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)

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)

We consider infinitary logic with only two variable symbols, both with and without counting quantifiers, i.e. L2 L∞ω2 and C2 L∞ω2mεω. The main result is that finite relational structures admit canonization with respect to L2 and C2: there are polynomial time com putable functors mapping finite relational structures to unique representatives of their equivalence class with respect to indistinguishability in either of these logics. In fact we exhibit in verses to the natural invariants that characterize structures up to L2- or (...) C2-equivalence, respectively. As a corollary we obtain recursive presentations of the classes of all boolean queries that are closed with respect to L2- or C2-equivalence. (shrink)

A teologia de Karl Rahner teve um grande impacto no concílio Vaticano II e no tempo que se Ihe seguiu. Em ordem a compreender-se o seu argumento teológico é importante tomar em conta as suas bases filosóficas, especialmente a sua compreensão do "método transcendental". Neste sentido, opresente artigo começa por prestar atenção à abordagem transcendental de Kant. Em seguida investiga a transformação do método transcendental operada na obra de Joseph Maréchal, o qual fez uso dele em ordem a demonstrar a (...) orientação dinâmica do conhecimento humano e da sua decisão em favor do "Absoluto do Ser". Deste modo, o autor do artigo demonstra até que ponto Maréchal fornece uma fundação para a metafísica, a qual é bem diferente da metafísica do racionalismo que Kant tinha criticado. Inspirado por Heidegger, Rahner deu a esta abordagem transcendental uma viragem fenomenológica, ao mesmo tempo que forneceu uma reinterpretação de termos-chave da metafísica clássica, a qual encara como não dependente de uma cosmologia ultrapassada e que ao mesmo tempo é de grande relevância existencial para a vida humana. O artigo visa demonstrar, deste modo, até que ponto esta reinterpretação influenciou o pensamento teológico de K. Rahner. /// The theology of Karl Rahner had an enormous impact on Vatican II and the time following. In order to understand his theological reasoning it is important to take into account his philosophical foundations, especially his understanding of the "transcendental method". This article pays attention to the transcendental approach of Kant. Then it investigates the transformation of transcendental method in the work of Joseph Maréchal who used it to show the constitutive function of the dynamic orientation of human knowledge and decision towards the "Absolute of Being". He thereby provides a foundation for metaphysics, which is quite different from the metaphysics of rationalism which Kant had criticised. Inspired by Heidegger, Rahner gave this transcendental approach a phenomenological turn. He provided a reinterpretation of key terms of classical metaphysics, which is not dependent on an outmoded cosmology and which is at the same time of existential relevance for human life. This reinterpretation influenced the theological thinking of K. Rahner. (shrink)

INTRODUCTION Phenomenology and analytic philosophy have skirmished often, but seldom in ways conducive to dialectical progress. ...