Let NBG be von Neumann-Bernays-Gödel set theory without the axiom of choice and let NBGA be the modification which allows atoms. In this paper we consider some of the well-known class or global forms of the wellordering theorem, the axiom of choice, and maximal principles which are known to be equivalent in NBG and show they are not equivalent in NBGA.
We show that it is not possible to construct a Fraenkel-Mostowski model in which the axiom of choice for well-ordered families of sets and the axiom of choice for sets are both true, but the axiom of choice is false.
In Zermelo-Fraenkel set theory with the axiom of choice every set has the same cardinal number as some ordinal. Von Rimscha has weakened this condition to “Every set has the same cardinal number as some transitive set”. In set theory without the axiom of choice, we study the deductive strength of this and similar statements introduced by von Rimscha.
Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2math image and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second.
In this paper we study some statements similar to the Partition Principle and the Trichotomy. We prove some relationships between these statements, the Axiom of Choice, and the Generalized Continuum Hypothesis. We also prove some independence results. MSC: 03E25, 03E50, 04A25, 04A50.
This is a continuation of [2]. We study the Tychonoff Compactness Theorem for various definitions of compactness and for various types of spaces . We also study well ordered Tychonoff products and the effect that the multiple choice axiom has on such products.
We investigate the set theoretical strength of some properties of normality, including Urysohn's Lemma, Tietze-Urysohn Extension Theorem, normality of disjoint unions of normal spaces, and normality of Fσ subsets of normal spaces.
We study statements about countable and well-ordered unions and their relation to each other and to countable and well-ordered forms of the axiom of choice. Using WO as an abbreviation for “well-orderable”, here are two typical results: The assertion that every WO family of countable sets has a WO union does not imply that every countable family of WO sets has a WO union; the axiom of choice for WO families of WO sets does not imply that the countable union (...) of countable sets is WO. (shrink)
We study conditions for a topological space to be metrizable, properties of metrizable spaces, and the role the axiom of choice plays in these matters.
This challenging and provocative book argues against much contemporary orthodoxy in philosophy and the social sciences by showing why objectivity in the domain of ethics is really no different from the objectivity of scientific knowledge. Many philosophers and social scientists have challenged the idea that we act for objectively authoritative reasons. Jean Hampton takes up the challenge by undermining two central assumptions of this contemporary orthodoxy: that one can understand instrumental reasons without appeal to objective authority, and that the (...) adoption of the scientific world view requires no such appeal. In the course of the book Jean Hampton examines moral realism, the general nature of reason and norms, internalism and externalism, instrumental reasoning, and the expected utility model of practical reasoning. The book is sure to prove to be a seminal work in the theory of rationality that will be read by a broad swathe of philosophers and social scientists. (shrink)
An obituary of Jean E. Hampton (1954-1996) by the editors of Economics and Philosophy. At the time of her premature death, Jean was serving as a member of the Editorial Board of the journal.
In three experiments we tested hypotheses derived from the goal specificity literature using a real-world physics task. In the balance-scale paradigm participants predict the state of the apparatus based on a configuration of weights at various distances from the fulcrum. Non-specific goals (NSG) have been shown to encourage hypothesis testing, which facilitates rule discovery, whereas specific goals (SG) do not. We showed that this goal specificity effect depends on task difficulty. The NSG strategy led to rule induction among some participants. (...) Among non-discoverers, SG participants were faster and more accurate on difficult problems than NSG participants. The use of misleading exemplars (scale configurations that obscured the rule governing outcomes) led to fixation on inappropriate hypotheses for NSG but not SG participants. When more diagnostic learning exemplars were used, NSG non-discoverers still performed worse than SG participants on difficult problems. SG participants also outperformed NSG participants on a post-test of difficult problems. These findings qualify the generality of goal specificity effects. (shrink)
Psychotherapy clients read two consumer-oriented brochures: a general brochure on psychology and a brochure on the topic of client-therapist intimacy. Half of the participants read the general brochure first and the brochure on client-therapist intimacy second, and half the participants did the reverse. Participants reported favorable reactions to the brochures, indicating they thought both should be made available to psychotherapy clients; that neither were too long, too sensitive, or too difficult to read; and that the brochures should be made available (...) early during the therapeutic process. After reading the client-therapist intimacy brochure, participants also showed some changes in Likert-type scores measuring attitudes regarding intimate contact between clients and therapists. Although participants were more negative about issues of sexual misconduct after reading the client-therapist intimacy brochure, they did not indicate a decrease in trust of therapists, nor did they indicate a greater likelihood of filing a false complaint. We concluded that therapists' reservations about presenting clients with factual information regarding therapist sexual exploitation of clients are not empirically founded. (shrink)
Experiments show that psi differs from known physical processes in a variety of ways, and these differences are described herein. Because of these, psi cannot be accounted for in terms of presently known physical laws. A number of theories, of which we review a sampling, suggest ways in which known physical laws might be expanded in order to account for psi. However, there is no agreement on which of these theories, if any, will ultimately provide a general explanation. A further (...) problem in studying psi is that it is elusive, i.e., methods are not presently known by which it can be reliably produced. However, if psi is real, its study can open the door to a new frontier of knowledge and contribute to our understanding of consciousness. (shrink)
