Knobe reports that subjects' judgments of whether an agent did something intentionally vary depending on whether the outcome in question was seen by them as good or as bad. He concludes that subjects' moral views affect their judgments about intentional action. This conclusion appears to follow only if different meanings of “intention” are overlooked.
We point out that a certain complex compact manifold constructed by Lieberman has the dimensional order property, and has U-rank different from Morley rank. We also give a sufficient condition for a Kahler manifold to be totally degenerate (that is, to be an indiscernible set, in its canonical language) and point out that there are K3 surfaces which satisfy these conditions.
This sense of attributability, or internality, is the quarry in many of Frankfurt's articles, and it has proved to be an elusive one. In this paper I want to explore, in a tentative fashion, the question of why we should be interested in finding this quarry. It seems to me that there are at least two quite distinct kinds of reason for this concern, and that when they are distinguished the problem may look less difficult than it has seemed.
We recall the notions of weak and strong Euler characteristics on a first order structure and make explicit the notion of a Grothendieck ring of a structure. We define partially ordered Euler characteristic and Grothendieck ring and give a characterization of structures that have non-trivial partially ordered Grothendieck ring. We give a generalization of counting functions to locally finite structures, and use the construction to show that the Grothendieck ring of the complex numbers contains as a subring the ring of (...) integer polynomials in continuum many variables. We prove the existence of a universal strong Euler characteristic on a structure. We investigate the dependence of the Grothendieck ring on the theory of the structure and give a few counter-examples. Finally, we relate some open problems and independence results in bounded arithmetic to properties of particular Grothendieck rings. (shrink)
The notion of a D-ring, generalizing that of a differential or a difference ring, is introduced. Quantifier elimination and a version of the Ax-Kochen-Eršov principle is proven for a theory of valued D-fields of residual characteristic zero.
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