Many existence propositions in constructive analysis are implied by the lesser limited principle of omniscience LLPO; sometimes one can even show equivalence. It was discovered recently that some existence propositions are equivalent to Bouwer's fan theorem FAN if one additionally assumes that there exists at most one object with the desired property. We are providing a list of conditions being equivalent to FAN, such as a unique version of weak König's lemma. This illuminates the relation between FAN and LLPO. Furthermore, (...) we give a short and elementary proof of the fact that FAN is equivalent to each positive valued function with compact domain having positive infimum. (shrink)

This work brings in both the original German and English translation of over one hundred short essays in philosophical logic and the philosophy of mind of historical importance to understanding Wittgenstein's philosophical thought and development in the 1930's. Transcribed from the papers of Friedrich Waismann and dating from 1932-35, the majority are highly important dictations by Wittgenstein to Waismann, but also includes texts of redrafted material by Waismann closely based on the dictations. Many of these texts become the ultimate sources (...) of material on philosophy of language that constitutes the bulk of Waismann's book Logic, Sprache, Philosophy. The transcriptions throw light on the development of Wittgenstein's thought in this period and some of the topics are not covered in any of the existing publications of his writings, in particular his detailed attention to causal theories of meaning. They also contain texts covering psychological concepts such as expecting, intending and experience; these have no counterparts in Waismann's publications. (shrink)

Working within Bishop’s constructive framework, we examine the connection between a weak version of the Heine–Borel property, a property antithetical to that in Specker’s theorem in recursive analysis, and the uniform continuity theorem for integer-valued functions. The paper is a contribution to the ongoing programme of constructive reverse mathematics.

It is shown, with intuitionistic logic, that if every locally constant function from to has a property akin to constancy, then the fan theorem for -bars holds, and conversely.

It is shown that, relative to Bishop-style constructive mathematics, the boundedness principle BD-N is equivalent both to a general result about the convergence of double sequences and to a particular one about Cauchyness in a semi-metric space.

Nach Kant bleibt alles Denken auf das einzelne Subjekt des Denkens und seine Möglichkeiten zurückbezogen. Simon beschreibt Kants Werk als ein System, das den eigenen Denkansatz als einen Besonderen neben anderen begreift. Auch wenn das Subjekt anderes Denken nicht immer von sich aus versteht, bezieht es jenes als "fremde Vernunft" in seine Weltorientierung ein und erkennt es an. Damit ergibt sich die Notwendigkeit des Findens einer Sprache, in der im Ausgang vom eigenen Vorverständnis anderen etwas so gesagt werden kann, dass (...) es auch ihnen "etwas" bedeutet und in diesem Sinne als wahr erscheint. Von hier aus verändert sich dann der Begriff der Bedeutung und die Sprache der Philosophie. (shrink)

In a classic paper, Leon Roth asked »Is there a Jewish Philosophy?« to which he replied No. In this paper, focusing on the case of Medieval Jewish Philosophy, I argue, first, that we cannot characterize Jewish philosophy in terms of the identity, religious or secular, of its philosophers, in terms of a language in which it was written or conducted, in terms of a particular style or school, or in terms of content: as philosophy specifically of Judaism the religion. I (...) then go on to argue that all the medieval Jewish philosophers were doing was Philosophy, although I sketch two different conceptions of what a philosophical interpretation of Judaism and the Jews might be: a Saadyanic model and Maimonides’. However, even though there is no kind of philosophy called »Jewish philosophy« as opposed to simply »Philosophy,« I argue that we can identify (medieval) Jewish philosophy as a philosophical »tradition,« a causally related sequence of philosophers who influence and are influenced by each other and who engage in a distinguishable dialogue or conversation among themselves. In the last part of the paper, I critically discuss various recent arguments that purport to show that there is something paradoxical, self-contradictory, and philosophically illegitimate about the very idea of a Jewish philosophy. (shrink)