Ignace asked:

How do you see the relationship between mathematics and philosophy ? If anyone is searching for
answers, hasn't he got more chances to find them in proofs in maths than in philosophy ? What
makes the study of existing, unproved theories in philosophy more worthwhile than exact sciences?

I see philosophy as studying history more than actually trying to achieve something. There is a
relationship between them, but I think by merely studying history, this doesn't give any answers.

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One philosopher who would agree with you that philosophy is concerned with 'studying history' —
although perhaps not quite in the way that you mean — is R.G. Collingwood. In his Autobiography
(1939) and Essay on Metaphysics(1940) Collingwood develops a view of the core activity of
philosophy as the study of the 'absolute presuppositions' of different historical periods. Insofar as the
fundamental questions of philosophy have an answer, that answer consists in a description of the
different standpoints from which the universe and our place in it has been conceived at different
times, rather than a search for the one correct or truestandpoint.

While I find that Collingwood's account of truth in terms of seeking an 'answer to a question' is a
valuable reminder that explanations — say, the explanations offered by the historian, or the
philosopher — are relative to interest, that truth depends at least partly on what you are looking for,
his historicist view of the nature of philosophy seems unnecessarily defeatist. If Collingwood were
right, then we are merely deceiving ourselves when look for answers to the philosophical questions
that grip us. There is no 'right' or 'wrong' answer. All we are doing is investigating the presuppositions
of our beliefs, rather than setting out, if necessary, to change those beliefs if they fail to correspond
with reality.

I think philosophy can change our beliefs. You can take a view that is widely held — say, a view
about the nature of free will, or consciousness, or truth — and demonstrate that it is logically
incoherent. You can start with a truism, or set of truisms, and derive a conclusion that is very far from
being truistic. I don't feel the least bit embarrassed in talking about provingthings in philosophy.

Admittedly, proving things in philosophy is not like proving things in mathematics. In mathematics, a
proof establishes a result,something that can be put in the text books. As Wittgenstein remarks
somewhere, mathematicians do not usually 'come to blows' over whether a particular proof in
mathematics is valid. (There are notable exceptions: for example the controversy over the nineteenth
century mathematician Georg Cantor's proof of the existence of a hierarchy of infinite numbers.)

In philosophy, we are never completely sure of what we mean. Philosophers work with words, they
construct arguments — a dialectic — out of words using logic as their guide. The result is — more
words. The words suggest, rather than dictate, a certain way of seeing things, a vision.That in turn
generates more words, more dialectic, and so the process continues apparently without end. One
either has a taste for this kind of activity, or not. You evidently don't!

Geoffrey Klempner