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04-05-2013, 01:08 AM #1
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...
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).
Only the dogmatist says he will never change his mind. We all know that some of our opinions are wrong but none of us know which they are for if we did then they just wouldn't be our opinions. - JS Mill.
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04-05-2013, 04:26 PM #2
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 beingsMostly found in Oxfordshire, UK :)
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04-05-2013, 05:06 PM #3
Re: Philosophy of Math - Boring but an awareness is necessary
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?
We can not be sure of anything as we are part of the equation/system/life/whatever.
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.
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 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
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?"Last edited by DTLarca; 04-05-2013 at 05:10 PM.
Only the dogmatist says he will never change his mind. We all know that some of our opinions are wrong but none of us know which they are for if we did then they just wouldn't be our opinions. - JS Mill.
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04-05-2013, 09:46 PM #4
Re: Philosophy of Math - Boring but an awareness is necessary
Mostly found in Oxfordshire, UK :)
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14-05-2013, 01:08 AM #5
Re: Philosophy of Math - Boring but an awareness is necessary
right thats it see yah!