While computer algebra systems have dealt with polynomials and rational functions with integer coefficients for many years, dealing with more general constructs from commutative algebra is a more recent problem. In this paper we explain how one system solves this problem, what types and operators it is necessary to introduce and, in short, how one can construct a computational theory of commuta...

Wittgenstein characterises ‘necessary truths’ as rules of representation that do not answer to reality. The invocation has led many compare his work with Kant's. This comparison is illuminating, but it can also be misleading. Some go far casting Wittgenstein's later philosophy a specie transcendental idealism, an interpretation continues gather support despite scholars pointing its limitations....

the subject matter of this article is not to determine the priority of reason to heart or privacy of rationality to love, but find out the answers to these questions: what is role of reason and rational knowledge in attaining mystical intuitive visions? how far does the horizon of rational knowledge extend from perspective of ibn arabi? given the fact that mysticism is arena for esoteric vision...

Prof. Dr. Ekmeleddin İhsanoğlu’s new book released in November 2019 and titled Medreseler Neydi, Ne Değildi? Osmanlılarda Akli İlimlerin Eğitimi ve Modern Bilimin Girişi [What were Madrasas, What They not? Instruction of Rational Disciplines Introduction Science to the Ottomans] is a collection essays published last decades. In book’s prefice İhsanoğlu stresses newly emerged research interest m...

product innovation success has very much to do with the development of models ormetaphors that are able to guide actors. one can observe two traditions in thisregard: rational and non-rational models. apparently in the former the model, suchas “development funnel”, is regarded as a mechanism and rigid applicable, picturinginnovation as an orderly, goal-oriented, value-neutral, and systematic pr...

A Cartesian skeptic must not accept anything but what is ideally clear and distinct in her mind. She has only few beliefs, but all her beliefs have maximal certainty. Some philosophers recommend that a responsible believer should believe only what is beyond any doubt, namely logical and analytical truths. The common core of such proposals is that maximal certainty is held to be necessary and su...