This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, (...) the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties). (shrink)

In this paper, I defend teleological theories of belief against the exclusivity objection. I argue that despite the exclusive influence of truth in doxastic deliberation, multiple epistemic aims interact when we consider what to believe. This is apparent when we focus on the processes involved in specific instances (or concrete cases) of doxastic deliberation, such that the propositions under consideration are specified. First, I out- line a general schema for weighing aims. Second, I discuss recent attempts to defend the teleological (...) position in relation to this schema. And third, I develop and defend my proposal that multiple epistemic aims interact in doxastic deliberation—a possibility which, as of yet, has received no serious attention in the literature. (shrink)

BackgroundResuscitation and treatment of critically ill newborn infants is associated with relatively high mortality, morbidity and cost. Guidelines relating to resuscitation have traditionally focused on the best interests of infants. There are, however, limited resources available in the neonatal intensive care unit, meaning that difficult decisions sometimes need to be made. This study explores the intuitions of lay people regarding resource allocation decisions in the NICU.MethodsThe study design was a cross-sectional quantitative survey, consisting of 20 hypothetical rationing scenarios. There were (...) 119 respondents who entered the questionnaire, and 109 who completed it. The respondents were adult US and Indian participants of the online crowdsourcing platform Mechanical Turk. Respondents were asked to decide which of two infants to treat in a situation of scarce resources. Demographic characteristics, personality traits and political views were recorded. Respondents were also asked to respond to a widely cited thought experiment involving rationing.ResultsThe majority of respondents, in all except one scenario, chose the utilitarian option of directing treatment to the infant with the higher chance of survival, higher life expectancy, less severe disability, and less expensive treatment. As discrepancy between outcomes decreased, however, there was a statistically significant increase in egalitarian responses and decrease in utilitarian responses in scenarios involving chance of survival, life expectancy, and cost of treatment. In the classic ‘lifeboat’ scenario, all but two respondents were utilitarian.ConclusionsThis survey suggests that in situations of scarcity and equal clinical need, non-health professionals support rationing of life-saving treatment based on probability of survival, duration of survival, cost of treatment or quality of life. However, where the difference in prognosis or cost is very small, non-health professionals preferred to give infants an equal chance of receiving treatment. (shrink)

In this paper, I discuss whether different interpretations of the ‘aim’ of belief—both the teleological and normative interpretations—have the resources to explain certain descriptive and normative features of suspended belief (suspension). I argue that, despite the recent efforts of theorists to extend these theories to account for suspension, they ultimately fail. The implication is that we must either develop alternative theories of belief that can account for suspension, or we must abandon the assumption that these theories ought to be able (...) to account for suspension. To close, I briefly consider some of the reasons we have in favour of pursing each of these options, and I suggest that it is worth exploring the possibility that suspension is best understood as its own attitude, independently of theories of belief’s ‘aim’. (shrink)

Kengo Miyazono, in his work Delusions and Beliefs, defends a teleo-functional account of delusions. In my contribution to this symposium, I question one of Miyazono’s motivations for appealing to teleo-functionalism over its main rival, dry-functionalism. Miyazono suggests that teleo-functionalism, unlike dry-functionalism, can account for the compatibility of the theses (i) that delusions are genuine doxastic states (doxasticism about delusions) and (ii) that delusions do not perform the typical causal roles of beliefs (the causal difference thesis). I argue, however, that there (...) are also ways for dry-functionalism to account for this compatibility. If what I have to say is correct, then Miyazono is perhaps too hasty—at least in one important respect—to opt for teleo-functionalism over dry-functionalism. Dry-functionalism has an equally good chance of satisfying some of Miyazono’s explanatory goals. (shrink)

We re-express a previous general result in a way which seems easier to remember, using the terminology of infinite games. We show how this can be applied to construct recursive linear orderings, showing, for example, that if there is a ▵ 0 2β + 1 linear ordering of type τ, then there is a recursive ordering of type ω β · τ.

We extend results of Harizanov and Barker. For a relation R on a recursive structure /oA, we give conditions guaranteeing that the image of R in a recursive copy of /oA can be made to have arbitrary ∑α0 degree over Δα0. We give stronger conditions under which the image of R can be made ∑α0 degree as well. The degrees over Δα0 can be replaced by certain more general classes. We also generalize the Friedberg-Muchnik Theorem, giving conditions on a pair (...) of relations R and S under which the images of R and S can be made ∑α0 and independent over Δα0 in a recursive copy of /oA. (shrink)

A subspace V of an infinite dimensional fully effective vector space V ∞ is called decidable if V is r.e. and there exists an r.e. W such that $V \oplus W = V_\infty$ . These subspaces of V ∞ are natural analogues of recursive subsets of ω. The set of r.e. subspaces forms a lattice L(V ∞ ) and the set of decidable subspaces forms a lower semilattice S(V ∞ ). We analyse S(V ∞ ) and its relationship with L(V (...) ∞ ). We show: Proposition. Let U, V, W ∈ L(V ∞ ) where U is infinite dimensional and $U \oplus V = W$ . Then there exists a decidable subspace D such that U |oplus D = W. Corollary. Any r.e. subspace can be expressed as the direct sum of two decidable subspaces. These results allow us to show: Proposition. The first order theory of the lower semilattice of decidable subspaces, Th(S(V ∞ )), is undecidable. This contrasts sharply with the result for recursive sets. Finally we examine various generalizations of our results. In particular we analyse S * (V ∞ ), that is, S(V ∞ ) modulo finite dimensional subspaces. We show S * (V ∞ ) is not a lattice. (shrink)

Let be a recursive structure, and let R be a recursive relation on . Harizanov isolated a syntactical condition which is necessary and sufficient for to have recursive copies in which the image of R is r.e. of arbitrary r.e. degree. We had conjectured that a certain extension of Harizanov's syntactical condition would be necessary and sufficient for to have recursive copies in which the image of R is ∑α0 of arbitrary ∑α0 degree, but this is not the case. Here (...) we give examples illustrating some restrictions on the possible ∑α0 degrees. In these examples, the image of R cannot be ∑α0 of degree d unless d possesses an “α-table”. (shrink)

Gallie contends that historical narrative differs from the generalizing natural sciences and can be understood with peculiar directness. In following a story through contingent events to its conclusion, explicit explanation is needed only rarely. But although history is in some sense a narrative, Gallie fails to see that a story can be followed only if one has a fund of generalizations. Judgment about acceptable contingencies rests on prior appreciation of a framework of generalized expectations that are not falsified by particular (...) incidents. Contingencies are unique only because they are counter to. this framework - which serves to limit outcomes and the possible role of contingent happenings, not for deducing events. History is not entirely like art; we are interested in the connections of events, not only in the outcome of a story. (shrink)

The texts before us are relatively early works. They predate the famous Manifesto of the Communist Party of 1848. Their importance lies in this: that here historical materialism is outlined and defended for the first time. This new philosophy is elaborated in the course of Marx and Engels' effort to settle accounts with previous German philosophy—and, perhaps, with philosophy as such. The new outlook is developed, therefore, in the context of polemic against Hegel and Feuerbach, precisely the thinkers that they (...) most admired earlier in fact. (shrink)

The texts before us are relatively early works. They predate the famous Manifesto of the Communist Party of 1848. Their importance lies in this: that here historical materialism is outlined and defended for the first time. This new philosophy is elaborated in the course of Marx and Engels' effort to settle accounts with previous German philosophy—and, perhaps, with philosophy as such. The new outlook is developed, therefore, in the context of polemic against Hegel and Feuerbach, precisely the thinkers that they (...) most admired earlier in fact. (shrink)