The Sacks Density Theorem  states that the Turing degrees of the recursively enumerable sets are dense. We show that the Density Theorem holds in every model of P - + BΣ 2 . The proof has two components: a lemma that in any model of P - + BΣ 2 , if B is recursively enumerable and incomplete then IΣ 1 holds relative to B and an adaptation of Shore's  blocking technique in α-recursion theory to models of (...) arithmetic. (shrink)
Although Professor of Philosophy at Calvin College, Alvin Plantinga has developed a theodicy that is fundamentally Arminian rather than Calvinistic. Anthony Flew, although the son of an Arminian Christian minister, regards the Arminian view of ‘free will’ to be both unacceptable on its own terms and incompatible with classical Christian theism. In this paper I hope to disentangle some of the involved controversy regarding theodicy which has developed between Plantinga and Flew, and between Flew and myself. The major portion of (...) this paper is devoted to showing that Plantinga's theodicy contains some serious flaws and undesirable implications. (shrink)
In , Metakides and Nerode introduced the study of recursively enumerable substructures of a recursively presented structure. The main line of study presented in  is to examine the effective content of certain algebraic structures. In , Metakides and Nerode studied the lattice of r.e. subspaces of a recursively presented vector space. This lattice was later studied by Kalantari, Remmel, Retzlaff and Shore. Similar studies have been done by Metakides and Nerode  for algebraically closed fields, by Remmel  (...) for Boolean algebras and by Metakides and Remmel  and  for orderings. Kalantari and Retzlaff  introduced and studied the lattice of r.e. subsets of a recursively presented topological space. Kalantari and Retzlaff consideredX, a topological space with ⊿, a countable basis. This basis is coded into integers and with the help of this coding, r.e. subsets ofωgive rise to r.e. subsets ofX. The notion of “recursiveness” of a topological space is the natural next step which gives rise to the question of what should be the “degree” of an r.e. open subset ofX? It turns out that any r.e. open set partitions ⊿; into four sets whose Turing degrees become central in answering the question raised above.In this paper we show that the degrees of the elements of the partition of ⊿ imposed by an r.e. open set can be “controlled independently” in a sense to be made precise in the body of the paper. In , Kalantari and Retzlaff showed that givenAany r.e. set andany r.e. open subset ofX, there exists an r.e. open set ℋ which is a subset ofand is dense in and in whichAis coded. This shows that modulo a nowhere dense set, an r.e. open set can become as complicated as desired. After giving the general technical and notational machinery in §1, and giving the particulars of our needs in §2, in §3 we prove that the set ℋ described above could be made to be precisely of degree ofA. We then go on and establish various results on the mentioned partitioning of ⊿. One of the surprising results is that there are r.e. open sets such that every element of partitioning of ⊿ is of a different degree. Since the exact wording of the results uses the technical definitions of these partitioning elements, we do not summarize the results here and ask the reader to examine §3 after browsing through §§1 and 2. (shrink)
In , Metakides and Nerode introduced the study of the lattice of recursively enumerable substructures of a recursively presented model as a means to understand the recursive content of certain algebraic constructions. For example, the lattice of recursively enumerable subspaces,, of a recursively presented vector spaceV∞has been studied by Kalantari, Metakides and Nerode, Retzlaff, Remmel and Shore. Similar studies have been done by Remmel ,  for Boolean algebras and by Metakides and Nerode  for algebraically closed fields. In (...) all of these models, the algebraic closure of a set is nontrivial., is given in §1, however in vector spaces, cl is just the subspace generated byS, in Boolean algebras, cl is just the subalgebra generated byS, and in algebraically closed fields, cl is just the algebraically closed subfield generated byS.)In this paper, we give a general model theoretic setting in which we are able to give constructions which generalize many of the constructions of classical recursion theory. One of the main features of the modelswhich we study is that the algebraic closure of setis just itself, i.e., cl = S. Examples of such models include the natural numbers under equality 〈N, = 〉, the rational numbers under the usual ordering 〈Q, ≤〉, and a large class ofn-dimensional partial orderings. (shrink)
What are physical quantities, and in particular, what makes them quantitative? This book presents an original answer to this question through the novel position of substantival structuralism, arguing that quantitativeness is an irreducible feature of attributes, and quantitative attributes are best understood as substantival structured spaces.
This essay explores some of the central aspects of Aquinas's account of mental representation, focusing in particular on his views about the intentionality of concepts (or intelligible species). It begins by demonstrating the need for a new interpretation of his account, showing in particular that the standard interpretations all face insurmountable textual difficulties. It then develops the needed alternative and explains how it avoids the sorts of problems plaguing the standard interpretations. Finally, it draws out the implications of this interpretation (...) with the aim of correcting some persistent misunderstandings of the connection between Aquinas's views and those developed by contemporary philosophers of mind. (shrink)
Written over the last 18 months of his life and inspired by his interest in G. E. Moore's defence of common sense, this much discussed volume collects Wittgenstein's reflections on knowledge and certainty, on what it is to know a proposition for sure.
