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Philosophical texts always have a form as well as content. This seemingly self-evident fact is often overlooked by interpreters. Philosophy is frequently discussed as if it were solely concerned with formulating clear arguments and consistent concepts. The consequence of this fixation on content is that form is dismissed as little more than an incidental and insignificant packaging. However, a brief look at the history of philosophy reveals that neglecting form in this way creates a significant blind spot. -/- The choice (...) of a particular form often arises precisely in response to fundamental problems that are difficult to address in purely content-based terms. How can truth be expressed in language? How can others be inspired to lead a philosophical life? For this issue of Wijsgerig Perspectief, we have invited experts from different periods in the history of Western philosophy to reflect on the various ways in which the relationship between form and content in philosophical texts can be understood. -/- [In Dutch: Filosofische teksten hebben, behalve een inhoud, ook altijd een vorm. Dit schijnbaar evidente gegeven wordt lang niet altijd door interpreten in ogenschouw genomen. Vaak wordt er over de filosofie gesproken alsof zij alleen maar zou draaien om het formuleren van heldere argumenten en consistente concepten. Het gevolg van deze fixatie op de inhoud van de tekst is dat de vorm wordt afgedaan als weinig meer dan een toevallige en onbelangrijke verpakking. Een korte blik op de geschiedenis van de filosofie wijst echter uit dat een dergelijke veronachtzaming van vorm een grote blinde vlek creëert. -/- De keuze voor een bepaalde vorm komt vaak juist voort uit een reactie op fundamentele problemen die zich moeilijk aan de orde laten stellen in puur inhoudelijke termen. Hoe kan waarheid in taal worden uitgedrukt? Hoe kunnen andere mensen ertoe worden bewogen een filosofisch leven te leiden? Voor dit nummer van Wijsgerig Perspectief hebben we kenners van verschillende tijdvlakken in de geschiedenis van de Westerse filosofie uitgenodigd om te reflecteren op de verschillende manieren waarop de relatie tussen vorm en inhoud in filosofische teksten begrepen kan worden. (shrink)

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)

Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate (...) the natural notion of bisimulation equivalence in the setting of InqML. We compare the expressiveness of InqML and first-order logic in the context of relational structures with two sorts, one for worlds and one for information states, and characterise inquisitive modal logic as the bisimulation invariant fragment of first-order logic over various natural classes of two-sorted structures. (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)