The Instigator
dawkinist
Pro (for)
Losing
1 Points
The Contender
ssadi
Con (against)
Winning
5 Points

Maths cannot be proven true it is a human invention

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Post Voting Period
The voting period for this debate has ended.
after 1 vote the winner is...
ssadi
Voting Style: Open Point System: 7 Point
Started: 2/24/2016 Category: Philosophy
Updated: 1 year ago Status: Post Voting Period
Viewed: 640 times Debate No: 87203
Debate Rounds (3)
Comments (7)
Votes (1)

 

dawkinist

Pro

This is a popular philosophical question that really boils down to the epistemology of maths. Can maths be proven true? I think not, yes it is true by definition that relies on the fact that we accept the foundations of maths (axioms) without any proof.

Anyone is welcome!
ssadi

Con

I accept.

Since the Instigator didn't provide any definition, rule, etc., I will do it instead..




DEFINITIONS


Maths = Mathematics[1]:
The systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically.[2]

By Maths it should be meant Math as a whole, not something particular in mathematics. Because if one proves that a theorem is wrong, that would only mean that that theorem is wrong, not mathematics.


Prove (v): To establish the truth or genuineness of, as by evidence or argument.[3]

True: Being in accordance with the actual state or conditions; conforming to reality or fact; not false.[4]

Invent: To produce or create with the imagination.[5] (I think this is what Pro means by invention.)


Axiom: A proposition that is assumed without proof for the sake of studying the consequences that follow from it.[6]



BOP


The BOP is fully on Pro, since it is their claim. I will refute their arguments, without making any claim.

Pro argues that Maths cannot be proven.
Con provides rebuttals to refute Pro's arguments.



RULES

-
No restriction on structure of rounds.


-The only rule is to follow the definitions.

-If Pro disagrees with anything above, we can discuss it under comments and reconsider. Pro can post their arguments in round 2 if they agree to above definitions, rules, etc.



CONCLUSION


I look forward to Pro's opening arguments in round 2 and wish them best of luck!



SOURCES


[1] http://dictionary.reference.com...
[2] http://dictionary.reference.com...
[3] Def.1 in http://dictionary.reference.com...
[4] Def.1 in http://dictionary.reference.com...
[5] Def.2 in http://dictionary.reference.com...
[6] Def.3 in http://dictionary.reference.com...

Debate Round No. 1
dawkinist

Pro

Thank you for accepting con.

Maths is all around us and in everything that cannot be denied is it true? Well many say that it is true by definition. But why should we blindly accept this. Maths is based on axioms that, as the definition provided states are assumed without proof. Surely we should, as inquisitive beings, question just why we should assume these are true. Arguing that maths is all around us and is there to be discovered which is platonic. It would exist even if humans didn't exist it would be there no matter what. Many mathematicians regard themselves as 'hunters' or 'discoverers' that feel they are finding maths around us.

Assuming the above points then maths is no different than faith, in other words people who believe maths is there regardless of our existence they have faith that it is there. But is it true? Obviously in epistemology terms nothing is true we cannot know anything.

I feel that maths is a tool or a language that humans have created or invented with a purpose in mind to interpret reality and the world around us. We cannot see the number 2 for example, we can't find some where in the world where we can view the number two just like we cannot find the word apple. This suggests that it's limited within the human brain and any other life on any planets in our universe would have a completely different type of maths regarding that the same physics would apply for our universe.

To be clear I am not saying maths isn't helpful or vital of course it is but it is simply a human creation no different than language (respectively).

I look forward to your response!
ssadi

Con

I thank posting their arguments.



REBUTTALS



Pro: "Maths is all around us and in everything that cannot be denied is it true? Well many say that it is true by definition. But why should we blindly accept this."

We don't accept it blindly. Definition that you are talking about is like naming. For example, the word "two" or number"2" are such definitions and we know what one would mean when s/he says two or 2 apples. Would it be blindly accepting that s/he means apple and another apple when s/he says two or 2 apples? No, it wouldn't.

