It is shown that the 3-stratifiable sentences are equivalent in $\mathit{NFU}$ to truth-functional combinations of sentences about objects, sets of objects, sets of sets of objects, and sentences stating that there are at least $n$ urelements. This is then used to characterize the closed 3-stratifiable theorems of $\mathit{NFU}$ with an externally infinite number of urelements, as those that can be nearly proved in $\mathit{TTU}$ with an externally infinite number of urelements. As a byproduct we obtain a rather simple demonstration of (...) the consistency of 3-stratifiable extensions of $\mathit{NFU}$. (shrink)

Counterexamples to reassurance relative to a relation between models of the logic of paradox are provided. Another relation, designed to fix the problem in logic without equality, is introduced and discussed in connection with the issue of classical recapture.

We prove the cut-elimination theorem, Gentzen's Hauptsatz, for the system for stratified comprehension, i. e. Quine's NF minus extensionality.

We characterize the notion of validity relatively to models, for comprehension axioms, containing gluts.

We characterize the 3-stratifiable theorems of NF as a 3-stratifiable extension of NF 3 ; and show that NF is equiconsistent with TT plus raising type axioms for sentences asserting the existence of some predicate over an atomic Boolean algebra.

It is shown that the 3-stratifiable sentences are equivalent in to truth-functional combinations of sentences about objects, sets of objects, sets of sets of objects, and sentences stating that there are at least urelements. This is then used to characterize the closed 3-stratifiable theorems of with an externally infinite number of urelements, as those that can be nearly proved in with an externally infinite number of urelements. As a byproduct we obtain a rather simple demonstration of the consistency of 3-stratifiable (...) extensions of. (shrink)

In his article "Reassurance via Translation" Marcel Crabbe proposed a formalism to obtain reassurance and classical recapture in the setting of minimal FDE. His formalism proved to be general enough to be extended in order to formalize other forms of non-monotonic systems based on preference relations. It is the aim of this article to show how his result can be extended in a natural way by combining two different reasoning systems, namely minimal FDE and circumscription, in order to get (...) a paraconsistent and paracomplete version of circumscription, which we will call paracomplistent circumscription, which has the advantages of FDE and circumscription but is neither explosive nor lacks modus ponens in consistent contexts. Furthermore, we will complete a proof Crabbe left unfinished. (shrink)

An ω-model (a model in which all natural numbers are standard) of the predicative fragment of Quine's set theory "New Foundations" (NF) is constructed. Marcel Crabbe has shown that a theory NFI extending predicative NF is consistent, and the model constructed is actually a model of NFI as well. The construction follows the construction of ω-models of NFU (NF with urelements) by R. B. Jensen, and, like the construction of Jensen for NFU, it can be used to construct α-models (...) for any ordinal α. The construction proceeds via a model of a type theory of a peculiar kind; we first discuss such "tangled type theories" in general, exhibiting a "tangled type theory" (and also an extension of Zermelo set theory with Δ 0 comprehension) which is equiconsistent with NF (for which the consistency problem seems no easier than the corresponding problem for NF (still open)), and pointing out that "tangled type theory with urelements" has a quite natural interpretation, which seems to provide an explanation for the more natural behaviour of NFU relative to the other set theories of this kind, and can be seen anachronistically as underlying Jensen's consistency proof for NFU. (shrink)

The article focuses on one of the central themes of Gabriel Marcel’s thought: the afterlife and the presence of the dead. Marcel approaches such a “mystery” through his plays, one of the most important aspects of his thought.

French existentialist philosopher Gabriel Marcel is one of the most influential thinkers of the twentieth century. The central themes of his philosophy, which are developed with a blend of realism, concreteness, and common sense, continue to be relevant for the plight of humanity in the twentieth-first century. Marcel's thought emphasizes: the attempt to safeguard the dignity and integrity of the human person by emphasizing the inadequacy of the materialistic life and the unavoidable human need for transcendence; the inability (...) of philosophy to capture the profundity and depth of key human experiences, and so the need to find a deeper kind of reflection; the importance of the experience of inter-subjectivity, which Marcel believes is at the root of human fulfillment, and which also finds expression in the transcendent dimension of human experience, a dimension that cannot be denied without loss, and that often gives meaning to our most profound experiences. Marcel is also one of the few contemporary thinkers who manages to do justice to the subjectivity and individuality of the human person, while avoiding the relativism and skepticism that has tended to accompany these notions, and that has plagued contemporary philosophy after Heidegger. He makes an unwavering effort to challenge the moral relativism and spiritual nihilism of his French rival, Jean-Paul Sartre, and of other representative existentialist philosophers. All of Marcel's important ideas are introduced here, ranging from his unique conception of philosophy; to his original approach to epistemology and the nature of knowledge; to his view on the nature of the human person, including the idea of being-in-a-situation and the importance of the "context" that the subject lives in for the subject's ideas and experiences; to his approach to religious themes, including the issues of the rationality of religious belief, the question of God's existence, and our longing for the transcendent; and his "concrete approaches" of fidelity, hope, love and faith. There are also selections in which he discusses some of his misgivings about the direction of contemporary culture, especially the effects of technology. Brendan Sweetman is Professor of Philosophy at Rockhurst University, Kansas City, MO. He has published over seventy articles and reviews. He is president of the Gabriel Marcel Society. (shrink)

In contemporary theology the doctrine of divine impassibility is a hot issue. The doubts about this doctrine in the present century have their earliest roots in British theology, where we can trace the passibilist tendency back to the last ten years of the nineteenth century. It received a powerful impetus from the First World War, and by the time the Second World War broke out it was almost generally accepted in British theology that God suffered. Since then this tendency has (...) spread to the rest of Europe, notably to France and Germany, to the United States and to Asia. Although it cannot be denied that most of the theologians who explicitly state their views on divine impassibility, hold that this doctrine is to a greater or lesser degree false, the debate over this issue is far from closed. Recently Richard Creel published a thorough study in defence of divine impassibility, which, I expect, will prove quite influential. Apart from him some other theologians defend the doctrine as well. Moreover, the fact that many authors consider it necessary at present to write books and articles in defence of divine passibility also indicates that the truth of the passibilist position is not yet taken for granted by everyone. (shrink)