The centerpiece of Jeffrey Bub's book Interpreting the Quantum World is a theorem (Bub and Clifton 1996) which correlates each member of a large class of no-collapse interpretations with some 'privileged observable'. In particular, the Bub-Clifton theorem determines the unique maximal sublattice L(R,e) of propositions such that (a) elements of L(R,e) can be simultaneously determinate in state e, (b) L(R,e) contains the spectral projections of the privileged observable R, and (c) L(R,e) is picked out by R and e (...) alone. In this paper, we explore the issue of maximal determinate sets of observables using the tools provided by the algebraic approach to quantum theory; and we call the resulting algebras of determinate observables, "maximal *beable* subalgebras". The capstone of our exploration is a generalized version of Bub and Clifton's theorem that applies to arbitrary (i.e., both mixed and pure) quantum states, to Hilbert spaces of arbitrary (i.e., both finite and infinite) dimension, and to arbitrary observables (including those with a continuous spectrum). Moreover, in the special case covered by the original Bub-Clifton theorem, our theorem reproduces their result under strictly weaker assumptions. This added level of generality permits us to treat several topics that were beyond the reach of the original Bub-Clifton result. In particular: (a) We show explicitly that a (non-dynamical) version of the Bohm theory can be obtained by granting privileged status to the position observable. (b) We show that Clifton's (1995) characterization of the Kochen-Dieks modal interpretation is a corollary of our theorem in the special case when the density operator is taken as the privileged observable. (c) We show that the 'uniqueness' demonstrated by Bub and Clifton is only guaranteed in certain special cases -- viz., when the quantum state is pure, or if the privileged observable is compatible with the density operator. We also use our results to articulate a solid mathematical foundation for certain tenets of the orthodox Copenhagen interpretation of quantum theory. For example, the uncertainty principle asserts that there are strict limits on the precision with which we can know, simultaneously, the position and momentum of a quantum-mechanical particle. However, the Copenhagen interpretation of this fact is not simply that a precision momentum measurement necessarily and uncontrollably disturbs the value of position, and vice-versa; but that position and momentum can never in reality be thought of as simultaneously determinate. We provide warrant for this stronger 'indeterminacy principle' by showing that there is no quantum state that assigns a sharp value to both position and momentum; and, a fortiori, that it is mathematically impossible to construct a beable algebra that contains both the position observable and the momentum observable. We also prove a generalized version of the Bub-Clifton theorem that applies to "singular" states (i.e., states that arise from non-countably-additive probability measures, such as Dirac delta functions). This result allows us to provide a mathematically rigorous reconstruction of Bohr's response to the original EPR argument -- which makes use of a singular state. In particular, we show that if the position of the first particle is privileged (e.g., as Bohr would do in a position measuring context), the position of the second particle acquires a definite value by virtue of lying in the corresponding maximal beable subalgebra. But then (by the indeterminacy principle) the momentum of the second particle is not a beable; and EPR's argument for the simultaneous reality of both position and momentum is undercut. (shrink)

give a proof of the existence of nonlocal influences acting on correlated spin-1/2 particles in the singlet state which does not require any particular interpretation of quantum mechanics (QM). (Except Stapp holds that the proof fails under a many-worlds interpretation of QM—a claim we analyse in 1.2.) Recently, in responding to Redhead's ([1987], pp. 90-6) criticism that the Stapp 1 proof fails under an indeterministic interpretation of QM, Stapp [1989] (henceforth Stapp 2), has revised the logical structure of his proof (...) including its crucial locality assumption. Our main aim is to show that this revision is a step in the wrong direction because it faces two difficulties which undermine the resulting proof's significance (3.1) and validity (3. 2). We also clarify and extend the Stapp 1 proof (1. 1) with the aid of Lewis' analysis of counterfactuals (1. 2) and causal dependence (2. 2 and 2. 3). In so doing, we are able to identify two new defects in the Stapp 1 proof (1. 3 and 2. 1) in addition to corroborating Redhead's criticism (2. 2). Also, the additional assumptions which save the Stapp 1 proof's validity are detailed (2. 3) and some new difficulties for the determinist are pointed out by exploiting a slightly extended version of the proof (2. 4). In providing this full analysis of the Stapp 1 proof, we also construct the necessary framework within which to provide a critique of Stapp 2's proof (3). *Portions of this paper were presented by R. K. Clifton to the 1988 British Society for the Philosophy of Science Conference at the University of Southampton. R. K. Clifton wishes to thank the Natural Sciences and Engineering Research Council of Canada, the Royal Commission for the Exhibition of 1851, and the Governing Body of Peterhouse at Cambridge University for support during this work. (shrink)

