Note to readers. What follows are drafts of six chapters of our book in progress, Seductions and Shortcuts: Fallacies in the Cognitive Economy, which is volume 3 of our omnibus work, A Practical Logic of Cognitive Systems, published by Elsevier/NorthHolland. The six chapters that appear here have been drafted as stand-alone pieces, and they have not yet been integrated into a smoothly flowing u...

Previously unpublished comments on John Cooper’s paper “The Psychology of Justice in Plato” (American Philosophical Quarterly 14 (1977) 151-157). These comments were presented, as they appear here, along with Cooper’s paper, in a symposium at the Pacific Division meeting of the American Philosophical Association in Portland, Oregon, March 1977. Since Cooper’s paper has been several times anthol...

Let (* ) u,, du + q(x, t) u = 0 in D x [0, T], where D c R3 is a bounded domain with a smooth boundary dD, T> d, d: =diam D, q(x, I) E C( [O, 2’1, L”(D)). Suppose that for every (**) ~I,+~=f(x, l)EC’(dDx [0, T]), the value u*,;,:= h(s, t) is known, where N is the outer normal to dD, u solves (* ) and ( ** ) and satisfies the initial conditions u = U, = 0 at I = 0. Then q(x, I) is uniquely deter...

There are well-known constructions of the exceptional simple Lie algebras of type E8 and F4 which go back to Witt [Wit41], as Z2-graded algebras g = g0̄⊕g1̄ with even part the orthogonal Lie algebras so16 and so9 respectively, and odd part given by their spin representations (see [Ada96]). Brown [Bro82] found a new simple finite dimensional Lie algebra over fields of characteristic 3 which presen...

Explicit solutions of the non-constant semi-dynamical reflection equation are constructed, together with suitable parametrizations of their structure matrices. Considering the semi-dynamical reflection equation with rational non-constant Arutyunov-Chekhov-Frolov structure matrices, and a specific meromorphic ansatz, it is found that only two sets of the previously found constant solutions are e...

The Planet-4D model introduced by Baroin 2011b is a richer model of pitch-class relationships than the standard cyclic model of the clock-face diagram: instead of the distribution of twelve points on a circle in a 2D plane, the Planet-4D model places the twelve pcs on a 4D hypersphere. Beyond the usual T/I group of symmetries, which is still featured in this new musical space, the additional di...

We report on various results, conjectures, and open problems related to KazhdanLusztig polynomials of matroids. We focus on conjectures about the roots of these polynomials, all of which appear here for the first time.

There is a typographical error in a sentence following (20) in [1, p.1681], in which an extra parenthesis appears. The corrected sentence is as follows. Therefore, p(v) is a Gibbs distribution p(v) = 1=Vintexp E . Also, the authors’ photographs and biographies did not appear in [1], and they now appear below. In addition, some of the information in references [9], [24], and [28] has changed. Th...