This paper examines al-Fārābī's logical thought within its Arabico-Islamic historical background and attempts to conceptualize what this background contributes to his logic. After a brief exposition of al-Fārābī's main problems and goals, I shall attempt to reformulate the formal structure of Arabic linguistics (AL) in terms of the ontological and formal characteristics that Arabic logic is built upon. Having discussed the competence of al-Fārābī in the history of AL, I will further propose three interrelated theses about al-Fārābī's logic, in terms (...) of which I will attempt to redefine it: the logico-linguistic conception, the project of logicization, and nuclear logic. The final question that will arise is how Aristotle's logic could be built upon AL, which has a nature contrary to logic. The present paper also contributes to examining our traditional research habits in Arabic studies. (shrink)

Paraconsistent logics may be viewed as one of the last elementsin a series of rapid developments in science in the 19th and early 20th c.,triggered by the appearance of non-Euclidean geometries. The philosophyof conventionalism, which gave a metatheoretical framework to the basicchanges involved, may also help in evaluating the truth import of logic and in determining its relation to ontology.

Aristotle's logical and metaphysical works contain elements of three distinct types of formal theory: an ontology, a theory of consequences, and a theory of reasoning. His formal ontology (unlike that of certain later thinkers) does not require all propositions of a given logical form to be true. His formal syllogistic (unlike medieval theories of consequences) was guided primarily by a conception of logic as a theory of reasoning; and his fragmentary theory of consequences exists merely as an adjunct to the (...) syllogistic. When theories of consequences took centre stage in the Middle Ages, the original motivation for the theory of the syllogism was forgotten. (shrink)

The aim of this article is to reconstruct Bocheński’s method of philosophical analysis as well as to clarify the purpose of that method and its basic elements. In the second part of the paper I will compare Bocheński’s method with the methods of modern applied ontology.

RésuméHeinrich Scholz et J.M. Bocheski ont affirmé que les lois de la logique formelle étaient en fait les lois les plus générates qui caractérisent les choses, les propriétés, les relations, les états de choses etc. D'autres confondent la logique et la théorie des ensembles. Mais ľ interpretation des quantificateurs qu'on trouve chez Leśniewski montre que la logique ne fait partie ni de ľ ontologie, ni des mathématiques.

The main aim of this work is to evaluate whether Boolos’ semantics for second-order languages is model-theoretically equivalent to standard model-theoretic semantics. Such an equivalence result is, actually, directly proved in the “Appendix”. I argue that Boolos’ intent in developing such a semantics is not to avoid set-theoretic notions in favor of pluralities. It is, rather, to prevent that predicates, in the sense of functions, refer to classes of classes. Boolos’ formal semantics differs from a semantics of pluralities for Boolos’ (...) plural reading of second-order quantifiers, for the notion of plurality is much more general, not only of that set, but also of class. In fact, by showing that a plurality is equivalent to sub-sets of a power set, the notion of plurality comes to suffer a loss of generality. Despite of this equivalence result, I maintain that Boolos’ formal semantics does not committ second-order languages to second-order entities, contrary to standard semantics. Further, such an equivalence result provides a rationale for many criticisms to Boolos’ formal semantics, in particular those by Resnik and Parsons against its alleged ontological innocence and on its Platonistic presupposition. The key set-theoretic notion involved in the equivalence proof is that of many-valued function. But, first, I will provide a clarification of the philosophical context and theoretical grounds of the genesis of Boolos’ formal semantics. (shrink)

A brief review of the historicalrelation between logic and ontologyand of the opposition between the viewsof logic as language and logic as calculusis given. We argue that predication is morefundamental than membership and that differenttheories of predication are based on differenttheories of universals, the three most importantbeing nominalism, conceptualism, and realism.These theories can be formulated as formalontologies, each with its own logic, andcompared with one another in terms of theirrespective explanatory powers. After a briefsurvey of such a comparison, we argue (...) that anextended form of conceptual realism provides themost coherent formal ontology and, as such, canbe used to defend the view of logic as language. (shrink)