The study by Wilfredo Quezada Pulido and Carlo Apablaza Ávila offers a comprehensive reconstruction of Rolando Chuaqui Kettlun’s career, articulating his intellectual biography, philosophical work, and interdisciplinary contributions. It highlights his role in the development of logic and mathematics in Chile and clarifies his formative and collaborative ties with Alfred Tarski and Newton da Costa.
In contrast to Kant’s metatheoretical (“transcendental”) approach grounded in the operations of an abstract logical subject, Herbart and Bolzano aimed to avoid subject-dependent foundations of logic. They instead proposed formal logics founded, respectively, on the form of conceptual content (Herbart) and on the extensions of logical forms (Bolzano). Among the traditions originating from Herbart and Bolzano, we consider the role of Bolzano’s informal disciple Robert Zimmermann, who subsequently adopted Herbartianism, and Zimmermann’s own disciple, the mathematical logician and philosopher Albino Nagy. Special attention is given to Nagy’s analysis of expressive completeness and his treatment of the Jevons-Clifford problem: how many and which types and representatives of types there are of Boolean propositional functions. We transform this latter problem into the question of types of sequent refutations and examine the corresponding admissibility of the cut rule.
This paper aims to re-examine the so-called Ja & sacute;kowski's criterion. This guiding principle was initially proposed as a methodological instrument for delineating formal systems as either satisfactory or unsatisfactory paraconsistent logics. It is a historical fact that Ja & sacute;kowski's criterion has been, and remains, frequently overlooked in the relevant literature. In order to provide a detailed explanation of this fact and the argument for it being a regrettable state, there are three main points elaborated upon. Firstly, the philosophical motivations of Ja & sacute;kowski's work. Secondly, an overview of some early attempts of meeting requirements of Ja & sacute;kowski's criterion. Thirdly, its relevance to contemporary research in the field of philosophical logic, particularly in relation to recent discussions on the notion of 'philosophical interpretation'. From the above, philosophical conclusions are drawn, and avenues for further research are identified.
We present a new axiomatization for a truth-functionally complete version of & Lstrok;3, a three-valued propositional logic, using two propositional constants and the & Lstrok;ukasiewicz implication as primitive symbols. We develop a corresponding proof system that incorporates & Lstrok;ukasiewicz's axioms, a variant of S & lstrok;upecki's postulates for a 0-ary connective, and some properties of the Baaz delta operation. Using a weakened Deduction Theorem and adapting Henkin's method to this three-valued setting, we establish a Completeness Theorem for the system.
Glidel's ontological proof for the existence of God - as an inference from the level of rational, logical structure to the level of being was strongly influenced by Leibniz's monadology, which is based on the Ur-Monade - God - conceived as absolutely infinite. Glidel defines God as the maximum of positive properties and he characterizes this maximum (of being) with his postulates implicitly as an ultrafilter structure. Using maximality as criterion we have compared the set of positive properties in Scott's version of Glidel's theistic theory with modified variants of it to see whether a maximum is still achieved, or not, and what effect this has on modal collapse. The motivation for these, typically weakened, variants of Glidel's theistic theory has been to avoid modal collapse and the limited determinism associated with it, and to show that the necessary existence of God can still be proved with less strong axioms. A weakening of the maximality criterion of the ultrafilter structure imposed by Glidel's (and Scott's) postulates have thus been applied to the set of positive properties in order to allow for alternative models in which modal collapse does not hold. In these alternative models, however, the maximality criterion for the basic quantity of positive properties is abandoned, so that in them God as a "maximum" is not reached. We argue that this is contrary to Glidel's intention, and that for his conception of God, maximality and absolute infinity are non-negotiable. What Glidel had in mind, as we argue here, was a holistic - absolutely infinite - view of the world, i.e. with modal collapse, but without limited determinism.
