In modern academic career systems there are a large number of entry positions, much smaller numbers of intermediate positions, and still fewer full professorships. We examine how this system has developed in Germany, the country where the modern academic system was introduced, tracing the historical development of academic positions since the early 19th century. We show both a differentiation and professionalization. At first, professorships and private lecturer positions were the only formal positions, but later, lower formal academic positions emerged. Over (...) the whole period, the share of higher academic positions steadily decreased. This differentiation process was closely connected to professionalization: remuneration through salaries was extended from professors to almost everyone working in the German academic system. We propose that the process of differentiation and professionalization was induced by the expansion and democratization of higher education. Finally, our study shows that the opportunities for PhDs to obtain salaried doctoral positions have increased since the 1950s. On the other hand, opportunities for PhDs to become a professor or obtain another tenured job have decreased since the 1980s due to a slowdown of higher education expansion. (shrink)

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)

Kant asserts that we cannot represent to ourselves the non-existence of space. In his discussion of the Ontological Argument he maintains that there is nothing whose non-existence is inconceivable. He thus seems to contradict himself. If the non-existence of space is unthinkable, so is the non-existence of a part of space — a place. Indicating a particular place, we might say "There are no objects there", but it would be nonsense to say "There doesn't exist". We can say, as Aristotle (...) saw, "There is a place where there was water and where there is now air"; but to do so is to bind an adverbial variable with a quantifier, not to attach "exists" to the name of a place. To assert of a place, or of space, that it exists or that it does not exist would be nonsense, and the unthinkable in that sense is not something whose negation is, as Kant thought, a necessary truth. (shrink)

PAPERS IN LOGIC AND ETHICS by A. N. Prior. Duckworth, 1976. 233 pp. £8.95.THE DOCTRINE OF PROPOSITIONS AND TERMS by A. N. Prior. Duckworth, 1976. 143 pp. £5.95.

The paper looks at how Tsong kha pa, mKhas grub, and Go rams pa understood the third and fourth lemmas in the tetralemma, “both A and B” and “neither A nor B,” respectively.

In the modal literature various notions of "completeness" have been studied for normal modal logics. Four of these are defined here, viz. completeness, first-order completeness, canonicity and possession of the finite model property -- and their connections are studied. Up to one important exception, all possible inclusion relations are either proved or disproved. Hopefully, this helps to establish some order in the jungle of concepts concerning modal logics. In the course of the exposition, the interesting properties of first-order definability and (...) preservation under ultrafilter extensions are introduced and studied as well. (shrink)

The Hanf number for a set S of sentences in \ is the least infinite cardinal \ such that for all \, if \ has models in all infinite cardinalities less than \, then it has models of all infinite cardinalities. Friedman asked what is the Hanf number for Scott sentences of computable structures. We show that the value is \. The same argument proves that \ is the Hanf number for Scott sentences of hyperarithmetical structures.

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)

The existence of various physical phenomena stems from the concept called asymptotic emergence, that is, they seem to be exclusively reserved for certain limiting theories. Important examples are spontaneous symmetry breaking (SSB) and phase transitions: these would only occur in the classical or thermodynamic limit of underlying finite quantum systems, since for finite quantum systems, due to the uniqueness of the relevant states, such phenomena are excluded by Theory. In Nature, however, finite quantum systems describing real materials clearly exhibit such (...) effects. In this paper we discuss these apparently “paradoxical” phenomena and outline various ideas and mechanisms that encompass both theory and reality, from physical and mathematical points of view. (shrink)