Subcreative sets, introduced by Blum, are known to coincide with the effectively speedable sets. Subcreative sets are shown to be the complete sets with respect to S-reducibility, a special case of Turing reducibility. Thus a set is effectively speedable exactly when it contains the solution to the halting problem in an easily decodable form. Several characterizations of subcreative sets are given, including the solution of an open problem of Blum, and are used to locate the subcreative sets with respect to (...) the complete sets of other reducibilities. It is shown that q-cylindrification is an order-preserving map from the r.e. T-degrees to the r.e. S-degrees. Consequently, T-complete sets are precisely the r.e. sets whose q-cylindrifications are S-complete. (shrink)

Despite much research on the relationship between awareness and dementia little can be concluded concerning their relationship and the role of other factors. It is likely that studies capture different phenomena of awareness. This study aimed at identifying and delineating such variation by analysing data from three questionnaires obtained during the longitudinal study of awareness in 101 people with early-stage dementia. The data concerned awareness in relation to memory, activities of daily living and socio-emotional function. Significant differences in patterns of (...) discrepancies were obtained. This suggests that the awareness phenomena involved were structurally different; and that, in turn, this may reflect variation in the intrinsic linking between awareness and its ‘object’ . The identification of such differences is necessary so that appropriate methodologies can be applied to the study of awareness in different contexts. (shrink)

The theory of the conservation of energy and the Second Law of Thermodynamics have been described as the two most firmly established “findings” of modern science. Scientists frequently refer to them, not as theories or assumptions, but as facts. During the last two decades of the nineteenth century, however, Edmund Montgomery—an unsung Texas philosopher—repeatedly challenged, not only the notions that energy is convertible and is indestructible, but the very idea that there is such a thing as energy which can be (...) imposed ab extra upon matter. For his trouble he received censure and ridicule on every hand; friends usually apologized for this eccentricity of his. Montgomery, of course, has not been entirely alone in criticizing the theory of the conservation of energy, though he was the first to make a persistent attack on the merits of the theory as a principle of scientific explanation. Busse, for one, contended that if, as he thought likely, the theory were incompatible with psychophysical interactionism, it should be discarded on the grounds that the evidence in its behalf is far from compelling. Emergent evolutionists remind us occasionally that it is still within the province of reason to question this great dogma notwithstanding the fact that it is a god at whose feet many scientists worship with blind and jealous devotion. Of all these critics Montgomery attacked the theory where its greatest weaknesses lie. (shrink)

The mechanism of stellar aberration was explained and formulated by Bradley in terms of the existence of a unique reference frame for light propagation. However, Einstein's denial of the existence of such a frame appears to undermine Bradley's interpretation of the phenomenon. It is suggested that the recent evidence for a cosmologically-based inertial reference frame provides a new physical basis for Bradley's explanation in a manner consistent with the requirements of special relativity. It is shown that a “delay” effect is (...) also involved in our observation of the direction of nearby sources, and that the aberration and delay effects exactly compensate for nearby sources comoving with a terrestrial observer. (shrink)

Subcreative sets, introduced by Blum, are known to coincide with the effectively speedable sets. Subcreative sets are shown to be the complete sets with respect to S-reducibility, a special case of Turing reducibility. Thus a set is effectively speedable exactly when it contains the solution to the halting problem in an easily decodable form. Several characterizations of subcreative sets are given, including the solution of an open problem of Blum, and are used to locate the subcreative sets with respect to (...) the complete sets of other reducibilities. It is shown that q-cylindrification is an order-preserving map from the r.e. T-degrees to the r.e. S-degrees. Consequently, T-complete sets are precisely the r.e. sets whose q-cylindrifications are S-complete. (shrink)

Platon n’est pas sérieux lorsqu’il conduit Socrate à déduire que la poésie doit être essentiellement narrative avec juste un peu de dialogue. Non seulement cette argumentation est-elle intentionnellement fautive, mais Platon crée aussi un Socrate qui obscurcit à dessein une distinction fondamentale. Le Socrate de Platon fait ensuite semblant d’être confus par son propre obscurcissement. En nous obligeant à nous frayer un passage à travers les broussailles de son argumentation erronée, Platon nous donne l’occasion d’avoir une participation plus profonde aux (...) véritables problèmes sous-jacents et de découvrir son thème : une bonne personne est stoïquement indifférente à la fois au malheur et au bonheur. (shrink)

ABSTRACT: Careful analysis of the details of the text allows us to refine Socrates objections to his definition of manliness as prudent perseverance. He does not appreciate that Socrates objections merely require that he make his definition more precise. Nicias refuses to consider objections to his understanding of manliness as avoiding actions that entail risk. The two sets of objections show that manliness entails first calculating that a risk is worth taking and then subsequently not rejecting that calculation without due (...) consideration. (shrink)

