The Instigator
Peter_10
Pro (for)
The Contender
FuzzyCatPotato
Con (against)

Math is discovered and not invented

Do you like this debate?NoYes+0
Add this debate to Google Add this debate to Delicious Add this debate to FaceBook Add this debate to Digg  
Debate Round Forfeited
Peter_10 has forfeited round #3.
Our system has not yet updated this debate. Please check back in a few minutes for more options.
Time Remaining
00days00hours00minutes00seconds
Voting Style: Open Point System: 7 Point
Started: 4/8/2017 Category: Science
Updated: 1 year ago Status: Debating Period
Viewed: 680 times Debate No: 101812
Debate Rounds (5)
Comments (6)
Votes (0)

 

Peter_10

Pro

Round One is for acceptance only.

Pro/For: Math is discovered.
Con/Against: Math is invented.

*I accept Ad Hominem attacks.
FuzzyCatPotato

Con

I accept the topic as stated.

I will argue that math is like science: a system built by humans that has immense predictive power, rather than a "truth" that humans stumble upon.
Debate Round No. 1
Peter_10

Pro

I am supporting Plato's metaphysical view that mathematics is discovered. I am asserting that abstract mathematical objects exist independent of us.

1. Axioms are discovered. An axiom is a statement that is unprovable yet assumed to be true because it is self-evident. An example of an axiom is the statement A is equal to A. No matter where you are, an object is the same as that object. A human does not need to state that an apple is an apple. The concept is there independent of the mind.
2. The Pythagorean theorem and the concept of π do not change. The formula a2 + b2 = c2 can never change. If aliens existed, they would use that formula (unless they discovered another one) because the idea that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse is the same wherever you are in the universe. As for π, it also does not change. The ratio of a circle’s circumference to its diameter will always be the same.
FuzzyCatPotato

Con

Pro's logic is fatally flawed.

Their argument may be syllogized as follows:

Premise 1: Axioms are discovered. [Their argument 1.]
Premise: Math is axiomatic. [Their argument 2.]
Conlcusion: Math is discovered.

Both of Pro's premises are flawed -- and moreover, poorly supported in the first place.

PREMISE 1: AXIOMS ARE DISCOVERED

Pro's argument for this premise is very, very weak. Pro merely asserts that:

No matter where you are, an object is the same as that object. A human does not need to state that an apple is an apple. The concept is there independent of the mind.

Syllogizing this statement shows its absurdity:

P1: Humans know what apples [and axioms in general] are.
P2: If humans know what something is, then the idea of that something is independent of the mind.
C1: The idea of apples [and axioms in general] is independent of the mind.

It should be obvious that P2 is weak. Just because most humans innately understand what an apple is, does not mean that the concept of an apple is itself "innate". Let me show you two disproofs.

[1] First: Machine learning is incredibly good at recognizing objects like cars, mammals, buildings, and so on. (Search "Google Deep Dream" if you don't believe me.) Yet machine learning is not conscious, but is merely recognizing patterns of information and fitting mathematical functions to those patterns. If nonconscious algorithms can recognize things like apples, this suggests that it's possible to recognize things like apples without having an "idea" of an apple in the first place. And since human brains are known to function heuristically -- ie, somewhat machine-like -- it's reasonable to think that human brains have similarly, through the course of evolution, come to be able to recognize patterns like apples and faces and cars (and identify new patterns as well). And via Occam's Razor, we should presume the simpler idea -- humans can learn -- over the more complex idea -- ideas are ethereal and beyond physical. TLDR: If deterministic electrons can do it, you don't need a magical "idea"-land.

P1: If entities that have no ideas can identify apples, then the existence of a metaphysical "idea of an apple" is unnecessary.
P2: (Occam's Razor) If the existence of a metaphysical "idea of an apple" is unnecessary, then we should presume that it is false unless evidence is presented for it.
P3: No evidence is presented for the existence of a metaphysical "idea of an apple".
C1: The existence of a metaphysical "idea of an apple" should be presumed false.

[2] Second: Proof via counterexample. It is known that people's perceptions of colors are different. What you describe as "purple" might be "reddish blue" to me. Similarly, people's conceptions of "an apple" will be different. One person will think apples are red; another will think apples are green. One will think apples are big; another will think apples are small. This suggests that people don't all obtain their definition of appleness from a singular unified idea of appleness.

P1: If people's don't derive their idea of appleness from a singular "idea of an apple", then the existence of a metaphysical "idea of an apple" is unnecessary.
P2: (Occam's Razor) If the existence of a metaphysical "idea of an apple" is unnecessary, then we should presume that it is false unless evidence is presented for it.
P3: No evidence is presented for the existence of a metaphysical "idea of an apple".
C1: The existence of a metaphysical "idea of an apple" should be presumed false.

