Online research in philosophy

The starting-point is the distinction between concept and conception. Our conceptions of gold, for instance, are the different understandings we get when we hear the word ‘gold’ whereas the concept of gold consists in the scientific determination of what gold is. It depends on the context whether it is more reasonable to claim a concept or to look for fitting conceptions. By arguing against metaphysical realism and for non-metaphysical realism, I will elaborate on some philosophical reasons for dealing with conceptions (...) instead of concepts of God, and secondly, I will discuss how such conceptions should be critically assessed. (shrink)

Let X be any infinite, coinfinite r.e. set. We show that the index set $\{e: W_e \equiv_1 X\}$ is Σ 0 3 -complete, answering a question posed by Odifreddi in [2].

It will be shown that in the lattice of recursively enumerable sets one can define elementarily with parameters a structure isomorphic to (∑ 0 4 , ∑ 0 3 ), i.e. isomorphic to the lattice of ∑ 0 4 sets together with a unary predicate selecting out exactly the ∑ 0 3 sets.

It will be shown that in the lattice of recursively enumerable sets all lattices $\underline{L}(X)$ are elementarily definable with parameters, where X is Σ 0 3 and $\underline{L}^3(X)$ consists of all Σ 0 3 sets containing X.