The Instigator
nathan314
Pro (for)
Tied
0 Points
The Contender
ShabShoral
Con (against)
Tied
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Pure mathematics is worthwhile

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Voting Style: Open Point System: 7 Point
Started: 5/3/2015 Category: Science
Updated: 1 year ago Status: Post Voting Period
Viewed: 1,038 times Debate No: 74703
Debate Rounds (3)
Comments (3)
Votes (0)

 

nathan314

Pro

I would like to put forward the proposition that pure mathematics is worthwhile and has an overall benefit to society, culture, and the world as a whole.
By pure mathematics, I mean "Mathematics that studies entirely abstract concepts" and therefore does not neccessarily have a direct application outside of itself.
By worthwhile, I mean "Sufficiently valuable or important to be worth one's time, effort, or interest".

I eagerly await your response, and look forward to a good debate.
ShabShoral

Con

I accept.
Debate Round No. 1
nathan314

Pro

I strongly believe that, despite its criticism, pure mathematics is worthwhile and should continue to be done and taught.

1) It gives people pleasure
Firstly, many people get pleasure from the beauty of mathematics, they enjoy studying it, reading it, discovering it and telling people about it. It is widely agreed that human happiness is one of the main (if not the sole) goals for our existence, and therefore if people get pleasure from mathematics it is worthwhile.

It may not have direct uses (although it can do as I will come to later) but neither does art, poetry, sport...
In the words of C.S Lewis, "Friendship is unnecessary, like philosophy, like art.... It has no survival value; rather it is one of those things which give value to survival.”(1)
To that list I add mathematics, which I believe comes under the bracket of reasons why we want to live.

2) It doesn't require direct applications, but does have them
When the goal of a subject area is not to solve real world problem that area can expand beyond real world, present limits.
Mathematics, especially prime number theory, is a prime example of this. Hundreds of years ago, long before the necessity or capability for computer encryption, mathematicians were discovering things about prime numbers, not for a specific purpose but to expand our knowledge of mathematics.
Many years later, in the 1970s, people used this information discovered for its own sake in order to develop encryption methods used all over the world. (2) If mathematicians were only trying to solve problems in the present which required direct applications in the world at the time, this could not have happened. When you do not need applications, more is discovered which can be used in the future.

3) Studying pure maths improves your analytical, communication and problem solving skills
The heart of pure mathematics is logic, and the more you use and apply logic the better you get.
While, admittedly, the techniques of mathematics are useful to very few people, the structure behind it is used by everyone everyday.
The ability to make rational, logical decisions and solve problems effectively is so important in society today, whether it is deciding on which route to take on the London Underground or countless other everyday situations.
Mathematical ability also benefits studying other sciences, and encourages students to think and not just learn information as is common with other subjects.
Studying pure mathematics alongside applied maths also shows students that maths can be beautiful in itself, and isn't simply a collection of methods used to find the height of a ball 3 seconds after it is launched.

4) Numbers are a part of our universe, to study maths is to study the world
As Galileo wrote, "Mathematics is the language with which God wrote the Universe". (3)
One of humanity's core attributes is the desire to discover more about us and our world.
Physics looks out at the universe, biology looks into our body, history looks back at our past, geography looks around at our world, psychology looks at towards our mind, philosophy and maths look at everything.
That is why pure mathematics is important, it enables us to learn about some of the fundamental things about our universe and every other conceivable universe. Applied maths can tell you that, on Earth, a ball falls at about 9.8m/s^2. Pure maths can tell you that wherever you are, whoever you are with that the you can't find a fraction which when multiplied by itself gives 2, which I think is more worthwhile.

5) It doesn't really cost anything
Anyone can do maths in their spare time on the back of an envelope. It doesn't require expensive machinery, teams of thousands of full time technicians... All it requires is someone to enjoy it, and do it when they can. Some of the greatest works of pure mathematics were done by amateur mathematicians, Fermat being a good example whose career was as a lawyer. (7)
____
My final point is, would you rather be an Ancient Greek or a Roman?
This is, in essence, the discussion. The Romans learnt methods for calculating things in every day life, the are of their field, the height of the coliseum... while the Greeks learnt maths for the beauty of maths, giving them culture, happiness and a desire to discover more about the universe which they lived in. This is what makes pure mathematics worthwhile.

(1)http://www.brainyquote.com...
(2)https://en.wikipedia.org...(cryptosystem)
(3)http://www.quotes.net...
(4)https://www.dpmms.cam.ac.uk...
(5)http://mrflip.com...
(6)http://mathwithbaddrawings.com...
(7)https://en.wikipedia.org...
ShabShoral

Con

By definition, things are worthwhile if they should be done. Things can be done for two reasons: for their own sakes or to help reach another goal. It stands to reason that things desired in themselves are greater goods than those that are desired for other ends. What, then, is the greatest good, for this thing will surely be the primary end desired in itself? Since the concept of “good” can only be known to an individual living as such, life qua man must be required for anything else to be valued, and, as such, it must be the ultimate value towards which all things are aimed.

