The movement for the Unity of Science has been making headway for a number of years, and each year more workers in the various scientific domains have expressed their interest in it by participating in the discussion of its aims and its specific problems. A characteristic feature of this movement which explains this growing interest is that it does not propose a “super-science” which is to legislate to the special sciences. Its proposal of a Unity of Science is of a (...) different kind, not based upon some grand metaphysical view of any sort. Those who are active within this movement are emphatic in their insistence that instead of aiming at a synthesis of the different sciences on the basis of a prior and independent philosophy, the special sciences will themselves supply their own synthesizing glue. For appreciating the significance of this movement it is therefore necessary to keep in mind that its tendency is toward a unified science, departmentalized into special sciences, and not toward an artificial and speculative juxtaposition of an autonomous philosophy and an autonomous group of sciences. (shrink)

How can we prove that some fragment of a given logic has the power to define precisely all structural properties that satisfy some characteristic semantic preservation condition? This issue is a fundamental one for classical model theory and applications in non-classical settings alike. While methods differ greatly, and while the classical methods can usually not be matched for instance in the setting of finite model theory, this note surveys some interesting commonality revolving around the use and availability of tractable representatives (...) in the relevant model classes. The construction of models in which simple invariants like partial types based on some weak fragment control all the relevant structural properties, may be seen at the heart of such questions. We highlight some constructions involving degrees of acyclicity and saturation that can be achieved in finite model constructions, and discuss their uses towards expressive completeness w.r.t. bisimulation based equivalences in hypergraphs and relational structures. The emphasis is on the combinatorial challenges in such more constructive approaches that work in non-classical settings and especially in finite model theory. One new result concerns expressive completeness w.r.t. guarded negation bisimulation, a back-and-forth equivalence involving local homomorphisms. (shrink)

Lyndon's Interpolation Theorem asserts that for any valid implication between two purely relational sentences of first-order logic, there is an interpolant in which each relation symbol appears positively (negatively) only if it appears positively (negatively) in both the antecedent and the succedent of the given implication. We prove a similar, more general interpolation result with the additional requirement that, for some fixed tuple U of unary predicates U, all formulae under consideration have all quantifiers explicitly relativised to one of the (...) U. Under this stipulation, existential (universal) quantification over U contributes a positive (negative) occurrence of U. It is shown how this single new interpolation theorem, obtained by a canonical and rather elementary model theoretic proof, unifies a number of related results: the classical characterisation theorems concerning extensions (substructures) with those concerning monotonicity, as well as a many-sorted interpolation theorem focusing on positive vs. negative occurrences of predicates and on existentially vs. universally quantified sorts. (shrink)

1. History of the philosophy of religion from Spinoza to the present day. 2 v.--2. Genetic-speculative philosophy of religion. 2 v.

Abzj proposed, in a fragment established and translated herein, two methods to build a parabolic mirror. The lack of demonstration, particularly for the first method, raises a difficult question of interpretation. To understand this method, O. Neugebauer used, in an unpublished article translated herein, concepts of descriptive geometry. He then eliminated the space construction used, to keep only simple geometrical considerations known by the Greeks. The second interpretation, given by R. Rashed, is based on the geometrical practices of al-Bnhzj from (...) Ibn Sinān seems to support this last interpretation. (shrink)

There are properties of finite structures that are expressible with the use of Hilbert's ε-operator in a manner that does not depend on the actual interpretation for ε-terms, but not expressible in plain first-order. This observation strengthens a corresponding result of Gurevich, concerning the invariant use of an auxiliary ordering in first-order logic over finite structures. The present result also implies that certain non-deterministic choice constructs, which have been considered in database theory, properly enhance the expressive power of first-order logic (...) even as far as deterministic queries are concerned, thereby answering a question raised by Abiteboul and Vianu. (shrink)

Este trabajo trata de mostrar cómo sobre la base de una filosofía del ingenio, Vico se dispone a delinear una representación figurada fundamentándose sobre una "convertibilidad" de los signos y de sus significados así como de los "conjuntos" de signos y su representación figurativa. La denominada "semiótica" viquiana se transforma a sí misma en una "sematología" de la "representación histórica".This paper intends to show how Vico sets himself to shape a figurative representation on the basis of the philosophy of wit. (...) In doing so, he takes as foundation the "convertibility" of signs and their meanings together with the "sets" of signs and their figurative representation. The so called Vichian "semiotics" is thus shifted into a "sematology" of the historical representation. (shrink)