Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. This book cuts through a host of technicalities that have obscured previous (...) discussions of these projects, and presents clear, concise accounts of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluate each and to compare different ones. The authors also offer critical discussion, rare in the literature, of the aims and claims of nominalistic interpretation, suggesting that it is significant in a very different way from that usually assumed. (shrink)

This is the first systematic survey of modern nominalistic reconstructions of mathematics, and for this reason alone it should be read by everyone interested in the philosophy of mathematics and, more generally, in questions concerning abstract entities. In the bulk of the book, the authors sketch a common formal framework for nominalistic reconstructions, outline three major strategies such reconstructions can follow, and locate proposals in the literature with respect to these strategies. The discussion is presented with admirable precision and clarity, (...) and should be accessible even to readers with only minimal background in logic and mathematics. There will be many who will turn directly to these pages and use them as a brief manual on the state of the art of nominalism in mathematics. But the most intriguing parts of this elegant book—at least in my view—are the introduction and the conclusion, where the authors examine the significance of reconstructive nominalism. (shrink)

Arsenic and phosphorus are group 15 elements with similar chemical properties. Is it possible that arsenate could replace phosphate in some of the chemicals that are required for life? Phosphate esters are ubiquitous in biomolecules and are essential for life, from the sugar phosphates of intermediary metabolism to ATP to phospholipids to the phosphate backbone of DNA and RNA. Some enzymes that form phosphate esters catalyze the formation of arsenate esters. Arsenate esters hydrolyze very rapidly in aqueous solution, which makes (...) it improbable that phosphorous could be completely replaced with arsenic to support life. Studies of bacterial growth at high arsenic:phosphorus ratios demonstrate that relatively high arsenic concentrations can be tolerated, and that arsenic can become involved in vital functions in the cell, though likely much less efficiently than phosphorus. Recently Wolfe‐Simon et al. 1 reported the isolation of a microorganism that they maintain uses arsenic in place of phosphorus for growth. Here, we examine and evaluate their data and conclusions. (shrink)

We take another look at “Just-So” solar neutrino oscillations, characterizing them by the energy Eπ/2 at which the distance-varying angle is π/2, instead of by the usual Δm 2 . The rising spectrum recently observed by SuperKamiokande is consistent with an Eπ/2 ∼6–9 MeV and marginally with 48 MeV. The pp neutrinos must then be reduced to one-half the standard solar model prediction, and 7Be neutrinos must make up a significant part of the SAGE and GALLEX gallium signal. For Eπ/2 (...) close to 9 and 48 MeV, the 7Be neutrinos will also show a large seasonal variation, emphasizing the importance of direct measurements of the 7Be neutrinos. (shrink)

Peter Abelard (1079–1142 ce) was the most wide‐ranging philosopher of the twelfth century. He quickly established himself as a leading teacher of logic in and near Paris shortly after 1100. After his affair with Heloise, and his subsequent castration, Abelard became a monk, but he returned to teaching in the Paris schools until 1140, when his work was condemned by a Church Council at Sens. His logical writings were based around discussion of the “Old Logic”: Porphyry's Isagoge, aristotle'S Categories and (...) On Interpretation and boethius'S textbook on topical inference. They comprise a freestanding Dialectica (“Logic”; probably c.1116), a set of commentaries (known as the Logica [Ingredientibus], c. 1119) and a later (c. 1125) commentary on the Isagoge (Logica Nostrorum Petititoni Sociorum or Glossulae). In a work Abelard called his Theologia, issued in three main versions (between 1120 and c.1134), he attempted a logical analysis of trinitarian relations and explored the philosophical problems surrounding God's claims to omnipotence and omniscience. The Collationes (“Debates,” also known as “Dialogue between a Christian, a Philosopher and a Jew”; probably c.1130) present a rational investigation into the nature of the highest good, in which the Christian and the Philosopher (who seems to be modeled on a philosopher of pagan antiquity) are remarkably in agreement. The unfinished Scito teipsum (“Know thyself,” also known as the “Ethics”; c.1138) analyses moral action. (shrink)

We investigate the expressive power of fragments of first-order logic that are defined in terms of prefixes. The main result establishes a strict hierarchy among these fragments over the signature consisting of a single binary relation. It implies that for each prefix p, there is a sentence in prenex normal form with prefix p, over a single binary relation, such that for all sentences θ in prenex normal form, if θ is equivalent to , then p can be embedded in (...) the prefix of θ. This strengthens a theorem of Walkoe. (shrink)

