Do numbers EXIST? - Numberphile

An expert on the philosophy of mathematics, Dr Jonathan Tallant, outlines some of the key arguments about whether or not numbers ACTUALLY EXIST?
More links & stuff in full description below ↓↓↓

Exploring platonism, nominalism and fictionalism.

NUMBERPHILE

Videos by Brady Haran

[MegaKoutsou]

My congratulations to numberphile for making a philosophy of mathematics video. In my opinion, this is a very interesting side of math that gets almost completely overlooked and it should get more attention

[OnlyShadow]

I've told my bank I'm a mathematical fictionalist... they looked at my account and agreed, but still expect my bills to be paid on time.

[AkhilDixitKhatoBiscuit]

He starts with "we are gonna be thinking about three different schools of thoughts on this"! So he believes that the number 3 exists!

[SkySumisu]

Easter Egg:
In the thumbnail: RIIDIICIIIPO
R2-D2 and C-3P0

[vernaaquino]

I ended up from A4 paper sizes to the square root of 2 to whether numbers even exist..i love youtube

[Vyselink]

This was one of the most fascinating videos I've watched in a long time. Thank you so much @Numberphile. 

[Dallior]

This guy (who I'm assuming is a professor) is really knowledgeable about the subject. This video is the only place on the entire internet that explains the battle concisely and well. Thanks, Numberphile!

[luck]

I used to be a nominalist before I entered university. Then linear algebra started, and this is when nominalism totally collapsed for me. It was a momentary aha moment. All it took was to reflex on the axiomatic definition of what a vector is. Vectors aren't unique concepts in this manner, but it was the thing that striked me. Vectors and vector space create a world completely detached from reality. You don't need anything real to define vector space, and you actually can't use anything real to define a vector. Some vectors can be discribed using numbers and some basis, but vectors aren't those sequences of numbers. And there are vectors that can't be fully described using numbers, for example vectors in spaces with infinite dimensionality. And everything can be a vector if operations are defined. Vectors are literally "anything, for which operations of addition and scaling is defined and well behaved". Look, I say, that I define operation multiply(my bed, any number) = my bed; add(my bed, my bed) = my bed, vector space = set, containing only my bed. Now my bed (a literal physical object that I am sitting on right now) is a vector, because it satisfies all the axioms of vector space! Not a description of the bed, not a representation of the bed, but the bed itself is a vector. And no, it's not like some vector is used to represent my bed, but my bed IS a vector in this context.

[donottrustgoogle]

That portrayal of mathematical fictionalism was very far from neutral.

[erdavtyan]

“All models are wrong, but some are useful” - George E. P.

[SecularMentat]

I really like the talks about the philosophy of numbers. I feel they could go in depth about each one and more about where it's troubles are, and maybe even how they've gone alone historically (with more resolution). It's an interesting topic.

[sean..L]

Do ideas exist? Is existence dependent on materiality? What defines existence?

[AlqGo]

Mathematics is just the study of abstract ideas, the properties and facts of abstract objects that obey axioms. The subject emerged out of studying physical objects, and in modern times, has now been generalised to study abstract problems. Mathematics exists in the realm of thoughts.

[jsoldi]

The problem with nominalsim is, even for simple concepts like the number 3, if you have 3 apples on one hand and 3 oranges on another, what do these two sets of fruits have in common? Would we say they have the same quantity, but that there's no such thing as quantity?

[Tofufisch]

Thanks for this channel. I'm very interested in Maths, so this channel is the best opportunity. But my english isn't so good at all so I'm training with your videos my english to. The prounciation of all Numberphile members is very good/perfect. So I have no problems with searching for a translation if there is a vocab which I don't know.
Thanks for all :*

[Lewis]

Brilliant. Thank you Dr.Tallant. This is a fascinating lecture that clarified some questions I had about the subject. Although there are concerns and issues with each of the three philosophies, I am leaning towards nominalsim at this point.

[aarnar]

It's fascinating as well as depressing to see something so much powerful and magical can't even define it's existence.

[maximusgarahan]

I think the (truncated) platonist idea is that numbers have properties—like primeness—independently of how you conceive of them—hence you can misconceive of a number—and therefore they have mind independent properties. As such, they exist.

[XaadeTheBlade]

I don't agree with any of those completely, but I see pieces of each.

Math doesn't really exactly describe objects. If you have 2 apples, those 2 apples are different, therefore you don't have an exact two apples, you have two sets of mass that are separate from each other that are relatively the same. And therefore an approximation of what you actually have.

There is no physical depiction of a circle that has a surface, volume, or area that can be accurately calculated by pi. In fact, a circle itself is just another abstract object. I don't have a circle for a mirror, I have a mirror shaped approximately like a circle.

Mathematical objects are just tools, like a hammer. The hammer strikes a nail, but the full surface of the hammer doesn't meet the full surface of the nail, there are grooves that hide surface away from each other, but at the end of the day, the job is done just as well.

[geirtwo]

This video made me think about this more than I thought I would.