There is a constructive method to define a structure of simple k-cyclic Post algebra of order p, L p,κ, on a given finite field F, and conversely. There exists an interpretation Ф₁ of the variety V generated by L p,κ into the variety V) generated by F and an interpretation Ф₂ of V) into V such that Ф₂Ф₁ = B for every B ϵ V and Ф₁₂ = R for every R ϵ V). In this paper we show how we (...) can solve an algebraic system of equations over an arbitrary cyclic Post algebra of order p, p prime, using the above interpretation, Gröbner bases and algorithms programmed in Maple. (shrink)

The author analyses Burrhus Frederick Skinner's book Beyond Freedom and Dignity (1971).

Analyses of Burrhus Frederick Skinner's book Beyond Freedom and Dignity (1971).

PARANORMAL IS ABNORMAL ACTION OF MIND ON MATTER.\\ ONE NEEDS FIRST A THEORY OF NORMAL ACTION OF MIND ON MATTER.\\ CLASSICAL THEORY INADEQUATE: NO `MIND' IN THE DYNAMICS.\\ QUANTUM THEORY IS FORMULATED AS A THEORY OF MIND-MATTER INTERPLAY!\\ SIMPLER THAN CLASSICAL PHYSICS!\\ I SHALL:\\ 1. SHOW HOW QUANTUM THEORY OF MIND-MATTER IS CONSTRUCTED.\\ 2. DO TWO IMPORTANT MIND-MATTER CALCULATIONS.\\ 3. LOOK AT RAMIFICATIONS FOR PARANORMAL.

B.F. Skinner was the voice of radical behaviourism for some five decades, fighting relentlessly against consciousness as a scientific question. While in public he always argued the case for behaviourism, in fact Skinner was deeply at odds with himself, as he reveals in several books. Surprisingly, as a college student he was deeply interested in becoming a stream-of-consciousness novelist. When that ambition failed, he reacted with a radical rejection of the conscious life. Decades later Skinner's inner struggle still continued, as (...) his autobiography shows. Like a mystery novelist, B.F. Skinner again and again provides the clues to his own secret. Skinner's conflict about consciousness was not just a personal idiosyncracy. Behaviourism and its radical rejection of personal experience was a major theme of the twentieth century, and continues even today. Rejection of consciousness became a core belief for academic psychologists and philosophers in the English-speaking world, justifying their claim to standing among the physical sciences. Skinner's life suggests that radical behaviourism may be associated with psychological conflict and some degree of dissociation. It also raises questions about the cultural climate that celebrated the rejection of consciousness. (shrink)

The present report is a, somewhat lengthy, addendum to "A new deconstructive logic: linear logic," where the elimination of cuts from derivations in sequent calculus for classical logic was studied ‘from the point of view of linear logic’. To that purpose a formulation of classical logic was used, that - as in linear logic - distinguishes between multiplicative and additive versions of the binary connectives.The main novelty here is the observation that this type-distinction is not essential: we can allow classical (...) sequent derivations to use any combination of additive and multiplicative introduction rules for each of the connectives, and still have strong normalization and confluence of tq-reductions.We give a detailed description of the simulation of tq-reductions by means of reductions of the interpre- tation of any given classical proof as a proof net of PN2 (the system of second order proof nets for linear logic), in which moreover all connectives can be taken to be of one type, e.g., multiplicative.We finally observe that dynamically the different logical cuts, as determined by the four possible combinations of introduction rules, are independent: it is not possible to simulate them internally, i.e., by only one specific combination, and structural rules. (shrink)

Let ξ ≥ 1 be a countable ordinal. We study the Borel subsets of the plane that can be made [Formula: see text] by refining the Polish topology on the real line. These sets are called potentially [Formula: see text]. We give a Hurewicz-like test to recognize potentially [Formula: see text] sets.

It is shown that there exists a low2 Harrington non-splitting base-that is, a low2 computably enumerable (c.e.) degree a such that for any c.e. degrees x, y, if $0' = x \vee y$ , then either $0' = x \vee a$ or $0' = y \vee a$ . Contrary to prior expectations, the standard Harrington non-splitting construction is incompatible with the $low_{2}-ness$ requirements to be satisfied, and the proof given involves new techniques with potentially wider application.

The present article is the second in a series of three that outlines the historical and conceptual background of B.F. Skinner’s radical behaviorism as a philosophy of science. Of special interest in this article are Skinner’s academic and research experiences between 1928, when he entered graduate school at Harvard, and the late 1930s, when he had assumed his first academic position. The article also examines the intellectual climate that emerged during the second quarter of the twentieth century, which is the (...) context out of which radical behaviorism developed as a unique position. Overall, the views for which Skinner is recognized were significantly influenced by such figures as Francis Bacon, Percy Bridgman, William Crozier, Jacques Loeb, Ernst Mach, Ivan Pavlov, Bertrand Russell, and John B. Watson. (shrink)

The present article is the third in a series of three that outlines the historical and conceptual background of B.F. Skinner’s radical behaviorism as a philosophy of science. Of special interest in this article is the intellectual context of a paper on operationism Skinner published in 1945, in which he first used the term “radical behaviorism” in print. Overall, Skinner’s radical behaviorism was a thoroughgoing behaviorism that provided a naturalistic account of the full range of human functioning, including the influence (...) on both verbal and nonverbal behavior of phenomena identified as "subjective.". (shrink)

The present article is the first in a series of three that outlines the historical and conceptual background of B.F. Skinner’s radical behaviorism. The series seeks to identify milestones in the development of Skinner’s position, as well as assess the impact of particular factors and events on Skinner himself. Of special interest in this article are the biographical details of Skinner’s life between June, 1926, when he received his undergraduate degree, and September, 1928, when he entered graduate school. The article (...) also examines the intellectual climate at the start of the second quarter of the twentieth century that led Skinner to become interested in the empirical study of behavior. Overall, Skinner’s views during this period were significantly influenced by such literary figures in the modernist tradition as H.G. Wells and Sinclair Lewis; and such scientific/philosophical figures as Francis Bacon, Jacques Loeb, Ivan Pavlov, Bertrand Russell, and John B. Watson. (shrink)