What Are Numbers?

Radical · May 18, 2015

csbrown28 said:
It sounds to me like you need to start from the beginning. Do we exist?...Unfortunately, the only reality is that there is no way to prove that my senses are giving me accurate information about reality because I'm bound by those same senses to figure it out. I make the assumption that my senses are in fact sometimes accurate. From there everything else that I know to be true should be able to be shown to be true via evidence... So the idea that sets do in fact exist in this universe can be shown to be true via evidence, but I don't think that numbers transcend this universe to all other universes.

Or have I terribly over thought your question?

You didn't over think anything; this is exactly what I'm looking for. Sense realism is assumed by most people, and it looks like us two as well. Let's start there. Stuff exists. The stuff does other stuff. Then we try to make sense of it all. The institution of understanding reality we call "science" (it used to be called "philosophy"... no one likes us philosophers any more...). This is really all the background I need to begin my stuff about quantity. Through our senses and our scientific instruments, understand structures. Stuff doesn't just exist, but It's not just about the matter, but also the organization of such matter. The structure/organization/form is just as real as the matter itself is, and just as important, not simply for subjective understanding, but it's how the universe objectively operates.

I'll easily concede that our subjective understanding requires empirical experience. That's a no-brainer for me. But ontologically, not epistemologically, I think matter has form. Science readily accepts this. Carbon often "double bonds", it has "6" protons, etc. These are descriptions of the structure of Carbon. However, they aren't the matter itself, but nevertheless ontologically necessary. What is not readily accepted by the scientific community, and I think is a big mistake, is that the "structure" of something (like Carbon) is immaterial/non-physical. Therefore, I think physicalism should be immediately rejected by anyone and everyone that appreciates the scientific advances of the last 6000 years. It's not a dualism, but a proper conception of our empirical data.

ashurbanipal said:
Something doesn't follow, here... You seem to simply dismiss nominalism without actually dealing with the arguments in its favor (I am not, incidentally, a nominalist).

Oh, nominalism. I actually share a few sympathies with nominalists. Specifically, I deny the existence of "humanity". That is just a word for an artificial collection. The collection itself is not a real thing. The real things are the individuals within the artificial collection. That was some great stuff. However, I readily accept the existence of abstract objects, which a second strain of nominalism will also deny. My main objection to this kind of nominalism is science. Science constantly uses abstract objects in their descriptions of our physical universe. That sounds quite a bit like nominalism, ya? But the mistake is to simply call them names. The structure of Carbon (which is an abstract object) is exactly what gives it all of it's real qualities. Science isn't just making names, it's understanding reality. If abstract objects are non-existent, as this type of nominalist claims, then science does not understand reality at all, and we must retreat back to skepticism. This is extremely impractical, considering all the useful predictions science can make using abstract objects.

Conceiving abstract objects as real is not only pragmatic, but has lots of ontological weight as well. The real things out there seem to do real stuff, and we can predict the real stuff based on structure. To keep my theme running, Carbon is in group 14, right? Because of similar structure, all group 14 elements have very similar qualities (4 electrons in outside shell, double bonding is very common, etc). The reality of abstract objects, therefore, is as just as true as sense realism. I would deny there is a universal "group 14" that exists, but it's just a collection of the real existing things with very similar structures. Because of the similar structure, we can make pragmatic categories like "group 14" that help our understanding of reality.

ashurbanipal said:
Finally, what is this? You go from talk of numbers being empirical to number "particles." There's no obvious relationship there.

I was just making an example of empirical quantity. That's the only way I can conceive of quantity being physical. The other extreme is that "3" is a free-floating object that exists in a realm of forms. But I hate Plato with the passion of a thousand burning suns, so I instead limit quantity within the empirical world. The abstract object does not exist as an independent thing. That's bonkers.

Radical · May 18, 2015

William Rea said:
I disagree, the example given in the OP specifically conflates the reality of numbers with the reality it is used to describe.

1. Numbers are not empirical data, they are a description of empirical data.

2. Numbers are not derived from the real world, they are a description of the real world.

3. Science uses mathematics to model/approximate/describe phenomena in the real world. The model/approximate/describe is NOT the real world and does not have any consequence for the real world which carries on doing what it does regardless of our attempts to model/approximate/describe it.

4. Our understanding of the world is achieved via mathematics, the world does not operate as a consequence of mathematics. F=mg is a way to model/approximate/describe falling objects, they do not fall because F=mg just like if I were to draw a map of a country it would not spring into existence because of that.