Moreover, Pro did nothing to support P2 in the previous round. As such, Pro provides no reason to believe Pro that axioms are independent of the mind. The null hypothesis would be that axioms are merely human ideas -- since "people have ideas" is vastly simpler than "people have ideas AND ideas exist outside of people". As such, Pro has failed their burden of proof (BOP) to support the premise that axioms are independent of the mind.

And if axioms aren't independent of the mind, then necessarily they cannot be "discovered" -- they are just human thoughts that humans happen to think are useful.

PREMISE 2: MATH IS AXIOMATIC

Pro's argument is that math is purely axiomatic. However, Pro fails to realize two fatal things:

FIRST: Math as a discipline is not produced in an axiomatic vacuum. It is a science, and people get things wrong. Euler's original theorems were based upon too many assumptins to be rigorous. Famed mathematician William Shanks famously calculated π wrong [1]. Many times, math that was widely accepted was overturned. Kempe's proof of the four color theorem not proven wrong for a decade. Lagrange's work was almost entirely based upon the idea that all real continuous functions on real intervals can be expanded as a power series except at a finite number of isolated points -- but Dirichlet's proper definition of "function" killed it. Similarly, Ampere "proved" any continuous function is differentiable except as finitely many points. Weirestrass found a counter example with a continuous but nowhere differentiable function.

My personal favorite: Daniel Biss, mathematics superstar, published a paper that was fatally flawed. After he published a retraction, he went from math to politics within the year (2011) [2].

If all the gibberish seems incomprehensible, the takeaway is this: math, like science, takes steps forward -- and sometimes steps back. Both are human endeveaurs, with human successes and failures. To treat mathematics as some sort of hyperlogical axiom-game is straight up wrong.

SECOND: Pro illogically conflates "not changing" with "being axiomatic". Even if the value of π is universal -- which Pro has not proven -- this does not prove that it exists outside of the minds of smart mathematicians. If we had used the wrong axioms to define π, then that value of π would not be constant. Consider: If we removed the axiom for division/multiplication -- if it was not possible to divide/multiply in our mathematical system -- then the value of π could not exist at all. Instead, properly defining π requires a system that can adequately describe geometric shapes and do prescribed funcitons with them.

Imagine that aliens have discovered a third basic function beyond add/subtract and multiply/divide. They might have whole concepts that never would have occurred to us -- because we had never adopted that mathematical function as an axiom.

In other words: math is the successful selection of axioms, not the axioms themselves. When math chooses wrong, it gets things wrong. When math chooses right, it gets things right.

The axioms themselves are just ideas that our minds mush together to produce logical inferrences -- no more, no less.

SUMMARY

There's no reason to think that metaphysical ideas exist in the first place. Pro hasn't presented evidence for it, and it's very reasonable to presume it's untrue.

And math itself is demonstrably a human endeavor about the choosing of axioms, not about "discovering" new axioms.

Finally: the burden of proof is on Pro, and they have not fulfilled it.

REFERENCES

[1] http://www.americanscientist.org...
[2] https://en.wikipedia.org...
Debate Round No. 2
This round has not been posted yet.
This round has not been posted yet.
Debate Round No. 3
This round has not been posted yet.
This round has not been posted yet.
Debate Round No. 4
This round has not been posted yet.
This round has not been posted yet.
Debate Round No. 5
6 comments have been posted on this debate. Showing 1 through 6 records.
Posted by sboss18 1 year ago
sboss18
Peter, the Pythagorean Theorem does not hold true in all forms of geometry, just Euclidean. It won't work in spherical geometry, for example.
Posted by vi_spex 1 year ago
vi_spex
kid..
Posted by PowerPikachu21 1 year ago
PowerPikachu21
vi_spex tends to speak strange. I believe he means that math already exists, we're just discovering information. Something like that, anyways. (This is also my perspective)

I'm sure this is a truism; something that can't be argued against without kritiks or semantics. A kritik challenges the assumption of the topic [Lexus is a user that often uses kritiks]. Semantics are also known as the Equivocation Fallacy; using an irrelevant definition of a word to form an argument around [MagicAintReal uses this a lot]. And before someone tries redefining the words, post definitions for Math, Discover, and Invent.
Posted by vi_spex 1 year ago
vi_spex
just adding pieces to the puzzle
Posted by Peter_10 1 year ago
Peter_10
Pardon? I don't quite get what you meant by that comment.
Posted by vi_spex 1 year ago
vi_spex
doing math=does it fit or add up to my experience of it
This debate has 4 more rounds before the voting begins. If you want to receive email updates for this debate, click the Add to My Favorites link at the top of the page.