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From the definition from Wikipedia:

Philosophy is the study of general and fundamental problems, such as those connected with reality, existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational argument.

As said in definition it doesn't address problems by its "critical, generally systematic approach and its reliance on rational argument" etc. So my question is: how does philosophy study the fundamental problems mentioned above? Does it use mathematics to study them? For example if it wants to study what mind is. Where would the examples come from? Based on which truth and facts would philosophy make an argument which would be true?

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I think you understood the wiki definition wrong. Philosophy DOES, other than different sciences, use a "critical, generally systematic approach and its reliance on rational argument". –  iphigenie Sep 26 '12 at 12:52
    
you understood the wiki quote wrong. it means that philosophy does use critical, generally systematic approach and its reliance on rational argument. –  Mukul Goel Nov 2 '12 at 17:11
    
What philosophy is is itself a philosophical question. Some, such as Gilson, argue against systems in the modern philosophic sense (although perhaps not some kind of sytematicity) largely because, as the quote attributed to Hegel goes, they often sacrifice reality at the altar of the system. In any case, since you ask "How" philosophy goes about its business, I would recommend looking into various ideas on the methodology of philosophy. Off hand, I know Stanislaw Kaminski gave serious treatment to this subject, although I know much of his works remain untranslated. –  danielm Nov 5 '12 at 9:58
    
sometimes by turning its back to it... –  Mozibur Ullah Mar 7 at 12:21
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1 Answer

How does philosophy study the fundamental problems mentioned above?

As already pointed out in the comments: Philosophy does use a critical, generally systematic approach and it does rely on rational arguments. Logic as well as mathematics play a big role in philosophy.

For example if it wants to study what mind is. Where would the examples come from?

The examples come from our everyday life and from the sciences. Philosphy goes hand in hand with science in a lot of disciplines. Take for example Descartes Meditations. It shows very good how philosophy can work from everyday common life to a foundation for everything, and also a proof for god (if he is, or better, would be, right). Another big source are intuitions. I have the very strong intuition that I think. That presupposes a being. Therefore there is a being.

Based on which truth and facts would philosophy make an argument which would be true?

This is kind of answered above. Note that an argument always has a conditional form. It tells you that if the premisses are true, then the conclusion is true. It may very well be that the premisses are wrong, or will shown to be wrong somewhen in the future.

Maybe this link will help you: It is the article about metaphilosophy on the IEP.

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