Do numbers exist?

@vectorcube,

I think a better question is how much set theory is necessary to guarantee that number systems exist in that theory. More abstract than trying to define numbers is to define number systems. Then one may interpret numbers differently in different contexts. E.g., rather than defining real numbers in a particular way, one should define what a real number system is, e.g., as an ordered field such that every nonempty set with an upper bound has a least upper bound. Then whenever one encounters such a system, one can think of its elements as being real numbers. This is the modern way mathematicians tend to think of numbers. Of course, one doesn't want to study the theory of a number system if it is contradictory, and the standard way to be (fairly) confident one is not doing that is to show that one can prove that such systems exist in set theory (or some modification of that), but why one should be interested in some more general type of existence, or even whether there is some type of more general existence, I don't know.

@vectorcube,

Mathematics and nature are inextricably linked in mysterious and elegant ways. They co-exist. They can not be completely separated.

@prothero,

prothero;84936 wrote:

Mathematics and nature are inextricably linked in mysterious and elegant ways. They co-exist. They can not be completely separated.

There is nothing mysterious about it. The role of mathematics is in describing the laws of nature. If math can` t describe the laws, then we would use something else.

---------- Post added 08-22-2009 at 03:36 PM ----------

prothero;84653 wrote:

Yes, everyone should read Whitehead. Process philosophy and process theology, a philosophy which trys to integrate science with values, religion and aesthetics. The terminology is dense and difficult but the concepts are very insightful. Whitehead once said that all philosophy is merely commentary on Plato. Whitehead much preferred Plato an idealist to Aristotle who was more empirical.

---------- Post added 08-20-2009 at 10:32 PM ----------

I think the question about "do numbers exist" hinges on ones concept of what it means to "exist". Empiricists and materialists are probably going to argue numbers have no "real" existence. Those of us who are idealists, rationalist or believe in transcendental forms of existence are going to argue the affirmative. Thus the answers given are dependent on more basic philosophiical assumptions or metaphysical speculations about "existence" ontology.

Personally I think empiricism and materialism give a much too limited and very incomplete view of reality and experience. I do not think one can merely brush aside the elegance, beauty, power and explanatory value of mathematical presentations of nature. For me it almost seems mathematics preceeds nature not the other way around.

It is not always about what someone thinks. A good way to make sense of mathematical claims is to say they quantifies over some entities.

@vectorcube,

vectorcube;85005 wrote:

There is nothing mysterious about it. The role of mathematics is in describing the laws of nature. If math can` t describe the laws, then we would use something else.

Well, OK but what for instance?
---------- Post added 08-22-2009 at 03:36 PM ----------

It is not always about what someone thinks. A good way to make sense of mathematical claims is to say they quantifies over some entities.

Again OK, but it seems rather dismissive of what many regard as a much deeper philosophical problem, the relationship between mathematics, reason, logic and nature.

@vectorcube,

Not everyone understands what a metaphysical question is.

@prothero,

prothero;84936 wrote:

Mathematics and nature are inextricably linked in mysterious and elegant ways. They co-exist. They can not be completely separated.

That's because human beings had been born into nature, raised in nature, and observed nature for hundreds of thousands of years before human beings devised and systematized mathematics. It's no coincidence. Mathematics is abstracted out of experience.

@Aedes,

Aedes;85055 wrote:

That's because human beings had been born into nature, raised in nature, and observed nature for hundreds of thousands of years before human beings devised and systematized mathematics. It's no coincidence. Mathematics is abstracted out of experience.

That may be, but somehow my notion is that mathematics, like reason and logic, are hardwired into our experience (indeed into nature itself).

Somewhat in the same way that Hume suggests causality is a universal notion and Kant suggests that time and space are intrinsic mental features. They are not dependent on experience. I prefer ratiaonlism to empiricism.

@vectorcube,

From my understanding, numbers only exist as abstractions, not actual objective features of reality.

@hue-man,

hue-man;85062 wrote:

From my understanding, numbers only exist as abstractions, not actual objective features of reality.

Well, back to square one. What does it mean to say something exists?
It is true numbers have no material existence? If we confine our notion of what "exists" to material forms we will have a very limited notion of both "reality" and "existence". Much too limited in my view.

Say love, truth, beauty, ?

@prothero,

prothero;85066 wrote:

Well, back to square one. What does it mean to say something exists?
It is true numbers have no material existence? If we confine our notion of what "exists" to material forms we will have a very limited notion of both "reality" and "existence". Much too limited in my view.

Say love, truth, beauty, ?

If you reduce love to neurons and chemicals within the brain, then I guess it does exist as a feeling or emotion. If you reduce love to behavior, then I guess it does exist in that sense as well. Truth or knowledge does exist, but only in the sense that the objects truth depends on exist. Beauty 'exists' only as a sentiment, and so it is only an abstraction or concept.

@vectorcube,

I am afraid you are an empirical materialist and I am more a rational idealist.
What we will have here is "failure to communicate" due to profound differences in our underlying metaphysical assumptions about "reality" and "existence".

