The lambda calculus is a universal programming language. It can represent the computable functions, and such offers a formal counterpart to the point of view of functions as rules. Terms represent functions and this allows for the application of a term/function to any other term/function, including itself. The calculus can be seen as a formal theory with certain pre-established axioms and inference rules, which can be interpreted by models. Dana Scott proposed the first non-trivial model of the extensional lambda calculus, (...) known as $ D_{\infty }$, to represent the $\lambda $-terms as the typical functions of set theory, where it is not allowed to apply a function to itself. Here we propose a construction of an $\infty $-groupoid from any lambda model endowed with a topology. We apply this construction for the particular case $D_{\infty }$, and we see that the Scott topology does not provide enough information about the relationship between higher homotopies. This motivates a new line of research focused on the exploration of $\lambda $-models with the structure of a non-trivial $\infty $-groupoid to generalize the proofs of term conversion to higher-proofs in $\lambda $-calculus. (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)

"It is the purpose of this article to attempt to re-examine the account of Thrasymachus' doctrine in Plato's Republic, and to show how it can form a self-consistent whole. [...] In this paper it is maintained that Thrasymachus is holding a form of [natural right]." Note: Volume 40 = new series 9.

F.A.Hayek is generally considered to be a representative of what, in regard to the methodology of the human sciences, is commonly referred to as ?methodological individualism?; (MI). This paper is an attempt to determine the exact nature and significance of Hayek's own particular brand of ?individualism.?; In particular, it attempts to show that Hayek's MI is grossly misinterpreted when it is viewed as being merely another instance of the atomistic or analytic individualism characteristic of much modern thinking. The ?true?; individualism (...) that Hayek argues for is in fact one which highlights the irremediably social nature of human being that recent hermeneutical and postmodern writers have stressed. (shrink)

It seems worth while giving some account of this MS., because in recent years it has been said to contain certain pieces of the Moralia which it does not, and not to contain others which it does. At the foot of the first page of the text the MS. carries the pontifical shield with the arms of the Medici, and from this it is reasonable to suppose that there was a time when it belonged either to Leo X., who was (...) Pope from 1513 to 1521, or to Clement VII., who was Pope from 1523 to 1534. This being so, 1534 is established as the terminus ante quem of its writing. Towards the end of this century, about 1598, it was acquired by the Spanish Cardinal Saverio de Zelada. In 1801 the Cardinal Archbishop Antonio de Lorenzana bought in Rome a certain number of Greek and Oriental manuscripts which had formerly been in the collection of Cardinal Saverio de Zelada, and placed them in the Chapter Library at Toledo. Included with these was this MS. of the Moralia, which remains there to this day. (shrink)

All-encompassing text examines every aspect of coma from neurochemistry, monitoring, and treatments to prognostic factors.

In these two volumes, David P. Levine undertakes the systematic clarification and further development of the theoretical contributions of classical political economy. It focuses on such central issues in economic theory as: * need, value and exchange * capital and its production * the concept of labour * growth * the firm * price determination. Throughout the treatment is at a high level of abstraction.