To give another example, with that logic even the words we use in a language are also definitions. For example, we have the word "apple"
is a representative definition of a fruit. Why should we accept blindly that the word "apple" means the specified fruit? Simply because we have defined it so.. Therefore, we accept them to be so because we have defined them to be so.

For example, we have defined “=” to mean “is equal to”.. Why should we blindly accept that it means “is equal to”? First of all, it is not blindly accepting, but accepting because it is defined to be so.

Define: "to state or set forth the meaning of (a word, phrase, etc.)"[1]


Pro: "Maths is based on axioms that, as the definition provided states are assumed without proof. Surely we should, as inquisitive beings, question just why we should assume these are true."

Simply because we have defined them to be so.

Pro: "An axiom or postulate as defined in classical philosophy, is a statement (in mathematics often shown in symbolic form) that is so evident or well-established, that it is accepted without controversy or question...


"As used in mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". Logical axioms are usually statements that are taken to be true within the system of logic they define (e.g., (A and B) implies A), while non-logical axioms (e.g., a + b = b + a) are actually substantive assertions about the elements of the domain of a specific mathematical theory (such as arithmetic)."[2]

Pro:
"Arguing that maths is all around us and is there to be discovered which is platonic. It would exist even if humans didn't exist it would be there no matter what. Many mathematicians regard themselves as 'hunters' or 'discoverers' that feel they are finding maths around us.


Assuming the above points then maths is no different than faith, in other words people who believe maths is there regardless of our existence they have faith that it is there. But is it true? Obviously in epistemology terms nothing is true we cannot know anything.

I feel that maths is a tool or a language that humans have created or invented with a purpose in mind to interpret reality and the world around us. We cannot see the number 2 for example, we can't find some where in the world where we can view the number two just like we cannot find the word apple. This suggests that it's limited within the human brain and any other life on any planets in our universe would have a completely different type of maths regarding that the same physics would apply for our universe."


Pro actually summarizes their arguments in their last sentence:

Pro: "To be clear I am not saying maths isn't helpful or vital of course it is but it is simply a human creation no different than language (respectively)."


If someone asks you to prove that your language is correct, you simply give him/her a dictionary and let him/her compare it. If everything is done according to dictionary, then they are true. Similarly, to say that math is not true because it depends on definitions is pointless.. Math can be proven true simply by showing that it is true according to definitions. Accepting the definitions without proof is not accepting them blindly, but accepting them because we defined them to be so.


CONCLUSION

I refuted all Pro's arguments.. I will wait for their arguments in last round.



SOURCES



[1] http://dictionary.reference.com...

[2] https://en.wikipedia.org...

Debate Round No. 2
dawkinist

Pro

In addressing your first point on definition I would like to say that we may not physically 'blindly' accept maths but we accept it without any proof that it actually exists and is true, with or without human existence. We call an apple an apple because we perceive it to be so and we have given the apple the name of the apple but theoretically we do not know that it is an apple we have just named it so.

In relation to maths we have created axioms in which we can base mathematics off. What I would like to say is that we cannot prove maths to be solely true and we can't tell if it would differ on other planets with life (hypothetically speaking) maybe they would have a different concept of maths that is much more efficient. Just because we have defined a thing like an apple does not make the apple and apple. For example imagine on a remote island where the islanders call ,what we call apples, instead they call them rocks that does not make the 'apple' a rock and they may feel that what they perceive and define an apple is true but what we perceive is wrong.

I used the language comparison to show that maths is a creation, a human invention to interpret reality and communicate with reality. Trying to prove maths to be true by using our constructed definitions suited to our brains and the limits our minds hold is not substantial in proving maths to any other being than a human thus I argue that it is a human invention and cannot be proven true.

I apologise for the late reply and look forward to the final round!
ssadi

Con

Thank you for posting your arguments.


Note 1: Please refer to comment number 4 under comments for corrections to my R2 arguments!