If you are in the garden with an amorous prospect I suggest you do not express your feelings in terms of neurons, chemical neurotransmitters, PET scans and Skinner's behaviorism.

I still maintain that the fact that the universe is rational, ordered and predictable and expressible in mathematical terms is a philosophical or metaphysical problem worth pondering rather than dismissing.

@vectorcube,

I believe that numbers are only products of imagination, fed on by our need to count and further understand the world around us. It is an illusion that we use to comprehend reality in our world.

If there were a hundred flowers in the field, we can only see the amount of flowers, we cannot exactly see the number itself. Therefore, Numbers are only illusions, abstractions made by the human mind.

@prothero,

prothero;85018 wrote:

Again OK, but it seems rather dismissive of what many regard as a much deeper philosophical problem, the relationship between mathematics, reason, logic and nature.

They are simply wrong, or misguided. Mathematics is a tool for physics. That is all.

@vectorcube,

An extremely useful tool, eh?
And life and mind are just accidental, chance or coincidental happenings in an indifferent universe, too, eh?

@prothero,

Well we wouldn't be around to speak of this if the conditions weren't there in the first place to allow for our existence.

Mathematics is an evolutionary tool that allowed us to adapt to phenomena, or change. It is the wisdom of relativeness, lol. Now if mathematics were something real and inherent of the universe then you'd have to show me that objectively, the universe is something of relative value...while being purely objective.

@Aedes,

Aedes;85055 wrote:

That's because human beings had been born into nature, raised in nature, and observed nature for hundreds of thousands of years before human beings devised and systematized mathematics. It's no coincidence. Mathematics is abstracted out of experience.

But I say that the nature they were raised in was rational from the outset. This is why the ability it gives us to see into it is so much greater than what we can just ascertain through experience. Mathematics is not 'just a language' and neither maths nor language work by 'corresponding to objects of perception'. Instead the information we receive from objects of perception is realised, made real, by virtue of our rational nature, which far exceeds our mere conscious thought. This is also not to say that if nothing were perceived, nothing would exist, but it is to say that whatever existence it had would be inconceivable to us and therefore not able to be contemplated. Esse est percipe.

Something can only emerge if it were already present.

---------- Post added 08-23-2009 at 04:28 PM ----------

you see, I have decided to revert to a viewpoint that I believe was common to Liebniz, Spinoza and Descartes, even though they had so many other differences in so many respects.

We are a rational soul in an intelligible universe.

@jeeprs,

jeeprs;85091 wrote:

But I say that the nature they were raised in was rational from the outset. This is why the ability it gives us to see into it is so much greater than what we can just ascertain through experience. Mathematics is not 'just a language' and neither maths nor language work by 'corresponding to objects of perception'. Instead the information we receive from objects of perception is realised, made real, by virtue of our rational nature, which far exceeds our mere conscious thought. This is also not to say that if nothing were perceived, nothing would exist, but it is to say that whatever existence it had would be inconceivable to us and therefore not able to be contemplated. Esse est percipe.

Something can only emerge if it were already present.

do you believe numbers rather than being a discipline are more like names we give to attributes? qualities of things describing their quantity? at first i thought you were saying something that reminded me of which came first, the chicken or the egg. now i am confused...but i love that statement i underlined!

---------- Post added 08-23-2009 at 12:04 PM ----------

i would say though that the ability to express mathematics is derived from experiencing a need to do so

@vectorcube,

everybody is trying to explain everything by evolution. It doesn't work. Mathematics and rationality did not 'just evolve'. This is all part of a failed attempt to substitute science for philosophy. We have it all backwards, and this is why we see ourselves as victims and not the creators we are.

The underlined phrase indicates the primacy of consciousness (a.k.a. 'soul') in the creation of reality.

@prothero,

prothero;85087 wrote:

An extremely useful tool, eh?
And life and mind are just accidental, chance or coincidental happenings in an indifferent universe, too, eh?

Look, the use of math in physics is in the formulation of the laws of nature, and the application of those laws to practical problems. Take the simple statement

1) F=ma.

Simply right? But hidden in 1 contains the operation of

a) multiplication.

b) A connection between F and the second differative of position.

c) Given F and M, all higher differentive of 3 or more of position is zero.

d) 1 can be translated into : x'= v & v'= F/m such that there is a unique representation in phase space, and that all trajectory is determined by exactly two piece of information.

What can we say about 1? It is a compact way of expressing a-d. 1 is a contingent statement. It could very well be different in a different universe. ( perhaps something like F=ma').

---------- Post added 08-23-2009 at 06:42 AM ----------

jeeprs;85099 wrote:

everybody is trying to explain everything by evolution. It doesn't work. Mathematics and rationality did not 'just evolve'. This is all part of a failed attempt to substitute science for philosophy. We have it all backwards, and this is why we see ourselves as victims and not the creators we are.

The underlined phrase indicates the primacy of consciousness (a.k.a. 'soul') in the creation of reality.

ok, you can hold your view, but what problem can you solve by holding this view?

@vectorcube,

sometimes numbers make me sad.

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