This paper uses the notion of Galois-connection to examine the relation between valuation-spaces and logics. Every valuation-space gives rise to a logic, and every logic gives rise to a valuation space, where the resulting pair of functions form a Galois-connection, and the composite functions are closure-operators. A valuation-space (resp., logic) is said to be complete precisely if it is Galois-closed. Two theorems are proven. A logic is complete if and only if it is reflexive and transitive. A valuation-space is complete (...) if and only if it is closed under formation of super-valuations. (shrink)

Logical matrices for orthomodular logic are introduced. The underlying algebraic structures are orthomodular lattices, where the conditional connective is the Sasaki arrow. An axiomatic calculusOMC is proposed for the orthomodular-valid formulas.OMC is based on two primitive connectives — the conditional, and the falsity constant. Of the five axiom schemata and two rules, only one pertains to the falsity constant. Soundness is routine. Completeness is demonstrated using standard algebraic techniques. The Lindenbaum-Tarski algebra ofOMC is constructed, and it is shown to be (...) an orthomodular lattice whose unit element is the equivalence class of theses ofOMC. (shrink)

The notion of relative compability is introduced, according to which compatibility is construed as relative to individual quantum states. The compatibility domain of two observablesA, B is defined to be the set com(A, B) of states relative to whichA andB are compatible. Three basic categories of relative compatibility are then defined according to the character of com(A, B): absolute compatibility (ordinary compatibility), absolute incompatibility, and partial compatibility. Then com(A, B) is seen to be a subspace of Hilbert space invariant underA (...) andB; being a subspace, it corresponds to a quantum binary observable (projection), denotedc(A, B). IfA andB are themselves binary observables, thenc(A, B) is expressible as a quantum logical compound ofA andB using the lattice operations meet, join, and orthocomplement. This suggests extending the notion of relative compatibility to the theory of orthomodular lattices, as well as to more general lattice-theoretic formulations of quantum mechanics. (shrink)

The interpretation of quantum mechanics is discussed from the viewpoint of quantum logic (QL). QL is understood to concern the possible properties that can be ascribed to a physical system SYS. The micro-state of SYS at any given moment t is identified with the set of all properties actualized by SYS at time t. Minimal adequacy requirements are proposed for all interpretations of micro-states. A strict interpretation is defined to be one according to which the properties ascribable to SYS are (...) individuated by the projection operators on the associated Hilbert space. Two strict interpretations are examined. Kochen's interpretation is also discussed, and it is argued that it is not a strict interpretation. (shrink)

This paper presents a general formal semantic scheme for the interpretation of quantum mechanics, in terms of which van Fraassen's Copenhagen and anti-Copenhagen variants of the modal interpretation are examined. The general character of the modal interpretation is motivated in a discussion of classical statistical mechanics, the distinction being made between statistical states and micro-states. The notion of a quasi-classical (micro) state is introduced in a discussion of the theorem of Gleason and Kochen and Specker. It is shown that, according (...) to the anti-Copenhagen variant, the class of micro-states coincides with a special class of quasi-classical states. The paper concludes with two general criticisms of the anti-Copenhagen variant. (shrink)

Volume XXIX contains papers and commentaries presented to the Boston Area Colloquium in Ancient Philosophy during academic year 2012-13. The papers feature Plato's Republic and Timaeus, examine Aristotle on generation, analogy and method, and analyze Proclus on first principles.

A scholarly study of the Neoplatonic philosopher Plotinus (204/5-270) and his understanding of the soul; its chapters include: beauty and the good, forgetting the self, matter as indefinite and incorporeal, omnipresence and incorporeality, and omnipresence and transcendence. The work confirms much recent scholarly consensus on Plotinus, but many of the author's interpretations and general conclusions also give constructive challenges to some existing modes of understanding Plotinus's thought. The arguments and their textual evidence, with the accompanying Greek, provide the reader with (...) direct evidence for testing these conclusions as well as appreciating the nature of Plotinus' philosophizing. (shrink)

Management plays an important role in reinforcing ethics in organizations. To support this aim, managers must use incentive and goal programs in ethical ways. This study examines experimentally the potential ethical costs associated with incentive-driven and goal-induced employee behavior from a managerial perspective. In a quasi-experimental setting, 243 MBA students with significant professional work experience evaluated a hypothetical employee’s ethical behavior under incentive pay systems modeled on a business case. In the role of the employee’s manager, participants evaluated the ethicality (...) of the employee’s incentive-driven and goal-induced ethical/unethical behavior and the outcomes of behavior, with consequences that were either favorable or unfavorable to the organization. The results indicated that participants discounted the ethical considerations of incentive-driven and goal-induced behavior when consequences were favorable to the organization. Participants’ morals and outcome orientations were also significantly related to their ethical judgments and intentions to intervene. The implications of these findings for research and practice are discussed. (shrink)

Pickering & Garrod (P&G) consider the possibility that inner speech might be a product of forward production models. Here I consider the idea of inner speech as a forward model in light of empirical work from the past few decades, concluding that, while forward models could contribute to it, inner speech nonetheless requires activity from the implementers.

The sociobiology of bacteria, largely unappreciated and ignored by the microbiology research community two decades ago is now a major research area, catalyzed to a significant degree by studies of communication and cooperative behavior among the myxobacteria and in quorum sensing (QS) and biofilm formation by pseudomonads and other microbes. Recently, the topic of multicellular cooperative behaviors among bacteria has been increasingly considered in the context of evolutionary biology. Here we discuss the significance of two recent studies1,2 of the phenomenon (...) of “cheating” mutants and their exploitation of cooperating microbial populations of Pseudomonas aeruginosa. BioEssays 30:296–298, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

Ennead IV.4.30-45 and IV.5 retrieves the unity in this last section of Plotinus' treatise on Problems concerning the Soul. Combining translation with commentary, Gurtler enhances both the accuracy of the translation and the recovery of Plotinus' often unsuspected originality. This is especially true for IV.5, where previous translations fail to convey the concise nature of his argument against both the Aristotelian and Platonic theories of vision. Plato and Aristotle each claim that vision depends on the light between the eye and (...) the object, but Plotinus presents evidence that this is not the case and develops a novel theory of light as a second activity that moves from source to object directly, even arguing that color is in the light itself rather than merely a quality of the object. This theory of vision, in turn, depends on the nature of sympathy developed especially in IV.4.30-45, where Plotinus shows how action at a distance is both possible and necessary for the proper unity in diversity of the sensible cosmos. (shrink)

Volume 37 contains papers and commentaries presented to the Boston Area Colloquium in Ancient Philosophy during 2022. Works: _Phaedo_, _Statesman_, _De Caelo_, _Metaphysics N_, _Enneads_. Topics: immortality, Forms; dialectic, myth, law; elements, inclination, place; mathematics and explanation; mystical union.

An examination of Plotinus’s treatise on matter, II 4[12], reveals interesting paradoxes. He seems to use Aristotle’s matter to explain Plato’s receptacle. Attention to the text reveals that both matter and the receptacle are, in fact, recast in terms of the otherness of Plato’s Sophist. By this, Plotinus articulates how matter and the receptacle function as the condition of possibility for the sensible cosmos. His analysis of related terms further supports this rapprochement: privation and substrate exclude quality and quantity as (...) attributes of matter; and the indefinite, the unlimited, size and mass echo the paradoxical language of the Timaeus. (shrink)