This paper constructs two classes of models for the quantum correlation experiments used to test the Bell-type inequalities, synchronization models and prism models. Both classes employ deterministic hidden variables, satisfy the causal requirements of physical locality, and yield precisely the quantum mechanical statistics. In the synchronization models, the joint probabilities, for each emission, do not factor in the manner of stochastic independence, showing that such factorizability is not required for locality. In the prism models the observables are not random variables (...) over a common space; hence these models throw into question the entire random variables idiom of the literature. Both classes of models appear to be testable. (shrink)

One of Hume's most well-known works and a masterpiece of philosophy, A Treatise of Human Nature is indubitably worth taking the time to read.

Editorial preface to the fourth edition and modified translation -- The text of the Philosophische Untersuchungen -- Philosophische untersuchungen = Philosophical investigations -- Philosophie der psychologie, ein fragment = Philosophy of psychology, a fragment.

This groundbreaking work on logic by the brilliant 19th-century English mathematician George Boole remains influential to this day. Boole's major contribution was to demonstrate conclusively that the symbolic expressions of algebra could be adapted to convey the fundamental principles and operations of logic, which hitherto had been expressed only in words. Boole was thus the founder of today's science of symbolic logic. Summing up his innovative approach, Boole stated, "We ought no longer to associate Logic and Metaphysics, but Logic and (...) Mathematics." As the great English logician Augustus De Morgan later put it, in praise of Boole, his genius consisted in showing that "the symbolic processes of algebra, invented as tools of numerical calculation, should be competent to express every act of thought, and to furnish the grammar and dictionary of an all-containing system of logic." The Laws of Thought lays out this new system in detail and also explores a "calculus of probability." The story of Boole's life is as impressive as his work. Besides rudimentary lessons from his father and a few years at local schools, Boole was largely self-taught. Revealing his aptitude for many subjects at an early age, he began his career already at age 16 as a teacher at a village school. In his leisure time he tackled the daunting works of Newton, Laplace, and Lagrange on physics and mathematics. By the age of twenty-four he was submitting original papers to the Cambridge Mathematical Journal and at age twenty-nine he won a medal from the Royal Society for his contributions to mathematical analysis. He continued to so impress his contemporaries that five years later he was appointed professor of mathematics at Queens College, Cork in Ireland, even though he had no university degree. At his untimely death of forty-nine, Boole could never have guessed that his new symbolic logic would become essential in the next century for telephone switching and the design of computers. For this practical reason, as well as the sheer intellectual importance of his accomplishment, The Laws of Thought merits our attention today. (shrink)

A deterministic model that accounts for the statistical behavior of random samples of identical particles is presented. The model is based on some nonmeasurable distribution of spin values in all directions. The mathematical existence of such distributions is proved by set-theoretical techniques, and the relation between these distributions and observed frequencies is explored within an appropriate extension of probability theory. The relation between quantum mechanics and the model is specified. The model is shown to be consistent with known polarization phenomena (...) and the existence of macroscopic magnetism. Finally.. (shrink)

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