Elementary particles, regarded as the constituents of quarks and leptons, are described classically in the framework of the general relativity theory. There are neutral particles and particles having charges±1/3e. They are taken to be spherically symmetric and to have mass density, pressure, and (if charged) charge density. They are characterized by an equation of state P=−ρ suggested by earlier work on cosmology. The neutral particle has a very simple structure. In the case of the charged particle there is one outstanding (...) model described by a simple analytic solution of the field equations. (shrink)

During the past decade there has been a very effective campaign against any explanation of remembering whose basic concept is that of a causally mediating trace. This paper attempts to provide such an explanation by presenting an explicit deductive argument for the existence of the memory trace. The conclusion is shown to follow from reasonable, empirical assumptions of which the most interesting is a spatiotemporal contiguity thesis. Set-theoretic techniques are used to provide a framework of analysis and probabilistic definitions of (...) some causal notions, as that of a causal chain, are presented. (shrink)

This paper brings to light the significance of Merleau-Ponty’s thinking for contemporary physics. The point of departure is his 1956–57 Collège de France lectures on Nature, coupled with his reflections on the crisis in modern physics appearing in THE VISIBLE AND THE INVISIBLE. Developments in theoretical physics after his death are then explored and a deepening of the crisis is disclosed. The upshot is that physics’ intractable problems of uncertainty and subject-object interaction can only be addressed by shifting its philosophical (...) base from objectivism to phenomenology, as Merleau-Ponty suggested. Merleau-Ponty’s allusion to “topological space” in THE VISIBLE AND THE INVISIBLE provides a clue for bridging the gap between “hard science” and “soft philosophy.” This lead is pursued in the present paper by employing the paradoxical topology of the Klein bottle. The hope is that, by “softening” physics and “hardening” phenomenology, the “two cultures” (cf. C. P. Snow) can be wed and a new kind of science be born. (shrink)

According to the causal interpretation of quantum mechanics, one can precisely define the state of an individual particle in a many-body system by its position, momentum, and spin. It is shown in the EPR spin experiment that the quantum torque brings about an instantaneous change in the state of one of the particles when the other undergoes a local interaction, but that such a transfer of “information” cannot be extracted by any experiment subject to the laws of quantum mechanics.

Verifiable physical theories can deal only with reproducible phenomena. To the extent that some objectively real aspects of quantum phenomena are inherently not reproducible, to that extent quantum theory cannot be expected to provide a complete description of reality. Einstein, Podolsky, and Rosen argued, however, that quantum mechanics does not even provide a complete description of reproducible reality. But their reasoning fails to distinguish between the “predictability” and the “predictedness” of a physical quantity. It is shown that in quantum (...) mechanics, as in classical mechanics, predictability is not affected by a nondisturbing measurement, only predictedness is affected. Since Einstein, Podolsky, and Rosen define the (reproducible) reality of a quantity on the basis of its predictability, we find that the quantum mechanical description of this reproducible reality is unaffected by nondisturbing measurements and does not need to be considered incomplete. (shrink)