5. Mathematics can be done in an abstract sense without ascribing any meaning to the numbers or symbols.

6. There are six protons in a Carbon atom because that is how physical reality is, mathematics does not change that, it helps us understand that.

7. There is a conflation of number, quantity,mathematics etc going on all over this thread so, I'm out of it. that way lies insanity.

If I've communicated poorly, my apologies. The_Recruit has correctly identified the point I'm attempting to make. If he makes more sense in explaining my text, listen to what he says.

Manny · May 18, 2015

I think that quantum mechanics implies there is a finite, small but discreet value to physical space, the Planck length. Therefore the universe is "granular", or digital, not continuous. 1011011010111 is a descriptor. Numbers are adjectives in the sense that they describe the quantity of some noun, which is the thing. The noun is real, the adjective is the descriptor.

On the other hand, this is post # 28.

Paralogic · May 18, 2015

Radical said:
But what's a number? Is it real? If it is real, is it mind-independent or a mental construction? Is it physical/empirical?

Numbers are a human mental abstraction we have invented to try and explain Nature and the Universe.

Numbers don't exist. Nature doesn't work with numbers, however, numbers, and our ability to manipulate them to try and approximate and predict Nature, is a part of what I call "Cosmological Reality" (tm) -- the ability of a part of the universe to comprehend some or most of the rest of its own existence.

Numbers don't exist. They are symbols we have devised to deal with the logical and rational analysis of our surroundings.

Radical · May 19, 2015

Paralogic said:
Numbers are a human mental abstraction we have invented to try and explain Nature and the Universe.

Numbers don't exist. Nature doesn't work with numbers, however, numbers, and our ability to manipulate them to try and approximate and predict Nature, is a part of what I call "Cosmological Reality" (tm) -- the ability of a part of the universe to comprehend some or most of the rest of its own existence.

Numbers don't exist. They are symbols we have devised to deal with the logical and rational analysis of our surroundings.

Then what do they describe? Is what they describe real or fiction? Is there an infinite regress of fiction? If there is anything real, is it physical or non-physical? Finally, if it is just a fiction, then how would you explain "Carbon has "6" protons" without numbers?

At the very least, it's easier to be a realist. Why go down the road with worse pitfalls?

Paralogic · May 19, 2015

Radical said:
Then what do they describe? Is what they describe real or fiction? Is there an infinite regress of fiction? If there is anything real, is it physical or non-physical? Finally, if it is just a fiction, then how would you explain "Carbon has "6" protons" without numbers?

At the very least, it's easier to be a realist. Why go down the road with worse pitfalls?

They symbolize something real. Your word "fiction" is irrelevant to this discussion.

Carbon, indeed has 6 protons, but this is the way our intelligent mind is able to comprehend Carbon. It doesn't mean Nature picked that number to give to Carbon for its number of protons.

You're confusing several terms in your previous quote.

My recommendation is to start with the statement - a favorite of mine - that humans are irrelevant to the universe : Cosmological Reality axiom NO 1.

So, any endeavor we make into reality has to be consistent that any results we find out and realize and comprehend, have to be true whether or not humans exist or ever would exist to comprehend them.

For example, Gravity is real and not because we, humans, can comprehend it. Gravity is realy whether or not a fateful asteroid wiped out the dinosaurs and all mammals 65 million years ago.

ashurbanipal · May 19, 2015

radical said:
However, I readily accept the existence of abstract objects, which a second strain of nominalism will also deny. My main objection to this kind of nominalism is science. Science constantly uses abstract objects in their descriptions of our physical universe. That sounds quite a bit like nominalism, ya? But the mistake is to simply call them names. The structure of Carbon (which is an abstract object) is exactly what gives it all of it's real qualities. Science isn't just making names, it's understanding reality. If abstract objects are non-existent, as this type of nominalist claims, then science does not understand reality at all, and we must retreat back to skepticism. This is extremely impractical, considering all the useful predictions science can make using abstract objects.

The conclusion doesn't follow. A nominalist would say that the properties which are named in science inhere in the objects themselves; the names we give to those properties and objects are merely means of mental management. But no properties or relations (other than mental ones) flow from the names to the objects, or stand as intermediaries between them. Understanding, then, is a purely mental epistemic good. I suppose it might seem that something like Putnam's Twin Earth example would give the nominalist some trouble, but thinking it through a little more carefully suggests that the trouble isn't as bad as it might first appear. A nominalist would say that "water" is just a name for a stuff with certain properties. Should the inhabitants of earth and twin earth meet, and discover they use the same name for disparate stuffs, they just have some name-sorting to do.

radical said:
Conceiving abstract objects as real is not only pragmatic, but has lots of ontological weight as well.