If life is the only end-in-itself, and things are judged to be good or bad in relation to this, then that which furthers life is the good and that which destroys it is the bad. As such, for abstract maths to be worthwhile, it must further life. For something to further life, it’s clear that it must have a direct impact on it. In other words, for a thing to be good, it must be directly applicable to life, since all goods are aimed towards life and none are good in themselves outside of their relationship with life.
My opponent defines pure maths as something which “does not neccessarily have a direct application outside of itself.” Given the previous line of reasoning, it’s clear that pure maths cannot be valuable, since it does not further life.

Responses:

1) It gives people pleasure

My opponent makes the argument that, since people gain pleasure from maths, maths is worthwhile. This only works if it is assumed that things should be done not for any rational reason but solely because of “pleasure” (however that’s defined). This ignores the fact that there are many things that people find pleasurable that I doubt my opponent would advocate – for instance, the habitual use of cocaine or meth. If pleasure isn’t the standard of what is worthwhile or my opponent cannot justify why it should be, then this point fails.

He also makes the point that many other things (like art) are unnecessary, but are still commonly accepted as worthwhile. This argument is entirely dependent on consensus being infallible, which is faulty reasoning, considering that 50,000,000 Frenchmen can be just as wrong as one. Without a basis in consensus, my opponent will need to show why art, poetry, sport, etc., should be valued, rather than just saying that they are. He needs to provide a complete moral framework to support his stance.

2 + 3)

Here my opponent claims that there are “indirect” applications of abstract maths, whether intentional or not. He says that maths that was originally useless could later turn out to be useful and that the process of doing maths is able to help the study of other fields. However, even if these claims are true, they don’t make abstract maths worthwhile if there are much better ways to achieve its effects. For instance, if a new maths theorem is needed for a present problem, it’s much more reasonable to try to find it with the goal in mind and with a focus on direct applicability than to rely on the random tangents abstract mathematicians with nothing better to do go on. In the same way, even if abstract maths will help with logical skills, the direct study of logic with a view towards its application to the situation at hand will, in pretty much every case, produce better results. Given that the alternatives are much better than the study of abstract maths, such maths haven’t been shown to be worth the time and effort.

4) Numbers are a part of our universe, to study maths is to study the world

My opponent says that the abstract laws of maths are “fundamental” and that knowledge of them is valuable. However, he never justifies why this knowledge is useful. For his argument to work, such knowledge would have to be an end in itself, which, as discussed earlier, is impossible.

Applied maths is applicable to life. Pure maths is not. As such, applied maths is infinitely more worthwhile, regardless of its “beauty” – such things are irrelevant.

5) It doesn't really cost anything


Even if it costs almost nothing to do maths, it still costs something, so this argument begs the question – it only works if it is assumed that maths has some redeeming qualities in the first place.
____
The Romans, under your comparison, were much more respectable. They improved their lives via the work they did – they didn’t just do anything for the sake of it. The Romans had a vast empire that far overshadowed the Greeks precisely because the Romans were earth-oriented, as opposed to mystical and idealistic.
Debate Round No. 2
nathan314

Pro

My opponent has proposed that life is the only end-in-itself, which I fundamentally disagree with and believe his logic supporting this to be heavily flawed.
Just because life is required for "goodness" to be appreciated does not mean that life must be the sole goal, there must also exist the things to be appreciated. A life living only to form new life is not a good existence by almost any standard, it would eradicate all music, art, friendship, nice food, travel, religion, sport, learning, dance, philosophy... The list goes on until all we are left with is a group of people dedicated to procreating to the greatest extend possible, this does not sound good in the slightest. I repeat C.S Lewis' quote "Friendship is unnecessary, like philosophy, like art.... It has no survival value; rather it is one of those things which give value to survival.”
It is true that meaning without life is bad, however life without meaning is far worse. I would choose a world with 100 happy people over one with 1000 sad people.
Pure mathematics is not valuable because it give more life, but because it gives that life meaning, purpose and happiness.

1) It gives people pleasure

I think it is true that if people gain pleasure from something and it does not cause harm to others, then it is worthwhile.
The moral implications of drug usage is a very separate debate, but what distinguishes harmful drugs from mathematics (and the other example) is that they are harmful, they cause harm. Mathematics, art, poetry, friendship etc. do not inherently cause harm. If there was a drug with gave happiness without causing health issues, there would not be a problem.
Art and the other examples are valuable for the same reasons maths is, it brings happiness.

