Recall that B is PA relative to A if B computes a member of every nonempty $\Pi ^0_1(A)$ class. This two-place relation is invariant under Turing equivalence and so can be thought of as a binary relation on Turing degrees. Miller and Soskova [23] introduced the notion of a $\Pi ^0_1$ class relative to an enumeration oracle A, which they called a $\Pi ^0_1{\left \langle {A}\right \rangle }$ class. We study the induced extension of the relation B is PA relative (...) to A to enumeration oracles and hence enumeration degrees. We isolate several classes of enumeration degrees based on their behavior with respect to this relation: the PA bounded degrees, the degrees that have a universal class, the low for PA degrees, and the ${\left \langle {\text {self}\kern1pt}\right \rangle }$ -PA degrees. We study the relationship between these classes and other known classes of enumeration degrees. We also investigate a group of classes of enumeration degrees that were introduced by Kalimullin and Puzarenko [14] based on properties that are commonly studied in descriptive set theory. As part of this investigation, we give characterizations of three of their classes in terms of a special sub-collection of relativized $\Pi ^0_1$ classes—the separating classes. These three can then be seen to be direct analogues of three of our classes. We completely determine the relative position of all classes in question. (shrink)

Working toward showing the decidability of the $\forall \exists $ -theory of the ${\Sigma ^0_2}$ -enumeration degrees, we prove that no so-called Ahmad pair of ${\Sigma ^0_2}$ -enumeration degrees can join to ${\mathbf 0}_e'$.

Collection of works on literature theory, translated into Mongolian language.

This paper discusses the role the question of being plays in the development of Heidegger’s thought. It is shown that the basic question of traditional ontology doesn’t provide a Leitfaden for Heidegger’s philosophical development as a whole. Actually, in his first academic writings, Heidegger sh..

Teachings of Muslim saints to earn bread by honest means.

This is a welcome reprint of a book that continues to grow in importance.

The author presents and defends three theses: (1) "the first is that it is not profitable for us at present to do moral philosophy; that should be laid aside at any rate until we have an adequate philosophy of psychology." (2) "the second is that the concepts of obligation, And duty... And of what is morally right and wrong, And of the moral sense of 'ought', Ought to be jettisoned if this is psychologically possible...." (3) "the third thesis is that (...) the differences between the well-Known english writers on moral philosophy from sidgwick to the present day are of little importance." (staff). (shrink)

This book offers an introduction to the Sophists of fifth-century Athens and a new overall interpretation of their thought. Since Plato first animadverted on their activities, the Sophists have commonly been presented as little better than intellectual mountebanks - a picture which Professor Kerferd forcefully challenges here. Interpreting the evidence with care, he shows them to have been part of an exciting and historically crucial intellectual movement. At the centre of their teaching was a form of relativism, most famously expressed (...) by Protagoras as 'Man is the measure of all things', and which they developed in a wide range of views - on knowledge and argument, virtue, government, society, and the gods. On all these subjects the Sophists did far more than simply provoke Plato to thought. Their contributions were substantial and serious; they inaugurated the debate on many central philosophical questions and decisively shifted the focus of philosophical attention from the cosmos to man. (shrink)

Faults; religious aspects; Islam; Islamic daʻwah.

Muslim women; religious life; Islmic call.