Abraham ibn Ezra the Spaniard was one of the foremost transmitters of Arabic science to the West. His astrological and astronomical works, written in Hebrew and later translated into Latin, were considered authoritative by many medieval Jewish and Christian scholars. Some of the works he translated from Arabic are no longer extant in their original form, and on occasion his treatises provide information about earlier sources that is otherwise poorly preserved, if at all. Ibn Ezra seems to be the earliest (...) scholar to record one of the seven methods for setting up the astrological houses, and this method was subsequently used by Levi ben Gerson in southern France. (shrink)
[Correction Notice: An erratum for this article was reported in Vol 109 of Psychological Review. Due to circumstances that were beyond the control of the authors, the studies reported in "Models of Ecological Rationality: The Recognition Heuristic," by Daniel G. Goldstein and Gerd Gigerenzer overlap with studies reported in "The Recognition Heuristic: How Ignorance Makes Us Smart," by the same authors and with studies reported in "Inference From Ignorance: The Recognition Heuristic". In addition, Figure 3 in the Psychological Review (...) article was originally published in the book chapter and should have carried a note saying that it was used by permission of Oxford University Press.] One view of heuristics is that they are imperfect versions of optimal statistical procedures considered too complicated for ordinary minds to carry out. In contrast, the authors consider heuristics to be adaptive strategies that evolved in tandem with fundamental psychological mechanisms. The recognition heuristic, arguably the most frugal of all heuristics, makes inferences from patterns of missing knowledge. This heuristic exploits a fundamental adaptation of many organisms: the vast, sensitive, and reliable capacity for recognition. The authors specify the conditions under which the recognition heuristic is successful and when it leads to the counter-intuitive less-is-more effect in which less knowledge is better than more for making accurate inferences. (shrink)
Leon J. Goldstein critically examines the philosophical role of concepts and concept formation in the social sciences. The book undertakes a study of concept formation and change by looking at four critical terms in anthropology , politics , and sociology.
Jürgen Goldstein gibt Antwort auf diese Fragen, indem er zunächst den von Descartes vorausgesetzten Kontingenzbegriff in seiner Genese rekonstruiert – eine Begriffsgeschichte des Terminus "contingentia" stellt noch immer ein Desiderat ...
Ce texte constitue le chapitre 12 du livre de J. S. Goldstein, Long Cycles : Prosperity and War in the Modern Age, New Haven, Yale University Press, 1988. L'ensemble du livre est accessible ici. - Économie et Marxisme – Nouvel article.
Humans and animals make inferences about the world under limited time and knowledge. In contrast, many models of rational inference treat the mind as a Laplacean Demon, equipped with unlimited time, knowledge, and computational might. Following H. Simon's notion of satisficing, the authors have proposed a family of algorithms based on a simple psychological mechanism: one-reason decision making. These fast and frugal algorithms violate fundamental tenets of classical rationality: They neither look up nor integrate all information. By computer simulation, the (...) authors held a competition between the satisficing "Take The Best" algorithm and various "rational" inference procedures. The Take The Best algorithm matched or outperformed all competitors in inferential speed and accuracy. This result is an existence proof that cognitive mechanisms capable of successful performance in the real world do not need to satisfy the classical norms of rational inference. (shrink)
In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann’s analysis, the essence of which I shall review here, is basically correct. The most famous criticisms of Boltzmann’s later work on the subject have little merit. Most twentieth century innovations – such as the identiﬁcation of the state of a physical system with a probability distribution on its phase space, (...) of its thermodynamic entropy with the Gibbs entropy of , and the invocation of the notions of ergodicity and mixing for the justiﬁcation of the foundations of statistical mechanics – are thoroughly misguided. (shrink)
Bohmian mechanics and the Ghirardi-Rimini-Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about 'matter' moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of (...) space-time points. The role of the wave function then is to govern the motion of the matter. (shrink)
