Reveling in Complexity: Dittes' Male Metaphors and Their Bearing on the Crisis of Clergy Sexual Abuse

In Driven By Hope: Men and Meaning (1996b), James E. Dittes explores the distinctively religious character of men's experience in postindustrial modern western culture. In this article, I first explicate Dittes' developing perspective on men's experience—his middle way—by focusing on his exploration of classical and biblical metaphors of men's life experience, including Oedipus and Adam, the magi and the monarch, the pilgrim and the conquistador, and the son and father. Then, I extend Dittes' models of normative male development to reflect upon the current crisis around clergy sexual abuse in the Roman Catholic Church.     

Kripke Incompleteness of Predicate Extensions of the Modal Logics Axiomatized by a Canonical Formula for a Frame with a Nontrivial Cluster

We generalize the incompleteness proof of the modal predicate logic Q-S4+ p p + BF described in Hughes-Cresswell [6]. As a corollary, we show that, for every subframe logic Lcontaining S4, Kripke completeness of Q-L+ BF implies the finite embedding property of L.     

Kripke Incomplete Logics Containing KTB

It is shown that there is a Kripke incomplete logic in NExt(KTB ⊕ □² p → □³ p). Furthermore, it is also shown that there exists a continuum of Kripke incomplete logics in NExt(KTB ⊕ □⁵ p → □⁶ p). Presented by Michael Zakharyaschev     

On Interpreting Chaitin's Incompleteness Theorem

The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin's famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number to have Kolmogorov complexity larger than c. The received interpretation of theorem claims that the limiting constant is determined by the complexity of the theory itself, which is assumed to be good measure of the strength of the theory.I exhibit certain strong counterexamples and establish conclusively that the received view is false. Moreover, I show that the limiting constants provided by the theorem do not in any way reflect the power of formalized theories, but that the values of these constants are actually determined by the chosen coding of Turing machines, and are thus quite accidental.     

Stochastic Dominance and Opaque Sweetening

This paper addresses the problem of opaque sweetening and argues that one should use stochastic dominance in comparing lotteries even when dealing with incomplete orderings that allow for non-comparable outcomes.     

Löb's Theorem in a Set Theoretical Setting

We present a semantic proof of Löb's theorem for theories T containing ZF. Without using the diagonalization lemma, we construct a sentence AUT _T, which says intuitively that the predicate autological with respect to T (i.e. applying to itself in every model of T) is itself autological with respect to T. In effect, the sentence AUT _T states I follow semantically from T. Then we show that this sentence indeed follows from T and therefore is true.     

All Finitely Axiomatizable Tense Logics of Linear Time Flows Are CoNP-complete

We prove that all finitely axiomatizable tense logics with temporal operators for ‘always in the future’ and ‘always in the past’ and determined by linear fows time are coNP-complete. It follows, for example, that all tense logics containing a density axiom of the form ■ⁿ⁺¹_F p → ⁿ_F p, for some n ≥ 0, are coNP-complete. Additionally, we prove coNP-completeness of all ∩-irreducible tense logics. As these classes of tense logics contain many Kripke incomplete bimodal logics, we obtain many natural examples of Kripke incomplete normal bimodal logics which are nevertheless coNP-complete.     

On the Predicate Logic of Linear Kripke Frames and some of its Extensions

We propose a new, rather simple and short proof of Kripke-completeness for the predicate variant of Dummett's logic. Also a family of Kripke-incomplete extensions of this logic that are complete w.r.t. Kripke frames with equality (or equivalently, w.r.t. Kripke sheaves [8]), is described.