the hard part isn't answering whether or not math is real but to define the concept of real in the first place ...
There are a few standard definitions used in analytic philosophy: https://plato.stanford.edu/entries/realism/
Is Mathematics Real? (2020)
41–50 of 59 posts
Re: Is Mathematics Real? (2020)
#42"Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same." I pretty sure it's true also for other areas, e.g. engineering. I believe that first vehicles created by some alien civilization would work on a similar principles as ours.
Beyond "more efficient to move stuff around" by whatever definition of effincy, what would those principles be?
Re: Is Mathematics Real? (2020)
#43“God made the integers, all else is the work of man” I’m not sure if even that is true. Integer counts and succession seem like human constructs to me. An apple isn’t fundamentally a single unit. If I take a bite out of it, is it still one apple?
Your conclusion doesn't follow your premise. Whether it's still an apple is a question of categorisation and a human construct (1). But once it's established it is indeed an Apple you can count the number of such Apples.
Counting is real and the number you count is "true" because it leads to real predictions. This tale of magic bucket is enlightening. (2)
(1): https://www.lesswrong.com/posts/aMHq4mA2PHSM2TMoH/the-catego...
(2): https://www.lesswrong.com/posts/X3HpE8tMXz4m4w6Rz/the-simple...
Re: Is Mathematics Real? (2020)
#44“God made the integers, all else is the work of man” I’m not sure if even that is true. Integer counts and succession seem like human constructs to me. An apple isn’t fundamentally a single unit. If I take a bite out of it, is it still one apple?
> Integer counts and succession seem like human constructs to me. There's definitely some "elementary" mathematical concepts that seem native to our universe. For example, in outer space stuff tends to come together in ways that approximates spheres. We see lattices in crystalline solids all the time. There's naturally-occurring fractals all over the place. The existence of fractals -- snowflakes, trees, broccoli --…
There are no naturally occurring fractals, because all natural things have a minimal feature size after which quantum mechanics makes them fuzzy.
Re: Is Mathematics Real? (2020)
#45I wonder why we ask this of mathematics and not, for example, physics.
We all kinda understand how real Physics is: the universe does weird things, we find rules and equations that fit these things. If planets go in circle (the Real - the Territory), we create orbital equations, Kepler's laws, etc (the Made up - the Map).
Isn't it the same with Math? In this universe, some fundamental rules seem to be obeyed: (at macro scale) objects tend to keep their delimitations, they add up and substract nicely, etc. So we make up words, language, equations to match.
Maybe it's just that the constructs Math tries to Map are more fundamental, harder to imagine a universe where they are different (a universe where 2+2 things makes 5 things)
Re: Is Mathematics Real? (2020)
#46"Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same." I pretty sure it's true also for other areas, e.g. engineering. I believe that first vehicles created by some alien civilization would work on a similar principles as ours.
I believe that first vehicles created by some alien civilization would work on a similar principles as ours.
The way vehicles work on Earth is mostly a function of the environment - we use wheels because they work well in our gravity, we use fossil fuels because the history of Earth has made them abundant, we use fixed-wing flight because it works in our relatively dense atmosphere. On an alien planet with much lower gravity they might never have invented the wheel, or one with a much less dense atmosphere they might never have managed to make a wing big enough to support flight. It assumes a lot about an alien work to suggest they have anything like the same sort of problems to overcome that we have.
Re: Is Mathematics Real? (2020)
#47“God made the integers, all else is the work of man” I’m not sure if even that is true. Integer counts and succession seem like human constructs to me. An apple isn’t fundamentally a single unit. If I take a bite out of it, is it still one apple?
Your conclusion doesn't follow your premise. Whether it's still an apple is a question of categorisation and a human construct (1). But once it's established it is indeed an Apple you can count the number of such Apples. Counting is real and the number you count is "true" because it leads to real predictions. This tale of magic bucket is enlightening. (2) (1): https://www.lesswrong.com/posts/aMHq4mA2PHSM2TMoH/the-cat…
There are different ways to understand reality. For spacial understanding we have cartesian and euclidean models, the former suggests reality is digital, the latter suggests reality is analog, both give real predictions, both are true? For temporal understanding we have declarative and imperative models, the former suggests infinity exists, the latter doesn't, both give real predictions, both are true?
Re: Is Mathematics Real? (2020)
#48"Real" for humans, is whatever we experience directly. Therefore, colour is as real to a blind man as snow to a person who's born in the equator. Is anger "real"? is love "real"? is depression "real"? - all those are very real for those who directly experienced them. Mathematics is only real for those who experienced it directly.
The blind man can hear a color described, but that is not very useful for something that is visual.
The person born in the equator can have the feeling of snow described and by walking into a walk in freezer they can understand cold, they probably already understand water, examples can be made to them. Furthermore they can see videos of major snowstorms from other places.
Thus there are different levels of real between the color for the blind man, and the snow for the person born in the equator.
Re: Is Mathematics Real? (2020)
#49Earlier quoted context omitted.
An apple is a single unit though. An apple is made up of constituent parts, but it is a singular thing. If you argue against an Apple being singular then you are essentially professing that nothing is singular. When you take a bite out of an apple you now have a subset of an apple “an apple with a bite out of it”. To me saying God made the integers is more akin to saying, there is and there isn’t, and all else is bui…
An apple is an abstraction. It's a combination of chemicals bonded together. Those chemicals are composed of atoms which are bonded together, each of which are composed of electrons, protons, and neutrons. Those particles are composed of quarks, and so on. An apple is a singular thing because it is useful for us to think of an apple as a singular thing in most contexts. It is not a singular thing when it is more usef…
Then take quarks. They are a fundamental particle with no known substructure. They are a single unit and they are countable.
Re: Is Mathematics Real? (2020)
#50Category theorist: What is the universal property for “realness”? https://en.wikipedia.org/wiki/Universal_property
The abstract objects which aren't self-defeating [0] are real in this sense. Of course, note that we can't simply quantify over such objects since there is no universal way to decide whether objects are self-defeating, but it is nonetheless a simple criterion. [0] https://terrytao.wordpress.com/2009/11/05/the-no-self-defeat...
A language that cannot express contradictions is too restricted for any practical purposes. —Any programmer
Contradiction != self-defeat.
Is just side effects. A becoming not-A.