We give a direct mathematical proof of the Mathias-Silver theorem that every analytic set is Ramsey.

If T is an isol let D(T) be the least set of isols which contains T and is closed under predecessors and the application of almost recursive combinatorial functions. We find an infinite regressive isol T such that the universal theory (with respect to recursive relations and almost recursive combinatorial functions) of D(T) is the same as that of the nonnegative integers.

We find necessary and sufficient conditions for compatibility of the Myhill and the Nerode extensions of a combinatorial function to the isols.

There is a fairly simple algebraic property that distinguishes isols from cosimple isols.

We examine the action of unary $\Delta^0_2$ functions on the regressive isols. A manageable theory is produced and we find that such a function maps $\Lambda_R$ into $\Lambda$ if and only if it is eventually $R\uparrow$ increasing and maps $\Lambda_R$ into $\Lambda_R$ if and only if it is eventually recursive increasing. Our paper concludes with a discussion of other methods for extending functions to $\Lambda_R$.

We examine the action of unary Δ 0 2 functions on the regressive isols. A manageable theory is produced and we find that such a function maps Λ R into Λ if and only if it is eventually $R\uparrow$ increasing and maps Λ R into Λ R if and only if it is eventually recursive increasing. Our paper concludes with a discussion of other methods for extending functions to Λ R.

We construct a recursive ultrapower F/U such that F/U is a tame 1-model in the sense of [6, §3] and FU is existentially incomplete in the models of II2 arithmetic. This enables us to answer in the negative a question about closure with respect to recursive fibers of certain special semirings Γ of isols termed tame models by Barback. Erik Ellentuck had conjuctured that all such semirings enjoy the closure property in question. Our result is that while many (...) do, some do not. (shrink)

An energy condition, in the context of a wide class of spacetime theories, is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be positive". The remarkable fact I will discuss in this paper is that such simple, general, almost trivial seeming propositions have profound and far-reaching import for our understanding of the structure of relativistic spacetimes. It is therefore especially surprising when one also learns that (...) we have no clear understanding of the nature of these conditions, what theoretical status they have with respect to fundamental physics, what epistemic status they may have, when we should and should not expect them to be satisfied, and even in many cases how they and their consequences should be interpreted physically. Or so I shall argue, by a detailed analysis of the technical and conceptual character of all the standard conditions used in physics today, including examination of their consequences and the circumstances in which they are believed to be violated. (shrink)

We argue that two well-known examples (strawberry distribution and Konigsberg bridges) generally considered genuine cases of distinctively _mathematical_ explanation can also be understood as cases of distinctively _generic_ explanation. The latter answer resemblance questions (e.g., why did neither person A nor B manage to cross all bridges) by appealing to ‘generic task laws’ instead of mathematical necessity (as is done in distinctively mathematical explanations). We submit that distinctively generic explanations derive their explanatory force from their role in ontological unification. Additionally, (...) we argue that distinctively generic explanations are better seen as standardly mathematical instead of distinctively mathematical. Finally, we compare and contrast our proposal with the work of Christopher Pincock on abstract explanations in science and the views of Michael Strevens on abstract causal event explanations. (shrink)

Many believe that objective morality requires a theistic foundation. I maintain that there are sui generis objective ethical facts that do not reduce to natural or supernatural facts. On my view, objective morality does not require an external foundation of any kind. After explaining my view, I defend it against a variety of objections posed by William Wainwright, William Lane Craig, and J. P. Moreland.

Science policy mandates across the industrialized world insinuate more active roles for publics, their earlier participation in policy decisions, and expanded notions of science and technology governance. In response to these policies, engaged scholars in science studies have sought to design and conduct exercises aimed at better attuning science to its public contexts. As demand increases for innovative and potentially democratic forms of public engagement with science and technology, so also do the prospects for insights from science studies to contribute (...) to policy agendas and institutional capabilities. This collection brings together an international set of scholars in science, technology and society who inquire into the meaning, efficacy and responsibility of engaged science studies scholarship as a public matter. (shrink)

The standard way of representing an epistemic state in formal philosophy is in terms of a set of sentences, corresponding to the agent’s beliefs, and an ordering of those sentences, reflecting how well entrenched they are in the agent’s epistemic state. We argue that this wide-spread representational view – a view that we identify as a “Quinean dogma” – is incapable of making certain crucial distinctions. We propose, as a remedy, that any adequate representation of epistemic states must also include (...) the agent’s research agenda, i.e., the list of question that are open or closed at any given point in time. If the argument of the paper is sound, a person’s questions and practical interests, on the one hand, and her beliefs and theoretical values, on the other, are more tightly interwoven than has previously been assumed to be the case in formal epistemology. (shrink)

We have argued that the counterfactual comparative account of harm and benefit (CCA) violates the plausible adequacy condition that an act that would harm an agent cannot leave her much better off than an alternative act that would benefit her. In a recent paper in this journal, however, Neil Feit objects that our argument presupposes questionable counterfactual backtracking. He also argues that CCA proponents can justifiably reject the condition by invoking so-called plural harm and benefit. In this reply, we argue (...) that Feit’s lines of criticism are both unsuccessful. (shrink)

Analyzing how Plotinus’ critical reception of the Aristotelian, Stoic and Middle-Platonist notions of 'that which depends on us' lead him to a highly original interpretation of the notion, this book shows the central role of this notion in the Plotinian account of human agency.

In this paper, we put forward two novel arguments against the counterfactual comparative account (CCA) of harm and benefit. In both arguments, the central theme is that CCA conflicts with plausible judgements about benefit and prudence.