sort, we could say yes, math as an entity exists. But why cause such pejoration when we already have such a good grasp of our own subjectivity?

 

[andyandy]

The universe does not operate according to mathematical principles.

that's a rather absolute statement....

 

[l0rca]

that's a rather absolute statement....

I think if these forums were more capable of less redundant debate, I'd be less absolute.

Anyway, I think it's a rather safe guess.

 

[Dave1001]

that's a rather absolute statement....

I think he qualifies it sufficiently (in fact perhaps qualifies it to the point he's overabsolutist in the other direction) here:

Now if we were to redefine math not as a computational ideal, but as an ambiguous, simple set of underpinnings for which things seem to operate, inversely identifiable by complex algorithms and the sort, we could say yes, math as an entity exists. But why cause such pejoration when we already have such a good grasp of our own subjectivity?

 

[Dave1001]

I think if these forums were more capable of less redundant debate, I'd be less absolute.

Anyway, I think it's a rather safe guess.

Are you a "hardcore mathematician?"

 

[l0rca]

I think he qualifies it sufficiently (in fact perhaps qualifies it to the point he's overabsolutist in the other direction) here:

I can't tell if you're agreeing with me or critiquing a small point.

Are you a "hardcore mathematician?"

Underneath that statement about being a hardcore mathematician, I typed: "Not that I enjoy math much."

 

[joobz]

They are as real as they need to be.

 

[Dave1001]

I can't tell if you're agreeing with me or critiquing a small point.

both

but more the former.