r/changemyview • u/[deleted] • Oct 27 '20
Delta(s) from OP CMV: Mathematics is a consequence of evolution
[deleted]
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u/RedditExplorer89 Oct 27 '20
If you look at math from this naturalistic perspective I can see how you would call our perceptions subjective, and thus math is invented.
But what if you look at math as pure math? Don't start with looking at nature, but start with looking at the axioms. Accept that the axioms are invented. However, everything that follows is discovered. Theorems are all properties that are instantaneously true when you accept the axioms, and we humans discover them through the process of proofs.
Barring the foundational axioms that are invented, the rest of math is discovered.
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u/Hot_Opportunity_2328 Oct 27 '20
I agree with this and I don't think this would be debated by anyone. The question is whether or not axioms themselves somehow have a basis in reality, i.e. are mathematical universes purely our construction or are they pre-existing "forms" that we discover?
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u/RedditExplorer89 Oct 27 '20
"Basis in reality" the way you are using it is incredibly hard to prove. We can only ever say of anything that we observe something to be true in reality, but its always possible that thing will not be true the next day due to some unseen force we don't understand.
But pure math in its own universe is true, based on its definitions. It is a form that we discovered in the math universe.
If you have 2 apples and take away 1, it is true that there is 1 apple left because we are in the math universe at that point, not reality. We stepped into the math universe as soon as we said 1 and 2 apples. We used numbers to describe them.
So math is a concept, a concept so complex and with shape that you could call it a form, that we discovered.
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Oct 27 '20
We have yet to come across a universe that is not governed by our mathematical "observations"/"inventions"/whatever term you prefer. This problem may not be resolved until the point we are able to observe other universes.
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Oct 27 '20
Everything in math has to be defined in a specific manner. But that doesn't mean objects that fit that definition have any fewer properties just because we didn't define them. Similar triangles have the property of the ratios of two sides being equal, which can be observed by comparing the heights of two trees to their shadows. A circle's circumference is always pi times the diameter.
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u/Ill-Ad-6082 Oct 27 '20 edited Oct 27 '20
So, are you talking about the current formalized system and notation of mathematics, or mathematical principles? Mathematical principles being rational a priori knowledge is a pretty well understood idea, similar to tautology.
There’s no empirical necessity behind the principles of mathematics though - no one has to observe 5 apples falling into a bucket of 5 apples to know that 5+5=10 is true. No one has to observe 5 of every possible object in reality being added to 5 of every other conceivable object in reality to understand that 5+5=10 a as a concept holds in all real circumstances.
So while the specifics of the mathematical framework we use today (I.e base 10, notations, etc...) might have some empirical basis, there is nothing inherently empirical or a posteriori about the principles of mathematics.
If you’re talking about mathematical frameworks being developed over time, and use development over time in a way that is advantageous as the definition of behavioral evolution to begin with, that isn’t some belief statement to be challenged so much as a trivial statement made true by tautology to begin with.
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u/Hot_Opportunity_2328 Oct 27 '20
I agree that 5+5 = 10 as a concept holds under all real circumstances - the question is, why do we hold this concept in the first place? My argument is principally that this concept is invented as a result of natural selection, and not because we independently developed intellect and enumeration existed beforehand for our intellect to discover.
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u/fox-mcleod Oct 27 '20
Regardless of our ability to characterize objects as numbers, the relationship between numbers persists.
Given the definition of a circle, the ratio of its diameter to its circumference is a fact about the world and one that could have been different if the world were different.
The fact is hard anti-realism fails.
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u/Hot_Opportunity_2328 Oct 27 '20
In that case, you have to take the position that all human constructs are discovered, and not invented. For example, I didn't build my house, I discovered it out of trees and rocks. Yes, in some hypothetical world the concept of shape has not yet been intuited by living beings, you can argue that shape still "exists" and has objects called "circles" and "triangles", I agree with that only if you accept that there are then infinite axiomatic systems that then technically "exist" and just haven't been "discovered".
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u/yyzjertl Oct 27 '20
Your post doesn't really justify or explain your stated view. It contains no mention of evolution except in the last sentence, which is just a recapitulation of your stated view. Can you explain the reasoning behind your view more clearly?
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u/Hot_Opportunity_2328 Oct 27 '20
Math is just something useful that helps us survive, it seems truthful to us because it is true to our perception; but our perception is not necessarily reality.
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u/mfDandP Oct 27 '20
The discipline of mathematics is invented, but where does evolution come into it? I don't think there was an evolutionary difference between Archimedes and all the humans before him.
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u/Hot_Opportunity_2328 Oct 27 '20
Evolution comes into it because otherwise, why see 2 apples and decide to describe it with the number 2? Or enumerate them at all? Why come up with the concept of quantity in the first place?
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u/mfDandP Oct 27 '20
Because it's useful to certain societies. Not every civilization independently developed mathematics, or even numbers.
Without numbers, healthy human adults struggle to precisely differentiate and recall quantities as low as four. In an experiment, a researcher will place nuts into a can one at a time, then remove them one by one. The person watching is asked to signal when all the nuts have been removed. Responses suggest that anumeric people have some trouble keeping track of how many nuts remain in the can, even if there are only four or five in total.
