Accepted quantum description is stochastic, yet history is nonstochastic, i.e., not representable by a probability distribution. Therefore ordinary quantum mechanics is unsuited to describe history. This is a limitation of the accepted quantum theory, rather than a failing of mechanics in general. To remove the limitation, it would be desirable to find a form of quantum mechanics that describes the future stochastically and the past nonstochastically. For this purpose it proves sufficient to introduce into quantum mechanics, by means of a (...) perfected formal correspondence, certain analogs of the classical initial-condition constants. Through the restoration of such parameters at the quantum level one accomplishes a natural accommodation of time anisotropy, wave-function reduction, and “event” description by quantum mechanical equations of motion alone, without the need for extra postulates (e.g., a projection postulate). This requires a complete restructuring of quantum measurement theory. (shrink)

. Ill BERGSONS THEORY OF ART . . .141 THE PHILOSOPHY OF INTENSIVE MANIFOLDS I I CINDERS ..... 215 APPENDICES A. REFLECTIONS ON VIOLENCE . . 249 B. PLAN FOR A ...

An analysis is presented of the significance and consequent limitations on the applicability of the von Neumann measurement postulate in quantum mechanics. Directly observable quantities, such as the expectation value of the velocity operator, are distinguished from mathematical constructs, such as the expectation value of the canonical momentum, which are not directly observable. A simple criterion to distinguish between the two types of operators is derived. The non-observability of the electromagnetic four-potentials is shown to imply the non-measurability of the canonical (...) momentum. The concept of a mechanical gauge is introduced and discussed. Classically the Lagrangian is nonunique within a total time derivative. This may be interpreted as the freedom of choosing a “mechanical” (M) gauge function. In quantum mechanics it is often implicitly assumed that the M-gauge vanishes. However, the requirement that directly observable quantities be independent of the arbitrary mechanical gauge is shown to lead to results analogous to those derived from the requirement of electromagnetic gauge independence of observables. The significance of the above to the observability of transition amplitudes between field-free energy eigenstates in the presence (and absence) of electromagnetic fields is discussed. E- and M-gauge independent transition amplitudes between field-free energy eigenstates in the absence of electromagnetic fields are defined. It is shown that, in general, such measurable amplitudes cannot be defined in the presence of externally applied time-dependent fields. Transition amplitudes in the presence of time-independent fields are discussed. The path dependence of previous derivations of E-gauge independent Hamiltonians and/or transition amplitudes in the presence of electromagnetic fields are related to the inherent M-gauge dependence of these quantities in the presence of such fields. (shrink)

Vitruvius has something interesting to say at De architectura 2.8.8: Non enim quae sunt e molli caemento subtili facie venustatis, non eae possunt esse in vetustate non ruinosae. itaque cum arbitrio communium parietum sumuntur, non aestimant eos quanti facti fuerint, sed cum ex tabulis inveniunt eorum locationes, pretia praeteritorum annorum singulorum deducunt octogesimas et ita – ex reliqua summa parte reddi pro his parietibus – sententiam pronuntiant eos non posse plus quam annos LXXX durare.Those structures made of soft rubble, for (...) all their subtle attractiveness, are not the ones that will resist ruin as time passes. And thus when assessors are appointed to evaluate party walls, they never assess soft rubble walls according to their initial cost, but rather, when they look at the price recorded in the original contracts, they deduct 1/80th of that sum for each subsequent year, and the remaining amount is fixed as the current value of the walls. They have rendered judgement, in effect, that such walls cannot last more than 80 years.By contrast, mud-brick walls were not depreciated at all if they were standing when assessed. The calculation performed for concrete walls demonstrates clear understanding of what we call ‘depreciation’ or ‘amortization’ in ancient Roman thought. It appears to have been overlooked to date. (shrink)

In preceding parts of this paper the possibility was examined of accomplishing the entirety of physical description by means of mechanics, without help from field-theoretical ideas. Apart from some easily obtained qualitative agreements with general descriptive features of nuclei and elementary particles, we were balked in this program by an inability to handle in purely mechanical terms the relativistic many-body problem. The present paper is addressed directly to the latter problem. No quantitative calculations are attempted, but three suggestions are made (...) — each of a quite radical nature — concerning the reformulation that will be necessary to restore mechanics to the mainstream of physics. (shrink)

We consider the relation between versions of Ramsey’s Theorem and König’s Infinity Lemma, in the absence of the axiom of choice.

Cognitive Development and Acquisition of Language.

Laland and colleagues have sought to challenge the proximate–ultimate distinction claiming that it imposes a unidirectional model of causation, is limited in its capacity to account for complex biological phenomena, and hinders progress in biology. In this article the core of their argument is critically analyzed. It is claimed that contrary to their claims Laland et al. rely upon the proximate–ultimate distinction to make their points and that their alternative conception of reciprocal causation refers to phenomena that were already accounted (...) for by standard theory. (shrink)

Catalepton 10 is a unique survival from antiquity: it is the only parody of an entire poem to reach us, and is written in pure iambic trimeters, a near intractable metre. Addressed to Sabinus, an upstart muleteer, the poem launches a stinging attack at him, and draws attention to his status as a parvenu. It remains incredibly close to its charming model—Catullus 4 —in structural, lexical, stylistic and metrical terms, but rather different in purport. In attempting to reassess a number (...) of problems in the text of the poem, the textual critic ought largely to be guided by the relationship of Sabinus ille to its model, as it is clear that the author of Catalepton 10 was an incredibly close reader of the Catullan text and sought not only to imitate through parody but also to subvert and deflate his predecessor's poem. (shrink)

Tarski [5] showed that for any set X, its set w(X) of well-orderable subsets has cardinality strictly greater than that of X, even in the absence of the axiom of choice. We construct a Fraenkel-Mostowski model in which there is an infinite strictly descending sequence under the relation |w (X)| = |Y|. This contrasts with the corresponding situation for power sets, where use of Hartogs' ℵ-function easily establishes that there can be no infinite descending sequence under the relation |P(X)| = (...) |Y|. (shrink)

"This is but an essay, incomplete, tentative--indeed, fumbling. I would ask for more attention to its outlook and technique or method than to its details, for the former come from me as a moral philosopher, which I am by profession, whereas the latter come from me as a moralist, which I am by conceit." -- From the Preface.

As interest in working memory is increasing at a rapid pace, an open discussion of the central issues involved is both useful and timely. This new volume compares and contrasts conceptions of working memory, with contributions from proponents of different views.

Originally published in 1957, this book collects together large sections of important tracts from a variety of political documents, particularly those concerned with democracy, communism, Protestantism or Catholicism. The extracts come from a wide range of authors including Bertrand Russell, Karl Marx, John Locke and Pope Pius XII. This book will be of value to anyone seeking an overview of the key political divisions in the late 20th century or who is interested in political theory generally.