I'm curious whether you've ever read Der Gedanke by Gottlob Frege. He had an argument for why we ought to think of abstract objects as real, existing in a third realm separate from both physical things and ideas. One of his major projects turns out to be a campaign against nominalism. He wanted mathematics to not turn out to rely on psychology (to use his terminology, here). The "thought" of, say, the pythagorean theorem that I have is just the same as the one you have. If the pythagorean theorem (or mathematics in general) relied on psychology, you and I might have very different ideas of the pythagorean theorem.

radical said:
The real things out there seem to do real stuff, and we can predict the real stuff based on structure.

OK. I'll buy that for the time being.

radical said:
To keep my theme running, Carbon is in group 14, right? Because of similar structure, all group 14 elements have very similar qualities (4 electrons in outside shell, double bonding is very common, etc).

Again, ok.

radical said:
The reality of abstract objects, therefore, is as just as true as sense realism.

First, sense realism? What is that? Do you mean something like qualitative transparency, or realism with respect to qualia? Or something else?

Anyway, if you mean to say that abstract objects are therefore real (i.e. real because of what you said about the elements in group 14 having similar properties), that doesn't follow. Abstract objects could just be names, and it could simply be the case that we've got the names right. Sort-of like using marks in clay to keep track of heads of cattle or something--the names just keep track of something. Saying there is a "structure" to a carbon atom is just to attribute certain properties to that atom. Those properties inhere in the atom, sure, but they're concrete. In short, the picture is that there are concrete properties, and then our names for them, and nothing else--positing the existence of something else would be metaphysically extravagant. Or, so a nominalist would say.

I think there is a good argument against this view--a compelling one, in fact. But it isn't the argument you've made so far.

ashurbanipal · May 19, 2015

radical said:
I would deny there is a universal "group 14" that exists, but it's just a collection of the real existing things with very similar structures. Because of the similar structure, we can make pragmatic categories like "group 14" that help our understanding of reality.

So, in your view, there are abstract objects, but no sets?

radical said:
I was just making an example of empirical quantity. That's the only way I can conceive of quantity being physical.

OK, but what does "physical" have to do with "empirical"? Berkeley was an empiricist, after all...

radical said:
The other extreme is that "3" is a free-floating object that exists in a realm of forms. But I hate Plato with the passion of a thousand burning suns

Really? Why do you hate Plato? He seems to have been a fine enough fellow, and he was certainly smarter than anyone I've ever met (not that smarts are the end-all, be-all of likability).

radical said:
so I instead limit quantity within the empirical world. The abstract object does not exist as an independent thing. That's bonkers.

Doesn't seem so bonkers to me. Why do you think it's bonkers?

blackjack50 · May 20, 2015

Radical said:
I have 10 fingers. The English alphabet has 26 letters. The table has 4 keys. Carbon has 6 protons.

But what's a number? Is it real? If it is real, is it mind-independent or a mental construction? Is it physical/empirical?

I think anyone who gives even the slightest credit to scientists must say numbers are real and mind-independent. How can you not? Numbers are used in every science as a part of the empirical data. If numbers are simply mental constructions, illusions, fictions, or what have you, and do not come from the real world, then science, which is based upon mathematics, also is simply a mental construction, illusion, fiction, or what have you. The understanding of our world is wrapped in mathematics, and it would all have to be thrown out if mathematics was not real.

I think it's also kind of ridiculous to conceive of numbers as empirical. What particle tells me there are 6 of the protons in carbon? There is no "6" particle nor a "2" particle nor a "7,000,000,000" particle. Quantity is not physical.

Quantity is a real, non-physical part of the universe.

Discuss

It is the universal language.

Radical · May 22, 2015

Paralogic said:
They symbolize something real.

Ok, perfect. Now this real thing symbolized by numbers: is it physical or non-physical? If it is physical, then what is this physical component of Carbon's protons that give it the "6", and why is it different that Oxygen's "8". If it's non-physical, welcome to the other half of reality, my friend, and let's begin metaphysics.

ashurbanipal said:
The conclusion doesn't follow. A nominalist would say that the properties which are named in science inhere in the objects themselves; the names we give to those properties and objects are merely means of mental management.