Current interpretations of Plato’s cave are obviously incorrect because they do not explain how what we hear does not come from what we see. I argue that Plato is saying that the colors we receive from our faculty of vision do not cause the sounds that we receive from our faculty of hearing. I also show how we do not see ourselves or one other, how the shadows on the wall of the cave are images of that which casts them (...) and therefore have less reality than them, and how the cave illustrates the divided line’s concern for the relationship between Forms and visible reality. The paper is structured around the two great riddles of the divided line: how Forms can be more real than everyday objects, and how one can know the unhypothesized beginning with complete certainty. I further argue that the puppets that cast shadows stand for the immanent Forms of the Phaedo and also for the moving Forms of the Timaeus. That of which these puppets are themselves images would thus stand for the Forms as they are in themselves of the Phaedo or the indestructible Forms of the Timaeus. ‘Plato used to ask whether the discussion was proceeding from or leading up to fundamental principles, just as in a race course there is a difference between running from the judges to the far end of the track and running back again.’ – Aristotle, Nicomachean Ethics 1095. (shrink)

Current interpretations of Plato’s cave are obviously incorrect because they do not explain how what we hear does not come from what we see. I argue that Plato is saying that the colors we receive from our faculty of vision do not cause the sounds that we receive from our faculty of hearing. I also show how we do not see ourselves or one other, how the shadows on the wall of the cave are images of that which casts them (...) and therefore have less reality than them, and how the cave illustrates the divided line’s concern for the relationship between Forms and visible reality. The paper is structured around the two great riddles of the divided line: how Forms can be more real than everyday objects, and how one can know the unhypothesized beginning with complete certainty. I further argue that the puppets that cast shadows stand for the immanent Forms of the Phaedo and also for the moving Forms of the Timaeus. That of which these puppets are themselves images would thus stand for the Forms as they are in themselves of the Phaedo or the indestructible Forms of the Timaeus. ‘Plato used to ask whether the discussion was proceeding from or leading up to fundamental principles, just as in a race course there is a difference between running from the judges to the far end of the track and running back again.’ – Aristotle, Nicomachean Ethics 1095. (shrink)

It is shown that Plato’s Lysis is full of positive content between the lines. At the close of the dialogue Socrates says that he considers Lysis, Menexenus, and himself to be friends of one another. Following up on the questions which the dialogue leads us to ask yields an explanation ofwhy each of these instances of friendship is, in fact, an instance of friendship. In addition, the dialogue shows that there are five types of motivation for desiring something.

It is shown that Plato’s Lysis is full of positive content between the lines. At the close of the dialogue Socrates says that he considers Lysis, Menexenus, and himself to be friends of one another. Following up on the questions which the dialogue leads us to ask yields an explanation ofwhy each of these instances of friendship is, in fact, an instance of friendship. In addition, the dialogue shows that there are five types of motivation for desiring something.

Socrates contradicts himself when he claims that a good doctor must have the experience of having an unsound body and when he claims that a good judge must have a sound soul, for the unsound of body will not be treated and how a judge decides the case of a good person is a matter of indifference. These pages are really about the meaning of simplicity of soul, and arguing against Glaucon's claim, 'to be moved by self-advantage is the end (...) which it is natural to pursue as good, until forcibly turned aside by law and custom to respect equality'. (shrink)

Even though the first book of the Republic ends with the claim that the definition of justice has not been determined, a careful analysis of the details of Socrates’ arguments with Polemarchus and Thrasymachus yields a definition of justice. Polemarchus should have defended the understanding of justice as helping friends and harming enemies by saying that, because one can use one’s knowledge either to help or to harm, a just person will choose to use his knowledge of an art either (...) to help his friends or to harm his enemies. Socrates’ art of wage-earning is not really an art at all, but merely amounts to having an ulterior motive for doing what one does. Socrates’ true position will be seen to be that just people use their knowledge for the sake of helping people—not for the sake of acquiring some supposed benefit for themselves in the future. (shrink)

This article shows that Plato is discussing Pauline predication and Pauline self-predication in the Phaedo. The key is the recognition that the “something else” of Phaedo 103e2-5 cannot be a sensible object because any such object which participates in Form ‘X’ can sometimes appear not to be x. It is argued that Plato has not written in a straightforward manner, but rather has written a series of riddles for the reader to solve. Thus this dialogue is an example of the (...) playful use of the written word discussed at Phaedrus 275ff. (shrink)

This article shows that Plato is discussing Pauline predication and Pauline self-predication in the Phaedo. The key is the recognition that the “something else” of Phaedo 103e2-5 cannot be a sensible object because any such object which participates in Form ‘X’ can sometimes appear not to be x. It is argued that Plato has not written in a straightforward manner, but rather has written a series of riddles for the reader to solve. Thus this dialogue is an example of the (...) playful use of the written word discussed at Phaedrus 275ff. (shrink)