Philosophy of mathematics
#1
Started this thread to continue on a discussion over at http://nirmukta.net/Thread-Why-negative-...05#pid6305 , that was turning out to be tangential to the topic.

Kanad said
Quote:Also, Mathematics is historically never been developed in CONJUNCTION with its applications as you seem to claim.Geometry is pretty old and it was developed and appreciated for its logical consistency. Infact almost all major mathematics concepts have been discovered in era which had no use of idea.

'Never' is too strong a word to be used in this context. Historical geometry was developed mainly for practical use. In Egypt, it was used to build pyramids. In Mesopotamia, mathematics evolved with the purpose of being useful to trade and administration. In India, sulva sutras and other Vedantic mathematics was written to assist in constructing altars for religious rituals. Now, this doesn't mean that all the mathematics of the ancient world was utilitarian. Basic human curiosity would have led some of the mathematicians to consider abstract generalizations of utilitarian geometry. I think it is because of interest in such abstract generalizations that ancient Greek mathematicians pioneered the method of proof. It is also possible that the complex geometrical shapes that ancient Indian priests prescribed for religious altars were due to such curiosity for the abstract and the non-utilitarian.

A reductionist view of the evolution of poetry and music can be an analogy, in my opinion, to the development of mathematics. Poetry (and some forms of music) originally served the purpose of facilitating the transmission of ideas in pre-literate history. This changed over time, in part, due to the growth of literacy. The greatness of many classical poets, even in before writing became prevalent, is because of their treatment of poetry as an intellectual exercise.
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#2
(19-Feb-2012, 11:50 PM)karatalaamalaka Wrote: 'Never' is too strong a word to be used in this context.

Totally agree with you. I got carried away smile


In context of this post by Mihiraj, I have some comments.
I think Mihiraj is committing an error with considering Mathematics as a branch of natural science. That is wrong as well as unwanted. Thus concepts of Mathematics needn't have any ontological representation. This doesn't make it useless. Its a great exercise in understanding rules and structure of logic.
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#3
(21-Feb-2012, 10:06 PM)Kanad Kanhere Wrote:
(19-Feb-2012, 11:50 PM)karatalaamalaka Wrote: 'Never' is too strong a word to be used in this context.

Totally agree with you. I got carried away smile


In context of this post by Mihiraj, I have some comments.
I think Mihiraj is committing an error with considering Mathematics as a branch of natural science. That is wrong as well as unwanted. Thus concepts of Mathematics needn't have any ontological representation. This doesn't make it useless. Its a great exercise in understanding rules and structure of logic.

Miscommunications/communication gaps are the limitations of the mode of communication we are adopting here, which could be easily avoided in face-to-face communication. However, we do not have any other option at present. It is good to have a sensible moderator for the discussion. I am happy that someone is starting a new threads for continuing the discussion.

Now, it is a wrong perception that I was trying to categorise mathematics as a natural science. In fact all my intention was to show the limitation of mathematics compared to natural science. This doenot mean that I belittle the importance of mathematics. All body of knowledge (natural science, or mathematics or literature or social studies) has its relevance, merits and also demerits. Unfortunately many time many people forget the limitations of mathematics. There is a danger of treating mathematics as another source of knowledge on material world, like natural sciences. Worse is considering it superior source of knowledge on material world than natural science. This is the result of absence of conceptual clarity on many interelated terminologies- intelligence, logic, reality, rationalism, truth... As long as logic help us in our search for our knowledge on material world, it is a powerful weapon. The moment it approaches its boundaries, we need to look back, observe, the physical world around us. Answers to logical fallacies will not come from logic itself, it comes mostly from natural science. With this understanding, I used to promote and encourage all attempt to explain mathematical concept with day to day examples, emphasis the historical origin of mathematical concept, relate mathematics with real world. (The intention is not explore the utility in everything). I know the task is not so easy and straightforward even for mathematicians. But I hope this is a check point, which will always causion us from keeping abstract ideas above physical reality.
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#4
(26-Mar-2012, 11:24 PM)mihraj Wrote:
(21-Feb-2012, 10:06 PM)Kanad Kanhere Wrote:
(19-Feb-2012, 11:50 PM)karatalaamalaka Wrote: 'Never' is too strong a word to be used in this context.

Totally agree with you. I got carried away smile


In context of this post by Mihiraj, I have some comments.
I think Mihiraj is committing an error with considering Mathematics as a branch of natural science. That is wrong as well as unwanted. Thus concepts of Mathematics needn't have any ontological representation. This doesn't make it useless. Its a great exercise in understanding rules and structure of logic.

Miscommunications/communication gaps are the limitations of the mode of communication we are adopting here, which could be easily avoided in face-to-face communication. However, we do not have any other option at present. It is good to have a sensible moderator for the discussion. I am happy that someone is starting a new threads for continuing the discussion.

Now, it is a wrong perception that I was trying to categorise mathematics as a natural science. In fact all my intention was to show the limitation of mathematics compared to natural science. This doenot mean that I belittle the importance of mathematics. All body of knowledge (natural science, or mathematics or literature or social studies) has its relevance, merits and also demerits. Unfortunately many time many people forget the limitations of mathematics. There is a danger of treating mathematics as another source of knowledge on material world, like natural sciences. Worse is considering it superior source of knowledge on material world than natural science. This is the result of absence of conceptual clarity on many interelated terminologies- intelligence, logic, reality, rationalism, truth... As long as logic help us in our search for our knowledge on material world, it is a powerful weapon. The moment it approaches its boundaries, we need to look back, observe, the physical world around us. Answers to logical fallacies will not come from logic itself, it comes mostly from natural science. With this understanding, I used to promote and encourage all attempt to explain mathematical concept with day to day examples, emphasis the historical origin of mathematical concept, relate mathematics with real world. (The intention is not explore the utility in everything). I know the task is not so easy and straightforward even for mathematicians. But I hope this is a check point, which will always causion us from keeping abstract ideas above physical reality.

Mihiraj, if your intent is to highlight that study of logic is no superior to study of the natural world, then I am with you. But you seem to over assert this to the point that any study not relevant to the natural world is not useful. This I want to contend. Infact your example of fallacies is totally wrong. Its abstract logic that helps in understand fallacies than natural world. Logic has huge place in ethics and morality, where you can't derive RIGHT from natural world ONLY.
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#5

Mihiraj, if your intent is to highlight that study of logic is no superior to study of the natural world, then I am with you.

- Yes that is my point.

But you seem to over assert this to the point that any study not relevant to the natural world is not useful. This I want to contend.

- No, All knowledge is important and relevant. We should be only be aware of its limitations and possibilities.

Infact your example of fallacies is totally wrong. Its abstract logic that helps in understand fallacies than natural world.

- Elaborate your idea. Prove it. Site examples

Logic has huge place in ethics and morality, where you can't derive RIGHT from natural world ONLY.

- Elaborate your idea. Prove it. Site examples
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#6
(27-Mar-2012, 09:12 PM)mihraj Wrote: Infact your example of fallacies is totally wrong. Its abstract logic that helps in understand fallacies than natural world.

- Elaborate your idea. Prove it. Site examples

In natural world, because of conditioning, correlation is treated as causation. But logic teaches us that its a fallacy.

(27-Mar-2012, 09:12 PM)mihraj Wrote: Logic has huge place in ethics and morality, where you can't derive RIGHT from natural world ONLY.

- Elaborate your idea. Prove it. Site examples

Tonnes of example here. Infact there is a name for this error "Naturalistic fallacy". Most objections to homosexuality are classic examples of this kind of fallacy
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