2 vs 1? Fine by me, much more interesting that way...
Originally posted by yinyinwang
"axiomatic" means no constrain.
You sure that you don't want to rethink this statement before trying to support it? By the nature of an axiomatic system, a statement is only considered to be true if it is a logical consequence of the axioms, otherwise, it is false, or has no truth value.
Originally posted by yinyinwang
you don't have to care much about the physical reality.
Your point being? A Philosopher is not one to tout physical reality, since many of their paradoxes simply cannot exist in a physical reality, and many of them deny the existence of said reality, so this point is one "against" both Mathematics and Philosophy.
Originally posted by yinyinwang
Have we ever seen a young successful philosopher who at least built a phi-structure of understanding?
I don't know if one exists. I haven't ever heard of one, but then I haven't done much searching for said Philosophers.
Originally posted by yinyinwang
How many young math men have we seen?
Quite a few, considering until a few years ago, a Mathematician's career was essentially considered finished by age 40, i.e. if they haven't discovered something by then, they never will. It is only recently with Andrew Wiles' proof of Fermat's Last Theorem (
he was over 40 when it was completed) that this idea began to change.
Originally posted by yinyinwang
The history performance tells that we have considerablly less philosopher than any other professions, why? And a successful profession become a philosopher in some way because they have to think that way.
You know, I was actually thinking of using a similar "rarity argument" to support my claims about Mathematics, but I did not, since I realized that this line of reasoning is fundamentally flawed. To take a logical extension of your argument, there are less postal workers than office workers, and by your logic, that implies that being a postal worker is more intellectually demanding, a fallacy. Thus, your line of reasoning is incorrect.
Originally posted by yinyinwang
Yes, any one can have his life philosophy and can challeng the pillar, that makes a success more difficult because there are limitless examiners around to attack you from all directions.
To the contrary, it makes it easier. Any point with a shred of truth to it can be argued just as well as an established idea, since there is no experimental evidence or previous standards to conform to, i.e. too much freedom, and too little structure makes a subject rather easy.
Originally posted by yinyinwang
As a mathman, the only thing you care is self-consistancy. You can assume the sun is made up of gold as a mathman, ...
It is true that in Mathematics, one is primarily concerned with self-consistency, since it is a measure of the strength of one's logic, but if one's constructs don't do something useful (
In the context of Mathematics) then there isn't much point to it. Again, your example doesn't work either, since anything having to do with physical reality is not a concern of Mathematics. Frankly, if assuming the sun is made of gold led to an interesting solution of a long-standing problem, e.g. the Riemann Hypothesis, then Mathematicians would have no problem doing so.
Originally posted by yinyinwang
... but if you do so as a phi-man, you become everybody's laugh stuff.
Do you realize you are contradicting yourself here? You were just lauding the freedom of Philosophy, and now are touting its system of checks and balances?
I could create a philosophical paradox that states the sun is composed of a substance that only looks like Hydrogen and Helium to our instruments, but is actually composed of tiny strings of energy that no device can currently detect, (
replacing "tiny strings of energy" with "tiny fragments of gold" will yield an analogue to your original example), but every measuring device that exists today cannot detect them, and this philosophical "paradox" currently has no resolution. It doesn't mean that it has any less validity since it goes against "Philosophical common sense", so even your absurd argument holds as much Philosophical validity as current Physics research.
Originally posted by yinyinwang
Yes a philosopher will not be easy to adapt to any profession, not because of the difficulty but the professional glossary.
So you're stating that Philosophers posses the proper tools to adapt to other fields, and the only barrier are the technical terms? Are you serious? Philosophy is not that efficient of an exercise for one's mind. The concepts in Mathematics are what present the difficulty, not the terminology, and I assert that Philosophy doesn't prepare one for the mental acrobatics that Mathematics requires.
Originally posted by yinyinwang
I think a phi-concept is far more difficult to grasp than a math one since you said they are"axiomatic".
Yes, but "axiomatic" ≠ easy. In Philosophy, almost all interpretations are equally valid, but this is not true in Mathematics. If one doesn't understand the definition of a limit, there is no "alternate and equally valid" idea to revert to, granted, there are certain pictures one can draw, and an intuitive notion is extremely helpful, but it all hinges upon the definition, and if one can't find some way to understand
that definition, then you're out of luck.
Originally posted by yinyinwang
How much effort is dependent on how much you want to gain, not the subject.
To the contrary, the effort one must put in to a field to understand it is
directly proportional to the difficult of the subject.
Originally posted by ProCop
In the domain of philosophy you can ask: What is mathematics?
Can you ask in the domain of mathematics: What is philosophy?
No, one cannot. But your comparison is flawed, since you biased it towards, you guessed it, Philosophy. Just as one cannot ask "
What is philosophy?" in Mathematics, one cannot ask "What are the solutions of x<sup>2</sup>-5x+6=0?" in Philosophy.
Originally posted by ProCop
Mathematics is a subordinate of philosophy.
Incorrect. See why below.
Originally posted by ProCop
Mastering a subdomain compared to the mastering in of the whole domain speaks for itself (at least for some).
Then mastery of Philosophy should imply mastery of Mathematics, however, it obviously does not, thus, Mathematics is not a subset of Philosophy. However, mastery of Mathematics implies a great deal of familiarity with logic, and thus, a mastery of certain aspects of Philosophy.
Originally posted by scilosopher
I personally think the fact that the greatest minds did tend to be people who studied and thought about many different fields - math, science, philosopy, art, is possibly causal not consequential.
From this statement, I tend to get the impression that you are defining a "
[great] mind" as one that is versed in many fields, however, this is not necessarily the case.
Newton was a great mind, but does that make
Cauchy,
Ramanujan, or
Euler, whose efforts were largely in the subject of Mathematics, not great minds? Are
Schrödinger, and
Einstein lesser minds since they dedicated their efforts to Physics? Certainly not.(
The links are to brief biographies of the historical personalities in question. I recommend that all the posters in the thread at least skim them, and refer to their host site; http://www-gap.dcs.st-and.ac.uk/~history/BiogIndex.html; for a rather comprehensive collection of biographies of Mathematicians, Physicists, and other notable scientists. To those who are wondering, no, I have no vested interest in the site, I just felt like sharing a useful link.)
Originally posted by scilosopher
If you exercise all the different basal abilities of your brain they improve and together they make your brain able to attack a question from many different angles, which brings out all sorts of different features that aren't initially apparent.
True, however it is not necessary to work in many different fields to achieve this result. See the examples above.
Originally posted by scilosopher
I think the difficulty level of the material would therefore be set by those who do it rather than what they are trying to do (as well as the amount of time and energy they pt into doing it).
Not necessarily. Material can still be difficult for those who have studied it their whole lives, simply because it requires one to use so many aspects of one's mental faculties, and material can be difficult simply because those who are working on it choose to unnecessarily complicate their subject. I contest that the former is the case for Mathematics, and the latter is the case for Philosophy.