A note on the “B” in REBT

In this brief article, I argue for the inclusion of B based on principles of classical and instrumental conditioning. It's time to manage our discomfort with the alignment of REBT with behavior therapy.former Co-Editor of thisJournal. He is a Professor Emeritus and a Licensed Psychologist in private practice in Roanoke, VA.     

Mary Astell’s critique of Pierre Bayle: atheism and intellectual integrity in the Pensées (1682)

ABSTRACT

This paper focuses on the English philosopher Mary Astell’s marginalia in Lady Mary Wortley Montagu’s personal copy of the 1704 edition of Pierre Bayle’s Pensées diverses sur le comète (first published in 1682). I argue that Astell’s annotations provide good reasons for thinking that Bayle is biased towards atheism in this work. Recent scholars maintain that Bayle can be interpreted as an Academic Sceptic: as someone who honestly and impartially follows a dialectical method of argument in order to obtain the goal of intellectual integrity. In her commentary, however, Astell suggests that: (i) if Bayle were honest and impartial in his inquiries, then he would not have pretended to attack popular superstition, only to undermine generally-held religious beliefs; and (ii) if Bayle valued intellectual integrity, then his argument for a society of virtuous atheists would not have relied upon a deceptive equivocation in terms. I conclude that the rediscovery of this marginalia is valuable for enhancing our appreciation of Astell as an astute reader of one of her most enigmatic contemporaries.     

A note on the ω-incompleteness formalization

The paper studies two formal schemes related to -completeness.LetS be a suitable formal theory containing primitive recursive arithmetic and letT be a formal extension ofS. Denoted by (a), (b) and (c), respectively, are the following three propositions (where (x) is a formula with the only free variable x): (a) (for anyn) ( _T (n)), (b) _{T x} Pr _T (^–(x)^–) and (c) _T x(x) (the notational conventions are those of Smoryski [3]). The aim of this paper is to examine the meaning of the schemes which result from the formalizations, over the base theoryS, of the implications (b) (c) and (a) (b), where ranges over all formulae. The analysis yields two results overS : 1. the schema corresponding to (b) (c) is equivalent to ¬Cons _T and 2. the schema corresponding to (a) (b) is not consistent with 1-CON _T. The former result follows from a simple adaptation of the -incompleteness proof; the second is new and is based on a particular application of the diagonalization lemma.Presented byMelvin Fitting     

A note on the proof theory the λII-calculus

The II-calculus, a theory of first-order dependent function types in Curry-Howard-de Bruijn correspondence with a fragment of minimal first-order logic, is defined as a system of (linearized) natural deduction. In this paper, we present a Gentzen-style sequent calculus for the II-calculus and prove the cut-elimination theorem.The cut-elimination result builds upon the existence of normal forms for the natural deduction system and can be considered to be analogous to a proof provided by Prawitz for first-order logic. The type-theoretic setting considered here elegantly illustrates the distinction between the processes of normalization in a natural deduction system and cut-elimination in a Gentzen-style sequent calculus.We consider an application of the cut-free calculus, via the subformula property, to proof-search in the II-calculus. For this application, the normalization result for the natural deduction calculus alone is inadequate, a (cut-free) calculus with the subformula property being required.This paper was written whilst the author was affiliated to the University of Edinburgh, Scotland, U.K. and revised for publication whilst he was affiliated to the University of Birmingham, England, U.K.Presented byDaniele Mundici     

A note on ‘scepticism and absurdity’

In ‘Scepticism and Absurdity’ (Inquiry, Vol. 7, No. 2) Ingemund Gullvag concludes that recent attempts to counter scepticism have failed. It is suggested that where the attempts Gullvåg investigates are complex theories of a sociological and linguistic‐psychological nature, we need only refer to a simple and inspectable fact of language to counter scepticism.     

A note on the deontic system DL of Jones and Pörn

I would like to thank Ingmar Pörn for valuable comments on an earlier version of this paper.     

A note on the relation between coefficient alpha and guttman's “split-half” lower bounds

Use of the same term split-half for division of ann-item test into two subtests containing equal [Cronbach], and possibly unequal [Guttman], numbers of items sometimes leads to a misunderstanding about the relation between Guttman's maximum split-half bound and Cronbach's coefficient alpha.Coefficient alpha is the average of split-half bounds in the Cronbach sense and so is not larger than the maximum split-half bound in either sense whenn is even. Whenn is odd, however, splithalf bounds exist only in the Guttman sense and the largest of these may be smaller than coefficient alpha.     

What wealth-happiness paradox? A short note on the American case

Happiness scholars have tried to resolve the seeming paradox that as Americans’ wealth increased substantially over the last few decades, their happiness did not. This article questions whether the paradox is real. Demonstrations of the paradox almost always rely on GDP per capita as the measure of wealth, but that is a poor measure of a people’s well-being. It is heavily and increasingly skewed; it does not account for effort. Using instead measures of household income, male income, and average wages eliminates the paradox; these indicators of affluence have grown only slowly or declined in the same period, paralleling the changes in happiness scores. Moreover, using these indicators reveals a modest but real correlation between material well-being and national happiness.     

A note on ‘knowledge,certainty, and probability'∗

In ‘Knowledge, Certainty and Probability’, Dr. Heidelberger claims to have shown ‘that it is a mistake to assimilate probability and rational belief to knowledge’. The conclusion may be true but his argument is faulty.