Does the Number "1" Actually Exist?

[Kraenen]

What do you mean by "really exist"?
They are not made of energy, nor particles, nor spacetime. They don't have a physical existence, but i am sure you didn't need me to tell you that.

really exist, as in, is there a perfect triangle in nature? likewise is there really 'one' of anything, or just some kind of approximation of 'one' of that perfect abstraction?

[Deleted]

I quoted this by Albert Einstein before and I don't mind doing it again:
"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

and perhaps also by the same author, "God does not care about mathematical difficulties; He integrates empirically".

Mathematics ignore reality and does not assume to exist. Nonetheless, it is a good method for a creature that has five fingers and has no problem counting them. It is not tied to logic though as such, as in symbols and philosophy, but only to assumption and approximation of definite figures.

Mathematics is entirely its own system and has no tie to reality, else it would probably be entirely unnecessary if it did. Physics creates its own reality. Logic connects to reality at least in man's mind.

Imagine if you have complete consciousness of reality; what is the use of mathematics if there are concrete incarnations of "cars" even if there happens to be "3" of them? They will only exist. Mathematics would be entirely unnecessary in grasping their existences because they are real and concrete existences.

Imagine if you counted everything you did - I now take 1 step, 2 step, 3 step. I now say 3 words. I take 1 breath. As well for as all things you were in connection with. I now sit in front of 1 computer. There are 4 walls around me. There is 1 screen. There are 2 lights on the laptop. There is 1 window. I am 1 person. There is 1 floor. There are are 2 trees in the driveway.
Mathematics only exist in man's mind as a system for himself. Reality does not need that though to exist and reality probably contains the existence of mathematics in man's mind. In the end, all concrete existences would be true in themselves and their existence would be defined by their actual incarnation and so, everything is all in itself. Mathematics probably exist, but only as a system in man's mind that the creature has developed. Every existence would reach its own singularity and have no need for any further meaning.

[Mormolyce]

Say that you have 2 pens and you add them together, but they differ by a single atom. Does adding them together still =2? What if two things have the same amount of atoms, but differ by a single proton or neutron. Do they still add up to 2?

What this says is that pens don't actually exist. Just two unrelated objects which the human eye is not powerful enough to see are different.

- - - Updated - - -

Say that you have 2 pens and you add them together, but they differ by a single atom. Does adding them together still =2? What if two things have the same amount of atoms, but differ by a single proton or neutron. Do they still add up to 2?

What this says is that pens don't actually exist. Just two unrelated objects which the human eye is not powerful enough to see are different.

[Kraenen]

No one said "physically exists". Obviously there isn't a one lying on the sidewalk. But to say that nothing you can't find lying on the sidewalk exists is a gross oversimplification (aka philosophical debate, and I say that as someone who enjoys it).

the thread, i assumed, was about whether in reality (or empirically if you like) there could ever be observed the quantity of 1 of something.

[Matchles]

The entire construct of mathematics is based on the fact that 1+1=2. But it is assumed that the number one exist in the first place.

If it does really exist, then mathematics has the power to model reality to absolute perfection once we figure out all the variables ( assuming that there are not infinite variables).

If it doesn't really exist, then it puts every single scientific theory ever constructed on a flawed foundation.

Explain the flawed foundation part. I fail to see how the existence of a number plays any role in undermining a scientific theory.

[Mormolyce]

2) Math, unlike physics, chemistry, biology etc, isn't concerned with things that are "real". In that sense, math isn't a real science. It is a science in the sense that the methodology is the same, but it isn't concerned with real things. Some fields of mathematics are useless and have no application in the real world whatsoever. Infact, mathematicians pride themselves in being useless.

Numbers do not exist. Vectors do not exist. Matrices do not exist. They are a product of our mind and help us to explain the world. They are not physical beings.

Mathematics is very much a science, it's just not an experimental science.

Philosophy
^
Logic
^
Science
^
Mathematics
^
Physics
^
Chemistry
^
Biology

Where "^" means "is a subset of". Although you could argue that the experimental side of physics etc sits separately under science.

[reef]

does the letter a exist? if it doesn't then i guess we failed at developing languages that use it. the number 1 exists because we defined it as being a single unit, thing, object, etc. defining a word, number, letter, object, etc gives it a meaning and an existence in language.

[Deleted]

really exist, as in, is there a perfect triangle in nature? likewise is there really 'one' of anything, or just some kind of approximation of 'one' of that perfect abstraction?

Well, look at yourself, Raybourne. Now take the set of all the Raybournes on Earth. Very likely, the cardinal of that set is identically, exactly "one".
Now, the set of all the red pencils i have on my table. That's also a set with cardinal "one". They are perfect "ones".

I'm curious about why you think that there aren't perfect triangles in nature. Are you talking about the angle sum = pi? That's more of a geometry problem, the universe geometry is hardly ever euclidian.

[torterra275]

Oh god we got into a whole debate about this in a philosophy class. Wouldn't want to discuss that again. We never really came to a complete conclusion on it though.