This is the sequel to the previously reviewed first volume of a proposed three volume study of Proust as philosopher. Good as the first volume is, this is even better. It is extremely difficult, unusually subtle, and demands slow and ruminative reading. For the present reviewer, the book falls naturally into two parts, each with its own peak or crescendo. The key to understanding the book is to hear the two crescendos in unison, or better, in harmony. The first crescendo (...) begins at about page 97 and culminates on page 112. A crucial passage: "Le point de création: le point instable et indécis, où la vague se lève, où le dessin, la plume en feront un duvet.... Tout est allégorie et possibilité de métaphore ou de métamorphose: les choses ne sont pas, elles ne savent pas; elles sont quelquefois l'attente, l'impatience. Il faut venir à point et dans le bon moment." And another: "C'est parce que rien n'est marqué dans une complexion définitive, imprimée dans l'espace, que l'art peut approcher, regarder, rectifier. Non pas décrire et reproduire: réinventer". The second crescendo begins with a distinction between voluntary and involuntary memory, with a long culminating passage extending from page 238 to page 265. This may be summarized as follows: I do not produce but await my memories, which come as if from another and construct what I am. Now to combine the two crescendos: I make the world, and the world makes me. The second crescendo is already anticipated in the first, e.g., p. 97: art does not invent but articulates and structures nature. The first crescendo is resumed or echoed in the second : the work of art is the most perfect form of reality. To give another formulation to the harmony of the two crescendos: in order to perceive, one must remember; yet one cannot remember unless one has perceived. Hence perception and memory remake each other. In sum, I am that spectator of the world who makes, and is made by, the world. We cannot really perceive things except via an image of them which we produce and which provides us, not with an objective representation of the perceived things, but with an equilibrium between our desires and emotions on the one hand, and the perceptions on the other. This produced image is presumably the aforementioned perception of a memory. And thus we respond to the uniqueness of our perceptions, via our produced images, by uniting them into a world, each of which is again unique, and yet, which is in each case the same single world in which we all dwell. On this reading, Proust's theme is the equilibrium between seeing and producing, or between theory and practice at the level of the constitution of the world. To oversimplify drastically, Proust teaches the Platonic demiurge but not the Platonic Ideas. As a consequence, one is intermittently reminded of a quasi-Husserlian phenomenology rooted in the primacy of intentionality as enacted in perception. But the mathematicism of Husserl is absent; the intentionality is that of a poet.-Stanley Rosen, Pennsylvania State University. (shrink)

This paper examines Rosen's claim that Bentham's principle of utility was a distributive rather than an aggregative principle.

The purpose of this paper is to resolve two paradoxes, which occur in quantum theory, by using the discussion of the theory of measurement presented in two earlier papers by the author [3], [4], [5]. The two paradoxes discussed will be the Schrödinger cat paradox and the Einstein, Podolski, Rosen paradox [2]. An introductory section will be included which summarizes the relevant results from the author's previous papers. Also a discussion will be made regarding the author's interpretation of the (...) density operator. (shrink)

Some seeming logical deficiencies in a recent paper are described. The author responds to the arguments of the work by de Muynck, De Baere, and Martens , who argue it is widely accepted today that some sort of nonlocal effect is needed to resolve the problems raised by the works of Einstein, Podolsky, and Rosen and John Bell. In MBM a variety of arguments are set forth that aim to invalidate the existing purported proofs of nonlocality and to provide, (...) moreover, a local solution to the problems uncovered by EPR and Bell. Much of the argumentation in MBM is based on the idea of introducing `nonideal` measurements, which, according to MBM, allow one to construct joint probability distributions for incompatible observables. The existence of a bona fide joint probability distribution for the incompatible observables occurring in the EPRB experiments would entail that Bell`s inequalities can be satisfied, and hence that the mathematical basis for the nonlocal effects would disappear. This relult would apparently allow one to eliminate the need for nonlocal effects by considering experiments of this new kind. (shrink)

Burgess, J.P. and Rosen, G. Subject with No ObjectElliott, R.Faking Nature.

b>: Replacing faulty nineteenth century physics by its orthodox quantum successor converts the earlier materialist conception of nature to a structure that does not enforce the principle of the causal closure of the physical. The quantum laws possess causal gaps, and these gaps are filled in actual scientific practice by inputs from our streams of consciousness. The form of the quantum laws permits and suggests the existence of an underlying reality that is built not on substances, but on psychophysical events, (...) and on objective tendencies for these events to occur. These events constitute intrinsic mind-brain connections. They are fundamental links between brain processes described in physical terms and events in our streams of consciousness. This quantum ontology confers upon our conscious intentions the causal efficacy assigned to them in actual scientific practice, and creates a substance- free interactive dualism. This putative quantum ontology has previously been shown to have impressive explanatory power in both psychology and neuroscience. Here it is used to reconcile the existence of physically efficacious conscious free will with causal anomalies of both the Libet and Einstein-Rosen-Podolsky types. (shrink)

The argument of Einstein, Podolsky, and Rosen is reviewed with attention to logical structure and character of assumptions. Bohr's reply is discussed. Bell's contribution is formulated without use of hidden variables, and efforts to equate hidden variables to realism are critically examined. An alternative derivation of nonlocality that makes no use of hidden variables, microrealism, counterfactual definiteness, or any other assumption alien to orthodox quantum thinking is described in detail, with particular attention to the quartet or broken-square question.