Bohmian mechanics, which is also called the de Broglie-Bohm theory, the pilot-wave model, and the causal interpretation of quantum mechanics, is a version of quantum theory discovered by Louis de Broglie in 1927 and rediscovered by David Bohm in 1952. It is the simplest example of what is often called a hidden variables interpretation of quantum mechanics. In Bohmian mechanics a system of particles is described in part by its wave function, evolving, as usual, according to Schrödinger's equation. However, the (...) wave function provides only a partial description of the system. This description is completed by the specification of the actual positions of the particles. The latter evolve according to the.. (shrink)
What is it to believe something might be the case? We develop a puzzle that creates difficulties for standard answers to this question. We go on to propose our own solution, which integrates a Bayesian approach to belief with a dynamic semantics for epistemic modals. After showing how our account solves the puzzle, we explore a surprising consequence: virtually all of our beliefs about what might be the case provide counterexamples to the view that rational belief is closed under logical (...) implication. (shrink)
A major disagreement between different views about the foundations of quantum mechanics concerns whether for a theory to be intelligible as a fundamental physical theory it must involve a ‘primitive ontology’ (PO), i.e. variables describing the distribution of matter in four-dimensional space–time. In this article, we illustrate the value of having a PO. We do so by focusing on the role that the PO plays for extracting predictions from a given theory and discuss valid and invalid derivations of predictions. To (...) this end, we investigate a number of examples based on toy models built from the elements of familiar interpretations of quantum theory. (shrink)
That all pleasure is good and all pain bad in itself is an eternally true ethical principle. The common claim that some pleasure is not good, or some pain not bad, is mistaken. Strict particularism (ethical decisions must be made case by case; there are no sound universal normative principles) and relativism (all good and bad are relative to society) are among the ethical theories we may refute through an appeal to pleasure and pain. Daniel Dennett, Philippa Foot, R M (...) Hare, Gilbert Harman, Immanuel Kant, J. L. Mackie, and Jean-Paul Sartre are among the many philosophers addressed. (shrink)
outrageous remarks about contradictions. Perhaps the most striking remark he makes is that they are not false. This claim first appears in his early notebooks (Wittgenstein 1960, p.108). In the Tractatus, Wittgenstein argued that contradictions (like tautologies) are not statements (Sätze) and hence are not false (or true). This is a consequence of his theory that genuine statements are pictures.
Schrödinger’s first proposal for the interpretation of quantum mechanics was based on a postulate relating the wave function on configuration space to charge density in physical space. Schrödinger apparently later thought that his proposal was empirically wrong. We argue here that this is not the case, at least for a very similar proposal with charge density replaced by mass density. We argue that when analyzed carefully, this theory is seen to be an empirically adequate many-worlds theory and not an empirically (...) inadequate theory describing a single world. Moreover, this formulation—Schrödinger’s first quantum theory—can be regarded as a formulation of the many-worlds view of quantum mechanics that is ontologically clearer than Everett’s. (shrink)
The most puzzling issue in the foundations of quantum mechanics is perhaps that of the status of the wave function of a system in a quantum universe. Is the wave function objective or subjective? Does it represent the physical state of the system or merely our information about the system? And if the former, does it provide a complete description of the system or only a partial description? We shall address these questions here mainly from a Bohmian perspective, and shall (...) argue that part of the difficulty in ascertaining the status of the wave function in quantum mechanics arises from the fact that there are two different sorts of wave functions involved. The most fundamental wave function is that of the universe. From it, together with the configuration of the universe, one can define the wave function of a subsystem. We argue that the fundamental wave function, the wave function of the universe, has a law-like character. (shrink)
Bohmian mechanics is a theory about point particles moving along trajectories. It has the property that in a world governed by Bohmian mechanics, observers see the same statistics for experimental results as predicted by quantum mechanics. Bohmian mechanics thus provides an explanation of quantum mechanics. Moreover, the Bohmian trajectories are defined in a non-conspiratorial way by a few simple laws.
