This paper reports some attempts undertaken in Poland in the 1930s to modernize Thomism by means of modern logic. In particular, it concerns J.M. Bocheski and J. Salamucha, the leading members of the CracowCircle. They attempted to give precise logical form to the Five Ways of Thomas Aquinas. Other works concerned the concept of transcendentals, the levels of abstraction, and the concept of essence.

Arguments by W. T. Stace and C. J. Insole show that metaphorical descriptions of God presuppose literal descriptions of God. This poses a problem for the metaphor of darkness which has often been used, for instance by Pseudo-Dionysius, in the context of negative theology and apophatic mysticism. Three strategies of dealing with the problem are discussed in this article. The negative, apophatic approach can be seen either as subverting itself, or as being restricted to certain properties, or as resting on (...) a self-excluding principle. Whereas the first two strategies have their difficulties, self-exclusion is linguistically founded and adequate to the purposes of negative theology. (shrink)

In Plato's Parmenides we find on the one hand that the One is denied every property , and on the other hand that the One is attributed every property . In the course of the history of Platonism , these assertions - probably meant by Plato as ontological statements of an entirely formal nature - were repeatedly made the starting points of metaphysical speculations. In the Mystical Theology of the Pseudo-Dionysius they became principles of Christian mysticism and negative theology. I (...) shall show that the two assertions can each be interpreted within the ontological framework of ancient and medieval logic in such a manner that it becomes true, and I shall make plausible that they were understood, with regard to their logical core, by pagan and Christian Platonic metaphysicians just as is indicated by that interpretation. The mentioned ontological framework is basically the Boolean algebra of first-order properties. The main points of the interpretation are on the one hand the identification of the One with the maximal element of the algebra of properties, and on the other hand two alternative intuitively prominent mereological definitions of ontic predication. (shrink)

We consider a logic which is semantically dual (in some precise sense of the term) to intuitionistic. This logic can be labeled as “falsification logic”: it embodies the Popperian methodology of scientific discovery. Whereas intuitionistic logic deals with constructive truth and non-constructive falsity, and Nelson's logic takes both truth and falsity as constructive notions, in the falsification logic truth is essentially non-constructive as opposed to falsity that is conceived constructively. We also briefly clarify the relationships of our falsification logic to (...) some other logical systems. (shrink)

IN the opening chapter of his book, Eclipse of God, Martin Buber recalls the hesitant but passionate reaction of a friend, an elderly scholar, against the author's repeated use of the word "God" in one of his writings.

This paper reports some attempts undertaken in Poland in the 1930s to modernize Thomism by means of modern logic. In particular, it concerns J.M. Bocheński and J. Salamucha, the leading members of the CracowCircle. They attempted to give precise logical form to the Five Ways of Thomas Aquinas. Other works concerned the concept of transcendentals, the levels of abstraction, and the concept of essence.

The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is (...) derived that all truths are, in fact, known. Nevertheless, the solution offered is in the spirit of the constructivist attitude usually maintained by defenders of the anti-realist premise. In order to avoid the paradoxical reasoning, a paraconsistent constructive relevant modal epistemic logic with strong negation is defined semantically. The system is axiomatized and shown to be complete. (shrink)