[Laize]

The entire construct of mathematics is based on the fact that 1+1=2. But it is assumed that the number one exist in the first place.

If it does really exist, then mathematics has the power to model reality to absolute perfection once we figure out all the variables ( assuming that there are not infinite variables).

If it doesn't really exist, then it puts every single scientific theory ever constructed on a flawed foundation.

Archimedes computed Pi to 99.9% accuracy without the use of calculus or even the number "0" (Which, if you look, is a far more interesting number than 1). He was one of the most brilliant mathematicians to ever live. At no point in his palimpsest is the number 1 called into question.

Therefore I must assume that you haven't passed 2nd grade math.

[Tribunal]

the thread, i assumed, was about whether in reality (or empirically if you like) there could ever be observed the quantity of 1 of something.

Usually the debate is framed slightly differently (defining existence/the Problem of Absolutes), however: one is a representation, which means it is defined contextually. In context, we see one of something all the time. However, if you want to get as empirical as possible, we are capable of single-atom synthesis of several elements. We are also capable of single electron switches. Unless we're combining the debate over the empirical nature of one with quantum theory (*yes, insert the trope about mentioning it means it doesn't apply here*), which is a bit ridiculous on the face, I would say that fulfils the requirements of an empirical one.

[DEATHETERNAL]

It doesn't matter. Mathematics is the best system we have by which we can represent the universe in such as way that we can manipulate the system and expect the result of that manipulation to represent what would occur in the universe if we were to manipulate the universe or a part of the universe in the same way that we manipulated the system. Whether it "exists" or not is irrelevant.

[YuneKirby]

If it does really exist, then mathematics has the power to model reality to absolute perfection once we figure out all the variables ( assuming that there are not infinite variables).

Go watch Jurassic Park so Jeff Goldblum can prove you wrong.

[Deleted]

and perhaps also by the same author, "God does not care about mathematical difficulties; He integrates empirically".

Haha that reminds me of that old method to integrate: they cut (very precisely, i take) a cardboard along the plot of the function they wanted to integrate, and then weighed it in a precision balance, compared it to the weight of a "unit" cardboard square, and obtained the value of the integral

- - - Updated - - -

Oh god we got into a whole debate about this in a philosophy class. Wouldn't want to discuss that again. We never really came to a complete conclusion on it though.

Because philosophy doesn't accept the dictatorial rule of reality XD

[DEATHETERNAL]

Haha that reminds me of that old method to integrate: they cut (very precisely, i take) a cardboard along the plot of the function they wanted to integrate, and then weighed it in a precision balance, compared it to the weight of a "unit" cardboard square, and obtained the value of the integral

Isaac Newton 1 : People with cardboard 0

[reef]

this short video talks about this question and it covers a lot.

[Mormolyce]

Oh god we got into a whole debate about this in a philosophy class. Wouldn't want to discuss that again. We never really came to a complete conclusion on it though.

If you came to an actual conclusion on a question like this you'd probably get an F for your philosophy class :P

Archimedes computed Pi to 99.9% accuracy without the use of calculus or even the number "0" (Which, if you look, is a far more interesting number than 1). He was one of the most brilliant mathematicians to ever live. At no point in his palimpsest is the number 1 called into question.

Therefore I must assume that you haven't passed 2nd grade math.

You don't need the number 1 to exist to estimate a value for pi.

Mathematics is a system of axiomatic reasoning, it starts from a set of unproveable axioms and constructs a system of proofs to explore their consequences. It doesn't care if these axioms are "real" or not. In fact many mathematical theorems have been proven not only within the standard axioms of mathematics, but in frameworks with entirely different axioms.

None of these axioms say "1 is real" either.

[Kraenen]

Mathematics is very much a science, it's just not an experimental science.

Philosophy
^
Logic
^
Science
^
Mathematics
^
Physics
^
Chemistry
^
Biology

Where "^" means "is a subset of". Although you could argue that the experimental side of physics etc sits separately under science.

I'd say it goes Philosophy > Logic > Mathematics > Empiricism

You can have math without it being empirical, but you cant have math without logic or philosophy. also you can't have any science without math, can you? The whole essence of science is that it is philosophy applied, observed, and recorded, etc.

[Deleted]

Isaac Newton 1 : People with cardboard 0

No, this was done in the XX century, before computers became commonplace.
You have to realize that not all functions are integrable, but they have integrals. And often you need to calculate the value of the integral.

Nowadays that's easily solved by solving the integral numerically (explanation for the non-initiated: it amounts to cut down the integration path into a lot of tiny bits, calculate the value of the function in the center of each of those bits, multiply it by the width of the bits, and sum all those values), which can be a total pain in the ass to do by hand. So, before computers, the carboard was the quick-and-dirty method.

[OzoAndIndi]

Well if not then I guess 2, 3, and all the rest can't either, since ya ain't gonna get to them without starting at one.

We're all just an illusion.