Quantum philosophy, a peculiar twentieth-century malady, is responsible for most of the conceptual muddle plaguing the foundations of quantum physics. When this philosophy is eschewed, one naturally arrives at Bohmian mechanics, which is what emerges from Schrodinger's equation for a nonrelativistic system of particles when we merely insist that 'particles' means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. The quantum formalism emerges when measurement situations are (...) analyzed according to this theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with quantum theory simply evaporate.Bohr's ... approach to atomic problems ... is really remarkable. He is completely convinced that any understanding in the usual sense of the word is impossible. Therefore the conversation is almost immediately driven into philosophical questions, and soon you no longer know whether you really take the position he is attacking, or whether you really must attack the position he is defending. (shrink)
In Bohmian mechanics elementary particles exist objectively, as point particles moving according to a law determined by a wavefunction. In this context, questions as to whether the particles of a certain species are real---questions such as, Do photons exist? Electrons? Or just the quarks?---have a clear meaning. We explain that, whatever the answer, there is a corresponding Bohm-type theory, and no experiment can ever decide between these theories. Another question that has a clear meaning is whether particles are intrinsically distinguishable, (...) i.e., whether particle world lines have labels indicating the species. We discuss the intriguing possibility that the answer is no, and particles are points---just points. (shrink)
Despite its extraordinary predictive successes, quantum mechanics has, since its inception some seventy years ago, been plagued by conceptual di culties. The basic problem, plainly put, is this: It is not at all clear what quantum mechanics is about. What, in fact, does quantum mechanics describe?
Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schr¨ odinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψ its configuration is typically (...) random, with probability density ρ given by |ψ|2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, naturally emerges in Bohmian mechanics from the analysis of “measurements.” This analysis reveals the status of operators as observables in the description of quantum phenomena, and facilitates a clear view of the range of applicability of the usual quantum mechanical formulas. (shrink)
In  John S. Bell proposed how to associate particle trajectories with a lattice quantum field theory, yielding what can be regarded as a |Ψ|2-distributed Markov process on the appropriate configuration space. A similar process can be defined in the continuum, for more or less any regularized quantum field theory; such processes we call Bell-type quantum field theories. We describe methods for explicitly constructing these processes. These concern, in addition to the definition of the Markov processes, the efficient calculation of (...) jump rates, how to obtain the process from the processes corresponding to the free and interaction Hamiltonian alone, and how to obtain the free process from the free Hamiltonian or, alternatively, from the one-particle process by a construction analogous to “second quantization.” As an example, we consider the process for a second quantized Dirac field in an external electromagnetic field. (shrink)
Against Hume and Epicurus I argue that our selection of pleasure, pain and other objects as our ultimate ends is guided by reason. There are two parts to the explanation of our attraction to pleasure, our aversion to pain, and our consequent preference of pleasure to pain: 1. Pleasure presents us with reason to seek it, pain presents us reason to avoid it, and 2. Being intelligent, human beings (and to a degree, many animals) are disposed to be guided by (...) reason, and hence by what there is reason to choose, seek, and prefer, when they act. (shrink)
A syntactically correct number-specification may fail to specify any number due to underspecification. For similar reasons, although each sentence in the Yablo sequence is syntactically perfect, none yields a statement with any truth-value. As is true of all members of the Liar family, the sentences in the Yablo sequence are so constructed that the specification of their truth-conditions is vacuous; the Yablo sentences fail to yield statements. The ‘revenge’ problem is easily defused. The solution to the semantical paradoxes offered here (...) revives the mediaeval cassatio approach, one that largely disappeared due to its incomprehending rejection by influential contemporary writers such as William Shyreswood and Thomas Bradwardine. The diagnosis readily extends to the set-theoretic paradoxes. (shrink)
Bohmian trajectories have been used for various purposes, including the numerical simulation of the time-dependent Schr¨ odinger equation and the visualization of time-dependent wave functions. We review the purpose they were invented for: to serve as the foundation of quantum mechanics, i.e., to explain quantum mechanics in terms of a theory that is free of paradoxes and allows an understanding that is as clear as that of classical mechanics. Indeed, they succeed in serving that purpose in the context of a (...) theory known as Bohmian mechanics, to which this article is an introduction. (shrink)