I thought this is what I was communicating as nominalism. I think the mistake of the nominalist is to say that "6" is just mental management. Mental management of what? If it is of something purely mental, then it doesn't aid in understanding reality. If it is of something real, you haven't escaped the conflict I want to expose. If "6" is real, it must be physical or non-physical.

ashurbanipal said:
I'm curious whether you've ever read Der Gedanke by Gottlob Frege...

I've never read anything from Frege himself, but only secondary material. The latest one that included him extensively was "Thinking about Mathematics" by Shapiro. Frege's understanding of a real, existence of numbers is as a property of a property. I have the property of having fingers, and that property has the property of "10" because that's the number of fingers. But this is contradicted by Russell a few years later.

ashurbanipal said:
First, sense realism? What is that? Do you mean something like qualitative transparency, or realism with respect to qualia? Or something else?

I mean the assumption that we're not in the matrix, that our senses are accurate to the real, external world. So much more like qualia realism. This comes with limitations, of course.

ashurbanipal said:
Anyway, if you mean to say that abstract objects are therefore real (i.e. real because of what you said about the elements in group 14 having similar properties), that doesn't follow... In short, the picture is that there are concrete properties, and then our names for them, and nothing else--positing the existence of something else would be metaphysically extravagant. Or, so a nominalist would say.

I think there is a good argument against this view--a compelling one, in fact. But it isn't the argument you've made so far.

My objection is just that is not entirely sensible to understand each Carbon atom as fundamentally different. We name things that are similar for mental organization, yes, but we also can understand ontological similarity, and nominalism denies ontological understanding. So nominalism claims "understanding" is just mental order. But when I say "there are four electrons in the outer shell of the atom", I'm talking about something really existing in multiple kinds of atoms, and this real existent thing is the cause of a multitude of effects.

If there's a better objection, please teach me. I like to learn, that's why I get on these websites.

ashurbanipal said:
So, in your view, there are abstract objects, but no sets?

Yes, but to be really precise, I don't think there are any things that do not have an instantiation. Sets don't have an instantiation.

This is about as pro-Aristotle as you can get, btw.

ashurbanipal said:
OK, but what does "physical" have to do with "empirical"? Berkeley was an empiricist, after all...

I've been using them interchangeably. Most non-philosophers use "empirical" to mean "physical".

ashurbanipal said:
Really? Why do you hate Plato? He seems to have been a fine enough fellow, and he was certainly smarter than anyone I've ever met (not that smarts are the end-all, be-all of likability).

I just like Aristotle so much more. A realm of forms is a bit ridiculous. Forms themselves are great, but lets not go crazy =p

ashurbanipal said:
Doesn't seem so bonkers to me. Why do you think it's bonkers?

Abstract objects, like structure, can be affected by the physical world. Hydrogen atoms can be compressed into helium atoms. Platonism champions forms as superior over this world of shadows, but it appears the exact opposite. Forms seem subservient to matter. Hylomorphism for the win!

Radical · May 22, 2015

stonewall50 said:
It is the universal language.

Oh come on! That doesn't answer the problem I was exposing.

hado117 · May 22, 2015

Radical said:
I have 10 fingers. The English alphabet has 26 letters. The table has 4 keys. Carbon has 6 protons.

But what's a number? Is it real? If it is real, is it mind-independent or a mental construction? Is it physical/empirical?

I think anyone who gives even the slightest credit to scientists must say numbers are real and mind-independent. How can you not? Numbers are used in every science as a part of the empirical data. If numbers are simply mental constructions, illusions, fictions, or what have you, and do not come from the real world, then science, which is based upon mathematics, also is simply a mental construction, illusion, fiction, or what have you. The understanding of our world is wrapped in mathematics, and it would all have to be thrown out if mathematics was not real.

I think it's also kind of ridiculous to conceive of numbers as empirical. What particle tells me there are 6 of the protons in carbon? There is no "6" particle nor a "2" particle nor a "7,000,000,000" particle. Quantity is not physical.

Quantity is a real, non-physical part of the universe.

Discuss

numbers are like letters from an other dimension dude

hado117 · May 22, 2015

hado117 said:
numbers are like letters from an other dimension dude

why dont we have capital numbers man. its totally whacked . whach those munkees they DO bite!!!!!

Radical · May 22, 2015

hado117 said:
why dont we have capital numbers man. its totally whacked . whach those munkees they DO bite!!!!!

Ha... Keep on topic please. This is philosophy, not "let's get high together". And yes, there's a difference.

blackjack50 · May 22, 2015

Radical said:
Oh come on! That doesn't answer the problem I was exposing.

