Jorge Martínez Stack

We address some phenomena about the interaction between lower semicontinuous submeasures on $${\mathbb {N}}$$ N and $$F_{\sigma }$$ F σ ideals. We analyze the pathology degree of a submeasure and present a method to construct pathological $$F_{\sigma }$$ F σ ideals. We give a partial answers to the question of whether every nonpathological tall $$F_{\sigma }$$ F σ ideal is Katětov above the random ideal or at least has a Borel selector. Finally, we show a representation of nonpathological $$F_{\sigma }$$ F σ ideals using sequences in Banach spaces.

In Aristotle’s system there is an important ambiguity between his religious positions or, if they could be so called, his religious ideas, and his theological thought. The first aspect makes room to popular beliefs and can be seen in some philosophically unimportant documents like his will, but also in some philosophically relevant writings like his Metaphysics and his treatise On The Heavens. The second aspect, his theological position, is in flagrant opposition to the first one. On the contrary, in Aquinas there is no contradiction between the object of faith in religion and his theological thought. Furthermore, religion entails ethical duties which can entirely be justified theologically, which is not the case with Aristotle. Natural law is the main concept that links the religious with the theological level in his thought.