Our paper ‘A new cosmological argument’ gave an argument for the existence of God making use of the weak Principle of Sufficient Reason (W-PSR) which states that for every proposition p, if p is true, then it is possible that there is an explanation for p. Recently, Graham Oppy, as well as Kevin Davey and Rob Clifton, have criticized the argument. We reply to these criticisms. The most interesting kind of criticism in both papers alleges that the W-PSR can (...) be justifiably denied by the atheist, and constitutes no improvement on the strong Principle of Sufficient Reason (S-PSR) which claims that every true proposition in fact has an explanation. The criticism is predicated on the fact that it can be shown that the W-PSR entails the S-PSR. We argue that the W-PSR's plausibility remains despite the criticisms. From this it can be seen to follow that the entailment relation between the W-PSR and the S-PSR gives one reason to believe the S-PSR. (shrink)

The Bell–Kochen–Specker theorem shows that, in any Hilbert space of dimension of at least 3, it is impossible to assign noncontextual definite values to all observables in such a way that the quantum-mechanical predictions are reproduced. This leaves open the issue of what subsets of observables may be assigned definite values. Clifton has shown that, for a system of at least two continuous degrees of freedom, it is not possible to assign simultaneous noncontextual values to two coordinates and their (...) conjugate momenta. In this Letter, it is shown that, for a system of a single continuous degree of freedom, it is not possible to assign noncontextual values to the coordinate and its conjugate momenta that satisfy a continuity assumption herein called the ‘ -Product Rule’.  2002 Elsevier Science B.V. All rights reserved. (shrink)

We show that three fundamental information-theoretic constraints -- the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment -- suffice to entail that the observables and state space of a physical theory are quantum-mechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a remaining open question about (...) nonlocality and bit commitment. (shrink)

We use the comparative method of language acquisition research to investigate children’s expression of directional expressions in two Eastern Mayan languages – K’iche’ and Mam. Both languages add clitics derived from verbs such as ‘go’ and ‘stay’ to their verb complex to express the direction an agent takes in the course of accomplishing an event. Historic changes to the prosodic structure of the verb complex in both languages explain why the directional clitics are predominately postverbal in K’iche’, while they occur (...) in preverbal and postverbal positions in Mam. Prosody explains why K’iche’ children initially produce clitics postverbally, while Mam children produce clitics both preverbally and postverbally. Prosody also explains why the children acquiring both languages produce morphemes in the verb complex that are relatively infrequent but prosodically prominent, while omitting obligatory morphemes that are prosodically weak. (shrink)

In this paper we argue that there are valuable consonances between democratic theory and music theory, and between democratization and musical performance and enjoyment. We suggest that this connection is not as trite as it may first appear, but that, since democracy is learned and practiced in a myriad ofways, music is one such place to learn democratic citizenship. The paper begins with a normative account of democratic theory that is present in two movements. The first, “foundations,” explicates the essential (...) components, criteria, and conditions of democracy. The second, “flows,” addresses the dynamism of democratization. Here is an account of what democracy looks like in action. We then turn to an explication of music theory and improvisation. Here, we focus on jazz as a way to hear the kind of interplay, responsiveness, accountability, discipline, and extemporaneousness that occurs in good jazz, and in authentic (radical) democracy. (shrink)

We study thorn forking and rosiness in the context of continuous logic. We prove that the Urysohn sphere is rosy (with respect to finitary imaginaries), providing the first example of an essentially continuous unstable theory with a nice notion of independence. In the process, we show that a real rosy theory which has weak elimination of finitary imaginaries is rosy with respect to finitary imaginaries, a fact which is new even for discrete first-order real rosy theories.