Pro: "We call an apple an apple because we perceive it to be so and we have given the apple the name of the apple but theoretically we do not know that it is an apple we have just named it so."


I think I see what you are saying, and I think I have figured out from what perspective you are looking. Let me now humbly introduce a different perspective to look from.



After reading your argument, I remembered a story by famous Muslim Scholar Mawlana Rumi in his famous Mathnawi (or Masnawi). He demonstrates a disagreement between four men. The story is shortly as follows.



A men gave a dirhem (let's say $5) to four persons; a Persian, an Arab, a Turk and a Greek. They wanted to buy something with that money.

The Persian said he wants “angur”. The Arab objected that he doesn’t want “angur”, but he wants “inab”. The Turk said he wanted neither “angur” nor “inab”, but he wanted “uzum”. The Greek objected to all saying that he wanted “istafil”. This disagreement eventually resulted in a fight among them.

The situation was no good until an esoteric and many-languaged man came and told them to listen to him. He told them that he can buy what each of them wants with that $5 only. Then the man buys grapes with that $5 and puts them in front of four of them tells each of them respectively:


“Here is your angur (to Persian), here is your inab (to Arab), here is your uzum (to Turk), and here is your istafil (to Greek).”[1]


Note 2: grapes is angur in Persian, uzum in Turkish, inab in Arabic and istafil in Greek!


Note 3: Shortly, the author brings this story to demonstrate how ignorance leads to unnecessary and pointless fights while knowledge and wisdom solves problems, fights etc.


As we see, what changes is the word defined for something differently in different languages, not that thing itself. In the case above, all four words mean grapes. The fruit grape itself doesn’t change for different people with different languages, what changes is the word they have defined for that fruit. Each of those men can think that the words used by others for grapes are wrong, and his own word is true (I think this is the point Pro is making). Now, if one of them was wrong about the word he used to be grapes, then how the many-languaged men could understand him? They all were using true words, but defined according to different languages. Since the many-languaged men knew all of those languages, then none of them was wrong for him and he proved that they all were correct, by bringing grapes and saying that he brought what each of them wanted.


Similarly, what changes is the definitions and axioms, not mathematics. One apple and two apples, for example, mean bir elmaand iki elma in Turkish. In English, adding one apple with another one apple will make two apples. And in Turkish, adding bir elma with another bir elma will make iki elma. As you see, what changed were the words defined for the specified fruit and for number 1 and number 2. An American uses different definitions and words for the same event than a Turk. But they both will be describing the same event with same inputs and same outputs according to reality, isn’t it? Does, the different words defined for same things change the reality? No! Since they both are describing the same event according to reality, then they both are true, according to definition given for “true” in round 1.


What is mathematics? “The systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. What may change is the symbols defined, not the systematic treatment, hence not mathematics.


Let me give another interesting example. Our parents have given us names. Can we prove that our names are true? Yes, we can, simply by showing an ID or a passport with a picture of us and our name on it. If policemen that work in airport who control our passports believed that one cannot prove his/her name and surname true, because they are human inventions (parents’ in most cases), then we would all have great troubles in airports.. We may not know the language of that policemen in airport in a different country, but we can prove our name and surname to be true even to them just by showing our passport.


Furthermore, in another country, people may use the word “mathematics” for what we call as “chemistry”. But that doesn’t make “mathematics according to English language” any different than “chemistry according to the language of that other country” according to reality, does it? Therefore, for a person who knows both languages, both of them are true.


Let me now address another point from Pro’s arguments.


Pro: “Just because we have defined a thing like an apple does not make the apple and apple. For example imagine on a remote island where the islanders call ,what we call apples, instead they call them rocks that does not make the 'apple' a rock and they may feel that what they perceive and define an apple is true but what we perceive is wrong.”


Not according to reality, but relatively according to each language. That is why we use ”according to definition”. You may think that “rock” is not a fruit (because according to you rock is a huge stone) as they claim and they may think that “rock” is not a huge stone (because rock is a fruit according to them) as you claim. But when I start to learn both languages, I find rock true (in accordance with reality) in both cases, because they have defined that word to mean different things in reality.. Therefore, for me both are true. In other words, since the reality doesn’t change and it is the definition that changes, then any word that is defined to mean something according to reality is true as far as it is used correctly according to its definition.