We consider the possibility that all particles in the world are fundamentally identical, i.e., belong to the same species. Different masses, charges, spins, flavors, or colors then merely correspond to different quantum states of the same particle, just as spin-up and spin-down do. The implications of this viewpoint can be best appreciated within Bohmian mechanics, a precise formulation of quantum mechanics with particle trajectories. The implementation of this viewpoint in such a theory leads to trajectories different from those of the (...) usual formulation, and thus to a version of Bohmian mechanics that is inequivalent to, though arguably empirically indistinguishable from, the usual one. The mathematical core of this viewpoint is however rather independent of the detailed dynamical scheme Bohmian mechanics provides, and it amounts to the assertion that the configuration space for N particles, even N “distinguishable particles,” is the set of all N -point subsets of physical 3-space. (shrink)
Conway and Kochen have presented a “free will theorem” [4, 6] which they claim shows that “if indeed we humans have free will, then [so do] elementary particles.” In a more precise fashion, they claim it shows that for certain quantum experiments in which the experimenters can choose between several options, no deterministic or stochastic model can account for the observed outcomes without violating a condition “MIN” motivated by relativistic symmetry. We point out that for stochastic models this conclusion is (...) not correct, while for deterministic models it is not new. In the way the free will theorem is formulated and proved, it only concerns deterministic models. But Conway and Kochen have argued [4, 5, 6, 7] that “randomness can’t help,” meaning that stochastic models are excluded as well if we insist on the conditions “SPIN”, “TWIN”, and “MIN”. We point out a mistake in their argument. Namely, the theorem is of the form deterministic model with SPIN & TWIN & MIN ⇒ contradiction , (1) and in order to derive the further claim, which is of the form stochastic model with SPIN & TWIN & MIN ⇒ contradiction , (2) Conway and Kochen propose a method for converting any stochastic model into a deterministic one . (shrink)
We consider an isolated, macroscopic quantum system. Let H be a microcanonical “energy shell,” i.e., a subspace of the system’s Hilbert space spanned by the (finitely) many energy eigenstates with energies between E and E + δE. The thermal equilibrium macro-state at energy E corresponds to a subspace Heq of H such that dim Heq/ dim H is close to 1. We say that a system with state vector ψ H is in thermal equilibrium if ψ is “close” to Heq. (...) We show that for “typical” Hamiltonians with given eigenvalues, all initial state vectors ψ0 evolve in such a way that ψt is in thermal equilibrium for most times t. This result is closely related to von Neumann’s quantum ergodic theorem of 1929. (shrink)
A source of much difficulty and confusion in the interpretation of quantum mechanics is a naive realism about operators. By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to the all too casual talk about measuring operators that occurs when the subject is quantum mechanics. Without a specification of what should be meant by measuring a quantum observable, such an expression can have no clear meaning. A definite specification is provided by (...) Bohmian mechanics, a theory that emerges from Schrödinger's equation for a system of particles when we merely insist that particles means particles. Bohmian mechanics clarifies the status and the role of operators as observables in quantum mechanics by providing the operational details absent from standard quantum mechanics. It thereby allows us to readily dismiss all the radical claims traditionally enveloping the transition from the classical to the quantum realm — for example, that we must abandon classical logic or classical probability. The moral is rather simple: Beware naive realism, especially about operators! (shrink)
In this paper I argue that there is a preface paradox for intention. The preface paradox for intention shows that intentions do not obey an agglomeration norm, requiring one to intend conjunctions of whatever else one intends. But what norms do intentions obey? I will argue that intentions come in degrees. These partial intentions are governed by the norms of the probability calculus. First, I will give a dispositional theory of partial intention, on which degrees of intention are the degrees (...) to which one possesses the dispositions characteristic of full intention. I will use this dispositional theory to defend probabilism about intention. Next, I will offer a more general argument for probabilism about intention. To do so, I will generalize recent decision theoretic arguments for probabilism from the case of belief to the case of intention. (shrink)
Pleasure is one of the strongest candidates for an occurrence that might be good, in some respect, unconditionally. Malicious pleasure is one of the most often cited alleged counter-examples to pleasure’s being an unconditional good. Correctly evaluating malicious pleasure is more complex than people realize. I defend pleasure’s unconditionally good status from critics of malicious pleasure.