Maths cannot be proven true it is a human invention
Anyone is welcome!
Since the Instigator didn't provide any definition, rule, etc., I will do it instead..
Maths = Mathematics: The systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically.
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.
True: Being in accordance with the actual state or conditions; conforming to reality or fact; not false.
Invent: To produce or create with the imagination. (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.
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.
-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.
I look forward to Pro's opening arguments in round 2 and wish them best of luck!
 Def.1 in http://dictionary.reference.com...
 Def.1 in http://dictionary.reference.com...
 Def.2 in http://dictionary.reference.com...
 Def.3 in http://dictionary.reference.com...
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!
I thank posting their arguments.
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.
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!
Thank you for posting your arguments.
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).”
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).
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”.
I hope Pro also enjoyed this debate and wish them best of luck in their life.
Vote Con please!
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