But I think that makes it very real doesn't it? Perhaps it is as real as language? A number is the definition of something that exists. And it is universal. It wouldn't be limited to our planet.

Radical · May 23, 2015

stonewall50 said:
But I think that makes it very real doesn't it? Perhaps it is as real as language? A number is the definition of something that exists. And it is universal. It wouldn't be limited to our planet.

"Real inside our heads" doesn't mean really real, so I had to poke you. I wasn't sure what you meant. Santa is real inside lots of kids heads. Are numbers like Santa? They explain lots of things and promote general well being? Or are numbers real regardless of our minds?

Then, the big question is if they are immaterial. I think they are. You can't take the number 10 and paint it green and play catch with it. It's an abstract object. I don't mean the two digits that I use to represent the object. "Ten" or "10" is referencing this other thing which describes how many fingers most of us have. But can I remove the "10" from my fingers? I can remove individual fingers, but that's not the same thing.

Paralogic · May 23, 2015

Radical said:
Ok, perfect. Now this real thing symbolized by numbers: is it physical or non-physical?

Everything is physical - as we presume you define that term. Nothing is non-physical. Nothing non-physical would exist, by definition.

blackjack50 · May 23, 2015

Radical said:
"Real inside our heads" doesn't mean really real, so I had to poke you. I wasn't sure what you meant. Santa is real inside lots of kids heads. Are numbers like Santa? They explain lots of things and promote general well being? Or are numbers real regardless of our minds?

Then, the big question is if they are immaterial. I think they are. You can't take the number 10 and paint it green and play catch with it. It's an abstract object. I don't mean the two digits that I use to represent the object. "Ten" or "10" is referencing this other thing which describes how many fingers most of us have. But can I remove the "10" from my fingers? I can remove individual fingers, but that's not the same thing.

It IS real. Equations can define the physical limits of our existence. But at any rate:

Gardener · May 23, 2015

The answer you seek is 42.

blackjack50 · May 23, 2015

Gardener said:
The answer you seek is 42.

Don't panic. And always bring a towel

zyzygy · May 23, 2015

BBC - Beautiful Equations
https://www.youtube.com/watch?v=erUQhXjY9ic

Rogue Valley · May 24, 2015

Numbers - per se - are not real objects. Mathematics is a conceptual language that exists and functions on a conceptual level. It is a conceptual tool that sheds insights on both the tangible and the intangible.

Radical · May 24, 2015

Paralogic said:
Everything is physical - as we presume you define that term. Nothing is non-physical. Nothing non-physical would exist, by definition.

So we can remove the "6" out of Carbon without messing with protons? Which is the "6" particle?

Simpleχity;1064651758 said:
Numbers - per se - are not real objects. Mathematics is a conceptual language that exists and functions on a conceptual level. It is a conceptual tool that sheds insights on both the tangible and the intangible.

So there are not "6" protons in Carbon? That's ridiculous. Of course numbers are real. If they're not, all of science has to be trashed. Carbon has "6" protons. You have "10" fingers. That abstract object totally exists. Otherwise I could cut off a finger and you couldn't sue me for removing one of your fingers. I'd just say "He didn't have 10 to start with".

zyzygy · May 24, 2015

Radical said:
So we can remove the "6" out of Carbon without messing with protons? Which is the "6" particle?

So there are not "6" protons in Carbon? That's ridiculous. Of course numbers are real. If they're not, all of science has to be trashed. Carbon has "6" protons. You have "10" fingers. That abstract object totally exists. Otherwise I could cut off a finger and you couldn't sue me for removing one of your fingers. I'd just say "He didn't have 10 to start with".

He may have had 11 minus one. Or thirteen minus two. Or.......

Rogue Valley · May 25, 2015

Radical said:
That's ridiculous. Of course numbers are real.

I don't think you quite understood. The relationships are real.

The arbitrary symbols (0123456789+%±√∑∮) are akin to language or vocabulary and are used to describe the relationships.

What Are Numbers?

Radical

Well-known member

Radical

Well-known member

Manny

Nay Sayer

Paralogic

Radical

Well-known member

Paralogic

ashurbanipal

ashurbanipal

blackjack50

Radical

Well-known member

Radical

Well-known member

hado117

hado117

Radical

Well-known member

blackjack50

Radical

Well-known member

Paralogic

blackjack50

Gardener

free market communist

blackjack50

zyzygy

Rogue Valley

Lead or get out of the way

Radical

Well-known member

zyzygy

Rogue Valley

Lead or get out of the way