We develop a basic theory of rosy groups and we study groups of small Uþ-rank satisfying NIP and having finitely satisfiable generics: Uþ-rank 1 implies that the group is abelian-by-finite, Uþ-rank 2 implies that the group is solvable-by-finite, Uþ-rank 2, and not being nilpotent-by-finite implies the existence of an interpretable algebraically closed field.

This article focuses on the relationship between evaluations of beauty and the ethics of living well. Separating these ideas typically involves understating how racism and patriarchy shape wider cultural and aesthetic sensibilities. I counter this tendency by foregrounding the precarity of vulnerable black children and the importance of self‐love in their efforts to flourish. My strategy involves placing Toni Morrison in conversation with Alexander Nehamas and Harry Frankfurt, philosophers who have carefully engaged the topics of beauty and love. By situating (...) aesthetic judgment within ongoing practices of social formation and political contestation, I reveal the importance of linking beauty with practices of self‐regard while also detailing my criticisms of thinkers who downplay their significance. The effect is to position Morrison as an instructive guide for scholars interested in aesthetics, ethics, and politics. (shrink)

We define a notion of residue field domination for valued fields which generalizes stable domination in algebraically closed valued fields. We prove that a real closed valued field is dominated by the sorts internal to the residue field, over the value group, both in the pure field and in the geometric sorts. These results characterize forking and þ-forking in real closed valued fields (and also algebraically closed valued fields). We lay some groundwork for extending these results to a power-bounded T-convex (...) theory. (shrink)

A survey of university students tested whether committing animal abuse during childhood was related to approval of interpersonal violence against children and women in families. Respondents who had abused an animal as children or adolescents were significantly more likely to support corporal punishment, even after controlling for frequency of childhood spanking, race, biblical literalism, and gender. Those who had perpetrated animal abuse were also more likely to approve of a husband slapping his wife. Engaging in childhood violence against less powerful (...) beings— animals—may generalize to the acceptance of violence against less powerful members of families and society—women and children. This paper discusses the implications of this process. (shrink)

In this paper, we prove the following:Theorem. Let M be a rosy dependent theory and letp,pbe non-þ-forking extensions ofp∈Switha0a1; assume thatp∪pis consistent and thata0,a1start a þ-independent indiscernible sequence. Thenp∪pis a non-þ-forking extension ofp.We also provide an example to show that the result is not true without assuming NIP.

Only recently have sociologists considered the role of nonhuman animals in human society. The few studies undertaken of battered women and their animal companions have revealed high rates of animal abuse co-existing with domestic violence. This study examines several aspects of the relationship between humans and animals in violent homes. The study explored the role of companion animals in the abusive relationship through in-depth, semi-structured interviews with clients at a battered women's shelter. In particular, the study focused on the use (...) of companion animals by women's violent partners to control, hurt, and intimidate the women; the responses of the animals to the women's victimization; and the role of pets as human surrogates and the resulting symbolic interaction between human and nonhuman family members. The significance of the findings for family violence research and application are discussed, as well as the broader implications for sociological investigation of human-animal interaction. (shrink)

Sociologists have largely ignored the role of animals in society. This article argues that human-animal interaction is a topic worthy of sociological consideration and applies a sociological analysis to one problematic aspect of human-animal relationships - animal cruelty. The article reformulates animal cruelty, traditionally viewed using a psychopathological model, from a sociological perspective.The article identifies social and cultural factors related to the occurrence of animal cruelty. Ultimately, animal cruelty is a serious social problem that deserves attention in its own right, (...) not just because of its association with human violence. (shrink)