If one starts from de Broglie's basic relativistic assumptions, i.e., that all particles have an intrinsic real internal vibration in their rest frame, i.e., hv 0 =m 0 c 2 ; that when they are at any one point in space-time the phase of this vibration cannot depend on the choice of the reference frame, then, one can show (following Mackinnon (1) ) that there exists a nondispersive wave packet of de Broglie's waves which can be assimilated to the nonlinear (...) soliton wave U 0 introduced by him in his double solution model of wave mechanics. (2) Since de Broglie's linear pilot waves can be considered to be real waves propagating as collective motions on a covariant subquantum chaotic “aether,” (3) these new solition waves can be considered as describing the particle's immediate neighborhood, i.e., the aether's reaction to the particle's motion in the stochastic interpretation of quantum mechanics. The existence of such a physical aether (which provides a perfectly causal interpretation of the action-a-distance implied by the Einstein-Podolsky-Rosen experiments) can now be proved by establishing the reality of de Broglie's waves in realizable experiments. (shrink)

Quantum entanglement has been focus of fundamental debate since the original paper of Einstein, Podolsky and Rosen [1] and the work of Bell [2], discussing its implications on fundamental issues related to the concepts of physical reality and locality. It has only been during the last few years when it has been recognized that this feature of Quantum Mechanics may also have important applications in the fields of communication and computation. In particular, it has been shown that using entanglement (...) would allow to perform certain computational tasks, such as factoring, much faster. On the other hand, it provides the basis for provably secure secret communication and cryptography. (shrink)

Perhaps one of the most neglected fields of philosophy is the philosophy of nature, “physics” in Aristotle’s sense. In The Science Before Science, Anthony Rizzi, a well-established theoretical physicist, examines the underlying assumptions of his discipline. Trained in physics without any background in philosophy, he found himself dissatisfied with contemporary accounts of science that reduced it to mere description and prediction. Reflecting on the structure of scientific explanation, he was quickly led to discussions of nature, causality, and truth. Taking Aristotle (...) and Aquinas as mentors in the difficult terrain of metaphysics and epistemology, he discovered with awe the larger philosophical landscape that placed his professional endeavor in a new perspective. From discussions of nature, knowledge, and God he moves to discussions of evolution, quantum mechanics, Bell’s theorem, and the Einstein–Podolsky–Rosen paradox. Rizzi brings to every topic a freshness denied the seasoned philosopher. He remains a physicist, but one who has discovered the insights provided by a realistic metaphysics. The book may be understood as a brief for wisdom in the Thomistic sense. It ends with an examination of evidence for the existence of God and the moral import of a teleological conception of nature. (shrink)

Assuming that future experiments confirm Aspect's discovery of nonlocal interactions between quantum pairs of correlated particles, we analyze the constraints imposed by the EPR reasoning on the said interactions. It is then shown that the nonlocal relativistic quantum potential approach plainly satisfies the Einstein causality criteria as well as the energy-momentum conservation in individual microprocesses. Furthermore, this approach bypasses a new causal paradox for timelike separated EPR measurements deduced by Sutherland in the frame of an approach by means of space-time (...) zigzags with advanced potentials. It is finally demonstrated that this inherent quantum causal direct interaction establishes permanent EPR correlations which are always restricted to spacelike separations and are instantaneous only in the center-of-mass rest frame of the two-particle system. (shrink)

Since weakly decaying particles are their own polarimeters, reactions like $\eta _c \to \Lambda \bar \Lambda , \psi \to \Lambda \bar \Lambda ,e^ + e^ - \to \mu ^ + \mu ^ -$ , etc. are interesting for testing the non-locality of quantum mechanical predictions. Although such reactions, in principle, do not exclude all classes of hidden variable theories, they can be used to complement current experiments with external polarimeters. The reaction $\eta _c \to \Lambda \bar \Lambda \to \pi ^ (...) - p\pi ^{ + - } \bar p$ is conceptually the simplest and most useful as agedanken experiment, although it has not yet been seen experimentally. The reaction $e^ + e^ - \to \Lambda \bar \Lambda \to \pi ^ - p\pi ^ + \bar p$ near threshold or at the φ resonance can be used for essentially the same test. This is feasible with presently available data and would be the first EPR experiment involving weak interactions. (shrink)