Seminarraum PH 133
Alle Interessierten sind herzlich eingeladen, an dem Kolloquium teilzunehmen.
Leon Horsten (joint work with Steven Delvaux and Rafael De Clercq):
Best equivalence-approximations and criteria of identity
Let there be given a finite graph G and a finite equivalence relation
E, also considered as a graph. We measure the degree of closeness of E
to G by the sum of the number of edges of G¤E and the number of
edges of E¤G. It is shown that the problem of finding a closest
equivalence relation to a given graph G is NP-complete. The extension
of the concept of closest equivalence relation to infinite graphs is also
discussed. Our technical observations are then brought to bear on philosophical
issues relating to criteria of identity for empirical objects, properties
and relations. These issues date back to Carnaps Aufbau and have
more recently been discussed by Timothy Williamson.
What Truth Depends on
The guiding idea of my talk is to replace Tarski's Convention T as an
criterion for theories of truth by the following specification of it:
Convention Td: a theory of truth is materially adequate if and only if
is derivable from it, where A is any sentence of the object language which
depends on non-semantical facts only. The object language is in turn
allowed to contain the truth predicate Tr.
But what is meant by 'depends on non-semantical facts only'? In order
to answer this question we introduce a notion of semantical dependence
holding between sentences and sets of sentences and we study its properties.
On the basis of this dependence relation, we are able to define dependence
on non-semantical facts only, and we can show that Convention Td may indeed
be satisfied despite the presence of vicious selfreferentiality or ungroundedness
in the object language.
General Frameworks for Possible Worlds, Truth-at-a-world and Tarskian
We look at some recent research into the kinds of abstract orderings
that support such hierarchies and frames. We report on some unpublished
work of Shavrukov and Solovay that has import in this area.
13 May, 2006
e-mail address (please replace "0" by the usual "@"
symbol): volker.halbach at philosophy.oxford.ac.uk