Homogeneous and Universal Dedekind Algebras

A Dedekind algebra is an order pair (B, h) where B is a non-empty set and h is a similarity transformation on B. Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called the configurations of the algebra. There are ₀ isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on called its configuration signature. The configuration signature counts the number of configurations in each isomorphism type which occur in the decomposition of the algebra. Two Dedekind algebras are isomorphic iff their configuration signatures are identical. It is shown that configuration signatures can be used to characterize the homogeneous, universal and homogeneous-universal Dedekind algebras. This characterization is used to prove various results about these subclasses of Dedekind algebras.     

Propositional Logic of Essence

This paper presents a propositional version of Kit Fine"s (quantified) logic for essentialist statements, provides it with a semantics, and proves the former adequate (i.e. sound and complete) with respect to the latter.     

Remarks on the Modal Logic of Henry Bradford Smith

H. B. Smith, Professor of Philosophy at the influential Pennsylvania School was (roughly) a contemporary of C. I. Lewis who was similarly interested in a proper account of implication. His research also led him into the study of modal logic but in a different direction than Lewis was led. His account of modal logic does not lend itself as readily as Lewis' to the received possible worlds semantics, so that the Smith approach was a casualty rather than a beneficiary of the renewed interest in modality. In this essay we present some of the main points of the Smith approach, in a new guise.     

CE is Not a Conservative Extension of E

The logic CE (for Classical E) results from adding Boolean negation to Anderson and Belnap"s logic E. This paper shows that CE is not a conservative extension of E.     

ONE BRAIN,TWO MINDS: AN ESSAY ON PRIMORDIAL AND ADVANCED MENTAL ACTIVITY

The Primordial Mind in Health and Illness: A Cross‐Cultural Perspective. By Michael Robbins. London/New York: Routledge, 2011. 240 pp.     

FINDING THE SOMETHING IN NOTHING

Formless Infinity: Clinical Explorations of Matte Blanco and Bion. By Riccardo Lombardi. Translated by Karen Christenfeld, Gina Atkinson, Andrea Sabbadini, and Philip Slotkin. London/New York: Routledge, 2016. 282 pp.     

EAST ASIA AND HUMAN KNOWLEDGE—A PERSONAL QUEST

This essay is a reflection on the ways we understand East Asia, as well as how East Asia is related to our knowledge construction. In spite of the personal tone, which I use strategically to formulate arguments in a carefully designed narrative flow, the article remains critical throughout and its conclusion is clear: exploration of the essence of East Asian civilization can constitute a meaningful effort to reevaluate and even restructure our current world of knowledge.     

Logic programming,probability, and two-system accounts of reasoning: a rejoinder to Oaksford and Chater (2014)

This reply to Oaksford and Chater’s (O&C)’s critical discussion of our use of logic programming (LP) to model and predict patterns of conditional reasoning will frame the dispute in terms of the semantics of the conditional. We begin by outlining some common features of LP and probabilistic conditionals in knowledge-rich reasoning over long-term memory knowledge bases. For both, context determines causal strength; there are inferences from the absence of certain evidence; and both have analogues of the Ramsey test. Some current work shows how a combination of counting defeaters and statistics from network monitoring can provide the information for graded responses from LP reasoning. With this much introduction, we then respond to O&C’s specific criticisms and misunderstandings.