J. E. Malpas discusses and develops the ideas of Donald Davidson, influential in contemporary thinking on the nature of understanding and meaning, and of truth and knowledge. He provides an account of Davidson's holistic and hermeneutical conception of linguistic interpretation, and, more generally, of the mind. Outlining its Quinean origins and the elements basic to Davidson's Radical Interpretation, J. E. Malpas' book goes on to elaborate this holism and to examine the indeterminacy of interpretation and the principle of charity. The (...) metaphysical and epistemological consequences of Davidson's approach are considered, particularly in relation to scepticism and relativism, the realist/anti-realist debate, and the problem of truth. Parallels are drawn between the Davidsonian emphasis on the centrality of the notion of truth and Heidegger's notion of truth as aletheia, as the book looks to structuralist, hermeneutical and phenomenological sources to illuminate Davidson's position. (shrink)
While it is generally accepted that we need to use our intelligence in order to get what we want, it is thought to be a cardinal error to imagine that by reasoning we can discover what we ought to want. Reason can in no way constrain the choice of ends, it can only constrain the choice of means once an end has been adopted. In Plato's philosophy we find a view strongly opposed to this attitude towards reason. It is widely (...) held, however, that to arrive at a position which is plainly opposed to common sense, Plato must have grossly confused reasoning about means with reasoning about ends. Evidence of this confusion is found in Plato's use of analogies between statecraft and navigation, and between virtue and skill. But the diagnosis of confusion rests on a misunderstanding of how Plato wanted to use the word translated ‘skill’, i.e. ‘ technē ’, and this misunderstanding is shared even by those who see Plato as rejecting the virtue/skill analogy. (shrink)
Bernard Williams is one of the most influential figures in ethical theory, where he has set a considerable part of the current agenda. In this collection a distinguished international team of philosophers who have been stimulated by Williams's work give responses to it. The topics covered include equality; consistency; comparisons between science and ethics; integrity; moral reasons; the moral system; and moral knowledge. Williams himself provides a substantial reply, which shows both the directions of his own thought and also his (...) present view of earlier work of his which has been extensively discussed for twenty years. This volume will be indispensable reading for all those interested in ethical theory. (shrink)
Traditionally Hume is seen as offering an ‘empiricist’ critique of ‘rationalism’. This view is often illustrated – or rejected – by comparing Hume's views with those of Descartes'. However the textual evidence shows that Hume's most sustained engagement with a canonical ‘rationalist’ is with Nicolas Malebranche. The author shows that the fundamental differences between the two on the self and causal power do indeed rest on a principled distinction between ‘rationalism’ and ‘empiricism’, and that there is some truth in the (...) traditional story. This, however, is very far from saying that Hume's general orientation is an attack on something called ‘rationalism’. (shrink)
It may seem strange, in view of the spate of recent literature on the subject, that yet another article should be forthcoming on what is certainly the most familiar, as well as the most vexed, of all Platonic passages. But it is precisely this spate of literature that has impelled me to write. The time seems to have come for an article which, rather than seeking desperately for something new, sets out instead to reaffirm those facts and conclusions that even (...) the most resolutely original of scholars could hardly venture to dispute. This article will therefore be based, not on any of the numerous modern interpretations, but on what Plato himself actually wrote. It will contain a number of tentative suggestions which, to the best of my knowledge, have not been made before. They can, and probably will, be rejected. But its primary purpose remains to restate, whenever possible in Plato's own words, a number of important facts that are at once so simple and so obvious that they seem repeatedly, and especially in recent years, to have been quite forgotten. (shrink)
Potential ethical issues can arise during the process of epidemiological classification. For example, unnatural infant deaths are classified as accidental deaths or homicides. Societal sensitivity to the physical abuse and neglect of children has increased over recent decades. This enhanced sensitivity could impact reported infant homicide rates. Infant homicide and accident mortality rates in boys and girls in the USA from 1940 to 2005 were analysed. In 1940, infant accident mortality rates were over 20 times greater than infant homicide rates (...) in both boys and girls. After about 1980, when the ratio of infant accident mortality rates to infant homicide rates decreased to less than five, and the sum of infant accident and homicide rates became relatively constant, further decreases in infant accident mortality rates were associated with increases in reported infant homicide rates. These findings suggest that the dramatic decline of accidental infant mortality and recent increased societal sensitivity to child abuse may be related to the increased infant homicide rates observed in the USA since 1980 rather than an actual increase in societal violence directed against infants. Ethical consequences of epidemiological classification, involving the principles of beneficence, non-maleficence and justice, are suggested by observed patterns in infant accidental deaths and homicides in the USA from 1940 to 2005. (shrink)
Recent literature on causation invokes a distinction between deviant and default behavior to account for token causation. Critical examination of two prominent attempts to employ a distinction between deviants and defaults reveals that the distinction is far from clear. I clarify and develop the distinction by appeal to the notion of a modally robust process, and show how the distinction can be employed by causal process theorists to respond to cases of causation by omission. This shows that the default/deviant distinction (...) is not so much a tool for counterfactual accounts of causation, but rather for causal process theory. (shrink)
A first-of-its-kind book that seriously and profoundly examines what it means philosophically to be Latino and where Latinos fit in American society. Offers a fresh perspective and clearer understanding of Latin American thought and culture, rejecting answers based on stereotypes and fear Takes an interdisciplinary approach to the philosophical, social, and political elements of Hispanic/Latino identity, touching upon anthropology, history, cultural studies and sociology, as well as philosophy Written by Jorge J. E. Gracia, one of the most influential thinkers of (...) Hispanic/Latino descent. (shrink)