136,694 research outputs found
Tracing the Territory. A Unitary Foundationalist Account
The paper offers an integrative interpretation of the different lines of thought Wittgenstein was inspecting in On Certainty and what he might have been looking for through them. It suggests that we may have been focusing our attention too strongly in the wrong place and comes to a new conclusion about where the real import of these reflections lies. This leads to an answer to the initially posed question of Foundationalism that revises the way in which there can be said to be a grounding intention in On Certainty
Ideal matrices. III.
In this paper ideal matrices with respect to ideals in the maximal order of an algebraic number field are connected with the different of the field and with group matrices in the case of normal fields whose maximal order has a normal basis
Fixed points for actions of Aut(Fn) on CAT(0) spaces
For n greater or equal 4 we discuss questions concerning global fixed points
for isometric actions of Aut(Fn), the automorphism group of a free group of
rank n, on complete CAT(0) spaces. We prove that whenever Aut(Fn) acts by
isometries on complete d-dimensional CAT(0) space with d is less than 2 times
the integer function of n over 4 and minus 1, then it must fix a point. This
property has implications for irreducible representations of Aut(Fn), which are
also presented here. For SAut(Fn), the unique subgroup of index two in Aut(Fn),
we obtain similar results
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