The term action of consciousness is used to refer to an influence, such as psychokinesis or free will, that produces an effect on matter that is correlated to mental intention, but not completely determined by physical conditions. Such an action could not conserve energy. But in that case, one wonders why, when highly accurate measurements are done, occasions of non-conserved energy (generated perhaps by unconscious PK) are not detected. A possible explanation is that actions of consciousness take place within the (...) limits of the uncertainty principle. Two models are reviewed that, using the latter assumption, propose that consciousness can originate an action potential in the brain. One (that of Eccles) uses the latter assumption only, and the other (that of Burns) additionally assumes that consciousness acts, within those limits, by ordering quantum fluctuations. (shrink)
Recent models of consciousness are reviewed which explore the relationship of consciousness to physical laws; many of these also explore the relationship of consciousness to biological findings. Issues investigated by these models are discussed, with the issues framed in a general way in order to provide a comparison between the models. In Part I the issues discussed are: (1) What is the causal relationship between consciousness and the physical world (physicalism, dualism, etc.)? and (2) What physical characteristics are associated with (...) the interface between brain/physical world and consciousness? (shrink)
It is shown that entropy increase in thermodynamic systems can plausibly be accounted for by the random action of vacuum radiation. A recent calculation by Rueda using stochastic electrodynamics (SED) shows that vacuum radiation causes a particle to undergo a rapid Brownian motion about its average dynamical trajectory. It is shown that the magnitude of spatial drift calculated by Rueda can also be predicted by assuming that the average magnitudes of random shifts in position and momentum of a particle correspond (...) to the lower limits of the uncertainty relation. The latter analysis yields a plausible expression for the shift in momentum caused by vacuum radiation. It is shown that when the latter shift in momentum is magnified in particle interactions, the fractional change in each momentum component is on the order of unity within a few collision times, for gases and (plausibly) for denser systems over a very broad range of physical conditions. So any system of particles in this broad range of conditions would move to maximum entropy, subject to its thermodynamic constraints, within a few collision times. It is shown that the spatial drift caused by vacuum radiation, as predicted by the above SED calculation, can be macroscopic in some circumstances, and an experimental test of this effect is proposed. Consistency of the above results with quantum mechanics is discussed, and it is shown that the diffusion constant associated with the above Brownian drift is the same as that used in stochastic interpretations of the Schrödinger equation. (shrink)
Even if all of the content of conscious experience is encoded in the brain, there is a considerable difference between the view that consciousness does independent processing and the view that it does not. If all processing is done by the brain, then conscious experience is unnecessary and irrelevant to behavior. If consciousness performs a function, then its association with particular aspects of brain processing reflect its functional use in determining behavior. However, if consciousness does perform a function, it cannot (...) be described entirely by known physical laws. Rather, even if the content of conscious experience follows physical encoding in the brain, consciousness must then be governed in part by a principle which is different from any known physical principle. (shrink)
Two forms of independent action by consciousness have been proposed by various researchers – free will and holistic processing. (Holistic processing contributes to the formation of behavior through the holistic use of brain programs and encoding.) The well-known experiment of Libet et al. (1983) implies that if free will exists, its action must consist of making a selection among alternatives presented by the brain. As discussed herein, this result implies that any physical changes mind can produce in the brain are (...) very small, and this in turn implies that holistic processing would also act to select among brain programs. The latter process would contribute to flexibility of behavior, which would therefore be an indication of the possible presence of consciousness in an animal. Because locomotion requires response to varying and unpredictable conditions, the above conclusions support the idea that simple forms of consciousness appear very early in the evolutionary line of the animal kingdom. (shrink)
Margaret Brazier has argued that, in the literature on reproductive technology, women's “right” to reproduce is privileged, pushed, and subordinated to patriarchal values in such a way that it amounts to women's old “duty” to reproduce, dressed up in modern guise. I agree that there are patriarchal assumptions made in discussions of whether women have a right to select which embryos to implant or which fetuses to carry to term. Forcing ourselves to see women as active, rational decisionmakers tends to (...) counteract any lingering patriarchal assumptions. But rational decisionmaking requires information. Voting wisely requires information about the candidates. Taking women's reproductive rights seriously means taking seriously women's need for relevant information to make rational decisions, including decisions about which embryos to implant or alter. I argue that preimplantation genetic profiles and prenatal test information should be made available to prospective parents, especially prospective mothers, unless doing so threatens to harm the resulting child or the larger society in specifiable and important ways. (shrink)
The possibility of empirical test is discussed with respect to three issues: (1) What is the ontological relationship between consciousness and the brain/physical world? (2) What physical characteristics are associated with the mind/brain interface? (3) Can consciousness act on the brain independently of any brain process?