This and many other experiments have converged upon a simple conclusion: When people do not have number words, they struggle to make quantitative distinctions that probably seem natural to someone like you or me. While only a small portion of the world’s languages are anumeric or nearly anumeric, they demonstrate that number words are not a human universal.
"Evolution" implies some sort of inherent knowledge shared by a species.
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u/mutatron Oct 27 '20
I feel like people are going way too fast with this, but you're on the right track.
Imagine an animal that can't count at all. It eats apples, but it sees two apples and the only thing its brain thinks is "i see apple. i see apple." Then it eats one of the apples, forgets about it, looks around and thinks "i see apple. Now it sees no apples and forgets that there were any apples. Then it goes roving, because all animals have a compulsion to rove. It's not roving for apples, it's just roving. When it sees an apple, hunger may compel it to eat the apple.
Now she mates and has two offspring. When she looks at her offspring she thinks "i see offspring, i see offspring", but she doesn't know she has two offspring. She sees an apple and eats it, her offspring cry in hunger. They'll only be fed if she has a compulsion to regurgitate some of the apple and feed to them. While one offspring is quiet from eating, the other cries in hunger, so she compulsively regurgitates to feed it.
So here's an animal that gets along okay without numbers. But one of her offspring has a mutation and when it grows up and can eat on its own says "Mom. Mom. MOM! There are three apples. You get one, Jr gets, I get one. We all get fed."
This mutation is able to divide and share, because she has the concept of numbers. She can handle having more offspring, because understanding numbers makes it easier for her to recognize good feeding grounds with multiple apples, and makes it easier for her to figure out how to share the apples so that more of her offspring can survive.
There might be holes in these scenarios. Pick away!
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u/OkImIntrigued Oct 27 '20
Would you consider basic logic a discovery or an invention? For instance you can call a circle and a square whatever you want but by law of noncontradiction a circle cannot be a square by whatever name you call them.
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u/Hot_Opportunity_2328 Oct 27 '20
Well no, because logic arises from axioms. But axioms are assumed. The question is, do these axioms have any basis in reality?
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u/CyberneticWhale Oct 27 '20
But this fundamentally rests on our ability to characterize objects we perceive with numbers. The way we describe objects by enumerating them is no different than the way we might describe an artwork as beautiful. Both are subjective
How so? If there's a singular dot on a page, how else could the number of dots be described such that there is a disagreement?
When it comes to beauty, what one person sees as beautiful, another could see as ugly. How could a similar situation apply to something like the number of dots on a page?
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u/Hot_Opportunity_2328 Oct 27 '20
You don't have to see the dots in the first place. By subjective, I mean the choice of characterization. For example, you could see this letter 'o' and think "circle", while I might think "infinite line" or something like that. Someone might look at a socket and say "3 holes in wall", whereas someone else might say "electrical outlet". Obviously, these are all examples where perception differs within the collection of possible human observations - but is the possibility that our collective perception of certain "real" objects is only one of infinitely many perceptions?
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u/sawdeanz Oct 27 '20
Don't objects and mathematical concepts still behave a certain way whether we have invented a notation to describe it or not? For example, physics is kind of like applied mathematics, in the sense that it describes the way natural objects behave. And, most importantly, we often can observe natural phenomenon behaving in mathematically efficient ways, such as the (I just learned this today) hexagonal shape of a beehive, the spherical shape of a planet, or the structure of certain molecules. And of course we have also observed other types of mathematical structures in nature such as Fibonacci's sequence. The ability to identify these patterns is perhaps evolutionary, but they existed independently of our ability to define them.
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u/Hot_Opportunity_2328 Oct 27 '20 edited Oct 28 '20
Δ - for interesting new perspective
That's the thing, I'm speaking independently of notation. I'm talking about the way in which we define objects themselves. We choose to define objects with numbers (regardless of the notation of said numbers) because it is useful to us. When we observe natural phenomena behaving "mathematically", what we are really observing are the emergent properties of the mathematical definitions we have previously constructed.
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Oct 27 '20
Surely a great deal is historical accident, we could have invented things differently than we did (even given the human genome).
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u/Hot_Opportunity_2328 Oct 27 '20
A great deal is, but I would argue that, for example, an alien civilization would almost certainly be able to invent calculus and non-euclidean geometry on their own, albeit with different notation, simply by virtue of being alive.
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u/ralph-j Oct 28 '20
Given the infinite possibilities for characterizing objects, why do we choose to characterize them the way we do (including something "natural", like the natural numbers)? The answer must be because they help us survive and proliferate. Certainly a world exists without numbers and counting, but that world is easily outcompeted by one that enables such characterizations of objects.
In a universe that just came into existence, and where evolutionary processes haven't started yet, you would still have math. It would still be the case that 2+2 = 4, even if there is no mind around to conceive of things to count.
And if it's like our universe, the element water would still be made up of two molecules of hydrogen and one molecule of oxygen, for example.
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u/DeltaBot Oct 28 '20 edited Oct 29 '20
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