Philosophy of Math - Boring but an awareness is necessary
I have learned this week that there is an area of philosophy that I am almost certainly not interested in. That is the philosophy of mathematics.
After reading the first few chapters with close attention I then skimmed quickly to the end over the next short period of about just 3 hours.
I agree with all his conclusions found on page 217 and 218.
For instance... and I quote conclusions 6, 7 and 8 only...
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6) ...diagrams can be rigorous proofs.
7) Mathematics is wedded to classical logic?
"One god, one flag, one logic", said Whitehead. Well, he was at least right about logic, and it is classical.
8) Mathematics is independent of sense experience?
Right again. This is the sense in which mathematics is a priori. It is not infallible, however. Experimental mathematics, it must be stressed, should not be confused with mathematics based on sensory evidence - there's no such thing.
http://www.amazon.co.uk/Philosophy-M.../dp/0415960479
And of course logic (including math) has to be a priori, has to be analytic, because otherwise something else would have to be.
The implications of that all pervasive problem of the criterion surely entail that the logics are all a priori.
"How can any criterion of reliable knowledge be chosen unless we already possess some reliable criterion for making that choice?"
If we are to even begin judging the world we have to already have an innate means, axioms, theorems etc, according to which the world can be judged.
How could we possibly even begin to conceive of the world without an a priori established, or given, conceptual framework? (Immanuel Kant).
Re: Philosophy of Math - Boring but an awareness is necessary
Its all just something that someone believes to be true (or not true). We can not be sure of anything as we are part of the equation/system/life/whatever.
You would need an external observer to be able to be objective. Peoples ego's often get in the way in working out whats going.
When you meet someoen who has worked out what life is all about, you find that few if any of the big intelectual questions are important, the most important thing it to be nice to our fellow beings :)
Re: Philosophy of Math - Boring but an awareness is necessary
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Originally Posted by
monkey spanners
Its all just something that someone believes to be true (or not true).
So if I believe that what you have just said is false then would you accept it as true that what you just said is false?
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We can not be sure of anything as we are part of the equation/system/life/whatever.
A extreme sceptic might argue that we cannot know for sure that we are not brains in a vat - in the Matrix - that sort of thing. Because both theories, that we are and that we are not, are equally supported by the evidence - the world looks exactly the way it would as suggested by both theories.
A mitigated sceptic would say that no we are not brains in a vat and indeed that actually is the sun I see rising. But this mitigated sceptic would say that whatever notions we invoke to try explain why the earth orbits the sun without any noticeable connection, like a steel cable, it is always possible that some better notion will come along. They call this the pessimistic meta induction - that since nearly all our past theories turned out to be false why should we expect any current theories to remain true.
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You would need an external observer to be able to be objective. Peoples ego's often get in the way in working out whats going.
Indeed, there is us, judging the world and then there are the facts out there in the world which we judge, but we cannot step outside of the world to look back at our judgements and then the facts to check that the judgements get it right. But then even if we could we might wonder if another step outside of that again would be necessary to check even that judgement.
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When you meet someone who has worked out what life is all about, you find that few if any of the big intelectual questions are important, the most important thing it to be nice to our fellow beings :)
Epicurus said that the ultimate end was happiness and happiness was the freedom from suffering and the feeling of contentment that comes from being in the flow of life. Happiness is not any means to an end - it is the ultimate end toward which all means aim. It has intrinsic value. Yet anyone who aims directly for happiness will not find it. Like a university is not something over and above all the buildings, fields, lecturers, books and students but just is all those things together. Like a chariot is not something over and above the wheels, axle, platform, supports, leather harness and all the rest - the chariot just is when all those things fall into the right place in relation to each other. Happiness is not something over and above the things in life - it just is all the things in life coming together.
When someone says they just want to be happy we can reply "You mean you want to get your sh*t together?" :)
For me, getting my sh*t together is comprised of answering the two questions "What can we know?" and "How can we come to know it?"
Re: Philosophy of Math - Boring but an awareness is necessary
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Originally Posted by
DTLarca
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So if I believe that what you have just said is false then would you accept it as true that what you just said is false?
No, not necessarily, it, truths are a personal truth, though there are a lot of truths we all ascribe to through traditions and beliefs we were brought up with and through fitting in with our friends and local culture. Many of us don't examine what we think and believe, many whom i have discussed looking deeper into life with find the idea frightening, having what seems to me to be a least said soonest mended attitude.
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A extreme sceptic might argue that we cannot know for sure that we are not brains in a vat - in the Matrix - that sort of thing. Because both theories, that we are and that we are not, are equally supported by the evidence - the world looks exactly the way it would as suggested by both theories.
A mitigated sceptic would say that no we are not brains in a vat and indeed that actually is the sun I see rising. But this mitigated sceptic would say that whatever notions we invoke to try explain why the earth orbits the sun without any noticeable connection, like a steel cable, it is always possible that some better notion will come along. They call this the pessimistic meta induction - that since nearly all our past theories turned out to be false why should we expect any current theories to remain true.
Personally i think we are people floating round in space on a planet we call Earth, it being the most likely explanation for my daily experiences. I am open to changing that belief in the face of new facts.
It is fun and interesting to investigate how life, the universe and everything came to be, but i don't think we should lose any sleep over pondering it. The knowledge is not as important as how we live our lives and treat others.
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Indeed, there is us, judging the world and then there are the facts out there in the world which we judge, but we cannot step outside of the world to look back at our judgements and then the facts to check that the judgements get it right. But then even if we could we might wonder if another step outside of that again would be necessary to check even that judgement.
Yes, it is impossible to be certain about things (i'm not sure its even important to be 100% right)
Quote:
Epicurus said that the ultimate end was happiness and happiness was the freedom from suffering and the feeling of contentment that comes from being in the flow of life. Happiness is not any means to an end - it is the ultimate end toward which all means aim. It has intrinsic value. Yet anyone who aims directly for happiness will not find it. Like a university is not something over and above all the buildings, fields, lecturers, books and students but just is all those things together. Like a chariot is not something over and above the wheels, axle, platform, supports, leather harness and all the rest - the chariot just is when all those things fall into the right place in relation to each other. Happiness is not something over and above the things in life - it just is all the things in life coming together.
When someone says they just want to be happy we can reply "You mean you want to get your sh*t together?" :)
For me, getting my sh*t together is comprised of answering the two questions "What can we know?" and "How can we come to know it?"
Life is an odd journey, we spend ages seeking something and then realise we had it all along, it seems more a case of unlearning rather than learning! Or in my case letting go of my past :)
Re: Philosophy of Math - Boring but an awareness is necessary