To quote Earl Nightingale, "We are at our very best, and we are happiest, when we are fully engaged in work we enjoy on the journey toward the goal we've established for ourselves. It gives meaning to our time off and comfort to our sleep. It makes everything else in life so wonderful, so worthwhile."

2+3) It doesn't require direct applications, but does have them & Studying pure maths improves your analytical, communication and problem solving skills

Again, I find myself disagreeing here.
Of course, it is sometimes more reasonable to use mathematical methods for a specific goal, but very often it isn't that way.
Without constraining effort to problems you are currently facing science and maths can go further, preparing for questions we do not yet have. We are not limited to current technology, development or issue but can go so much further, expanding horizons which we can reach later. Science and maths can be telescope to the future, seeing places we can't reach now, but might later.


4) Numbers are a part of our universe, to study maths is to study the world

We should study the universe (and by extension history, sociology, philosophy...) because knowledge breeds understanding, acceptance, a furthering of culture and an overall increase in happiness, meaning and satisfaction. My life has meaning to me because I find meaning in it through the pursuit of happiness, friendship, love, knowledge not because I have a beating heart, I breathe and I am alive. Life is not the end-in-itself, pleasure/happiness/satisfaction is.
Things like beauty are hardly irrelevant, they are what makes life worth living as they bring happiness, joy and satisfaction. That is what is worthwhile, not life itself.

5) It doesn't really cost anything

This point does not stand alone, but in combination with the others it does show while mathematics is worthwhile by itself as its benefits (mainly happiness and satisfaction) far outweigh the time spent.
____

Conclusion
I would rather have the smaller empire of Greeks with people curious about the world around them, finding pleasure and meaning in their lives, meeting people to form friendships not just more people, conquering the abstract not other people, writing plays not watching people fight to death, studying logic not battle, not being limited to the Earth but surveying the skies. (I am fully aware, most Greeks were not like this, it is admittedly a poor parallel)

I think this is the crux of the whole debate, happiness or life. I choose both. Thank you for the debate.
ShabShoral

Con

Meaning without life isn’t just “bad” – it’s completely and totally impossible. As such, for philosophy, art, maths, etc. to even be appreciated to any extent, live must be preserved – making it the ultimate value and the thing that must be put above all else. Even if this would lead to a meaningless existence, if it is the truth it cannot be disregarded. No matter how uncomfortable the prospect of it is, if life really is the ultimate value, then things with no applicability to the furthering of life are useless, and this has gone unchallenged except by some “intuitive” arguments that don’t have any clear logical grounding (e.g. that it’s bad to get rid of art, music, &c.). My opponent needed to show why the nihilism he saw in my position was its downfall instead of just saying that it was.


1) It gives people pleasure

My opponent has not answered why pleasure is good in itself.

The things listed do cause harm if they have no value in themselves – the harm comes from the time spent on them. If they have no positive value, then any negative value makes them absolutely wrong to pursue, just as, since the negatives of drugs outweigh the pleasure, drugs should not be pursued. My point was to show that pleasure, in itself, does not make something good – if it did, drugs, which are capable of producing the most pleasurable experiences open to humans, would surely be at least demonized to a lesser extent.



2+3) It doesn't require direct applications, but does have them & Studying pure maths improves your analytical, communication and problem solving skills

Which would be more worthwhile: digging random ditches in an attempt to find buried treasure or using a metal detector in order to find the only spot that needs to be dug up? While it’s true that abstract maths can be useful in the future, it makes much more sense to do things with a direct aim towards applicability, future or otherwise, rather than just because “theoretical knowledge is an end in itself”. You don’t have to sacrifice long-range thinking for real applications.


4) Numbers are a part of our universe, to study maths is to study the world

My opponent just asserts that these things have value – he never justifies why. I have shown that life must be the ultimate value via logical arguments, while my opponent has done nothing of the sort for his alternative values, and, as such, he has not properly refuted my framework.

5) It doesn't really cost anything

If my opponent has not shown why abstract maths has value, then, by virtue of even the most minimal amount of wasted time spent on it, it is destructive and wasteful.
____

Conclusion

I would rather only advance life, as that is the only end in itself that has been justified in this debate, and, as a result, I would only advocate things that directly did so, like applied mathematics as opposed to abstract maths.

Thanks to Pro for the debate.

Debate Round No. 3
3 comments have been posted on this debate. Showing 1 through 3 records.
Posted by ShabShoral 1 year ago
ShabShoral
No problem. Just making sure.
Posted by nathan314 1 year ago
nathan314
Yes it is. Forgot to mention that, sorry.
Posted by ShabShoral 1 year ago
ShabShoral
I'm assuming that the first round is for acceptance?
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