Similarly, it is not the thing defined as mathematics in English language (what it means or what it is in reality) that changes, but the definitions are what change. Therefore, what we have defined as mathematics in English language doesn’t change and is true according to reality. What changes is the definitions, axioms and symbols.. And still, we cannot say that those axioms, definitions or symbols are wrong according to reality (as they are defined), but we can only say that they are not true according to OUR DEFINITIONS (not according to reality).



CONCLUSION


This debate was really interesting and can be very confusing when not approached very carefully. The problem for this confusion is in definitions according to different situations, people etc. not according to reality.

I have negated the resolution that “Maths cannot be proven true it is a human invention”.


To Pro


I enjoyed this debate. I really like looking at a thing from different perspectives. What Pro did in this debate was looking from a different perspective (true or wrong) and I really want to congratulate them for that. I hope they will not give up doing it for different issues as well. I only want to give a humble and friendly advice to Pro. Looking at things from different perspectives, thinking out of the box etc. are great and very difficult to do. Therefore, doing so naturally requires much more attention and care than normal analysis. So, my humble and friendly advice is to pay much more attention and to be much more careful while doing so.


I hope Pro also enjoyed this debate and wish them best of luck in their life.

Vote Con please!

Debate Round No. 3
7 comments have been posted on this debate. Showing 1 through 7 records.
Posted by ssadi 1 year ago
ssadi
@Zarium,

Thanks for vote and good RFD.
Posted by ssadi 1 year ago
ssadi
@Zarium,

Will you then vote if you find the rest interesting as well, please? :)))
Posted by Zarium 1 year ago
Zarium
Awesome opens; Can't wait to see how it ends!
Posted by ssadi 1 year ago
ssadi
CORRECTIONS TO R2

1. I thank PRO FOR posting their arguments.

2."An axiom or postulate as defined in classical philosophy, is a statement (in mathematics often shown in symbolic form) that is so evident or well-established, that it is accepted without controversy or question...

I wrote "Pro:" for the above paragraph. Ignore the part "Pro:" please, this paragraph plus the succeeding paragraph are both quotations from Ref.2.

These are two main mistakes I did in R2, I really apologize for that.. Thanks for understanding.
Posted by ssadi 1 year ago
ssadi
@dawkinist,

There are some mistakes in my post, sorry for that. I was in a rush. I will write them here asap...
Posted by ssadi 1 year ago
ssadi
Yeah, I couldn't help but accept.. I couldn't miss such an interesting debate..
Posted by ssadi 1 year ago
ssadi
I would love to debate this, but I have 4 ongoing debates, so it will be difficult for me to take it if you wanted a serious debate..
1 votes has been placed for this debate.
Vote Placed by Zarium 1 year ago
Zarium
dawkinistssadiTied
Agreed with before the debate:-Vote Checkmark-0 points
Agreed with after the debate:-Vote Checkmark-0 points
Who had better conduct:--Vote Checkmark1 point
Had better spelling and grammar:Vote Checkmark--1 point
Made more convincing arguments:-Vote Checkmark-3 points
Used the most reliable sources:-Vote Checkmark-2 points
Total points awarded:15 
Reasons for voting decision: Great debate, In my opinion it goes to Con. Conduct is a Tie, both were courteous and friendly, no rules were broken in my perception. Grammar and spelling to Pro, however this may be a primary language issue, and unsure if this divides the vote - All mistakes I saw on Con's side were grammatical, which is expected. Arguments to Con, He succinctly provided his stance and in my opinion unequivocally answered the question posed. Well done! Sources to Con, for accuracy and the fact that Pro did not. Re-iterate Con's conclusion, bravo to Pro for his thought process, however I would agree that a little more thought is required to adequately maintain his stance.