0-categorical o-minimal structures were completely described by Pillay and Steinhorn 565–592), and are essentially built up from copies of the rationals as an ordered set by ‘cutting and copying’. Here we investigate the possible structures which an 0-categorical weakly o-minimal set may carry, and find that there are some rather more interesting examples. We show that even here the possibilities are limited. We subdivide our study into the following principal cases: the structure is 1-indiscernible, in which case all possibilities are (...) classified up to binary structure; the structure is 2-indiscernible, classified up to ternary structure; the structure is 3-indiscernible, in which case we show that it is k-indiscernible for every finite k. We also make some remarks about the possible structures of higher arities which an 0-categorical weakly o-minimal structure may carry. (shrink)

Concepts of stability and symmetry in irreversible thermodynamics are developed through the analysis of system energy flows. The excess power function, derived from a local energy conservation equation, is shown to yield necessary and sufficient stability criteria for linear and nonlinear irreversible processes. In the absence of symmetry-destroying external forces, the linear range may be characterized by a set of phenomenological coefficient symmetries relating coupled forces and displacements, velocities, and accelerations, whereas rotational phenomena in nonlinear processes may be characterized by (...) skew-symmetric components of the phenomenological coefficients. A physical interpretation of the nature of the skew-symmetric parts is given and the variational principle of minimum dissipation of energy is related to a stability criterion. (shrink)

The paper presents and applies Hilbert's Epsilon Calculus, first describing its standard proof theory, and giving it an intensional semantics. These are contrasted with the proof theory of Fregean Predicate Logic, and the traditional (extensional) choice function semantics for the calculus. The semantics provided show that epsilon terms are referring terms in Donnellan's sense, enabling the symbolisation and validation of argument forms involving E-type pronouns, both in extensional and intensional contexts. By providing for transparency in intensional constructions they support a (...) Model Conceptualism to contrast with traditional intensional logic's Modal Realism. But epsilon-terms also symbolise fictions, and through their difference from iota terms enable the solution of a number of outstanding puzzles about Direct Reference and de re beliefs. (shrink)

The scope of the thermodynamic theory of nonlinear irreversible processes is widened to include the nonlinear stability analysis of system motion. The emphasis is shifted from the analysis of instantaneous energy flows to that of the average work performed by periodic nonlinear processes. The principle of virtual work separates dissipative and conservative forces. The vanishing of the work of conservative forces determines the natural period of oscillation. Stability is then determined by the variations of the dissipative forces with amplitude of (...) oscillation. If the work is a minimum, under certain conditions, the motion is stable. Reduction to linear analysis shows the coincidence with the impedance analysis of electrical circuit theory. The theory is applied to the analysis of temporal interactions of nonlinear irreversible processes in the particular cases of synchronization and hysteresis. Characteristic nonequilibrium phenomena of directional energy transfers, self-excitation, system passivity, wave modulation, and “beat” phenomena are observed. Possible relationships with biological processes are discussed. (shrink)

Thanks to the exchange of arguments, groups outperform individuals on some tasks, such as solving logical problems. However, these results stem from experiments conducted among Westerners and they could be due to cultural particularities such as tolerance of contradiction and approval of public debate. Other cultures, collectivistic cultures in particular, are said to frown on argumentation. Moreover, some influential intellectual movements, such as Confucianism, disapprove of argumentation. In two experiments, the hypothesis that Easterners might not share the benefits of argumentation (...) was tested. In Experiment 1, Japanese participants had to solve a standard logical problem individually and then in groups. They performed significantly better in groups. In Experiment 2, Japanese participants had to estimate the weight of various animals. They did so individually, then after learning of another participant's estimates, then after discussing these estimates with the other participant, and then indi.. (shrink)

The paper presents and applies Hilbert's Epsilon Calculus, first describing its standard proof theory, and giving it an intensional semantics. These are contrasted with the proof theory of Fregean Predicate Logic, and the traditional (extensional) choice function semantics for the calculus. The semantics provided show that epsilon terms are referring terms in Donnellan's sense, enabling the symbolisation and validation of argument forms involving E-type pronouns, both in extensional and intensional contexts. By providing for transparency in intensional constructions they support a (...) Model Conceptualism to contrast with traditional intensional logic's Modal Realism. But epsilon-terms also symbolise fictions, and through their difference from iota terms enable the solution of a number of outstanding puzzles about Direct Reference and de re beliefs. (shrink)

Brian Wormald provides a fundamental reappraisal of one of the most complex and innovative figures of the late-Elizabethan and Jacobean age. In the centuries since his death, Francis Bacon (1561-1626) has been perceived and studied as a promoter and prophet of the philosophy of science--natural science--but he saw himself also as a clarifier and promoter of what he called "policy" or the study and improvement of the structure and function of civil states. Mr. Wormald shows that Bacon was concerned equally (...) with the knowledge of the world of nature and with that of policy. The junction between the two enterprises was effected by his work in history; and in the end it was Bacon's conception and practice of history that provided the answer to his efforts to advance policy and natural philosophy. (shrink)

A simple random walk model has been shown by Gaveauet al. to give rise to the Klein-Gordon equation under analytic continuation. This absolutely most probable path implies that the components of the Dirac wave function have a common phase; the influence of spin on the motion is neglected. There is a nonclassical path of relative maximum likelihood which satisfies the constraint that the probability density coincide with the quantum mechanical definition. In three space dimensions, and in the presence of electromagnetic (...) interaction, the Lagrangian for this optimal, nonclassical path coincides with the Lagrangian of the Dirac particle. The nonrelativistic, or diffusion, limit is shown to be a formal consequence of Einstein's dynamical equilibrium condition; the continuity equation reduces to the same diffusion equation derived from Schrödinger's equation. The relativistic, massless limit, which would describe a neutrino, is comparable (in the sense of analytic continuation) to a nonviscous liquid whose molecules possess internal degrees of freedom. (shrink)

The history of Athenian relations with Sicily in the fifth century is beset with difficulties; and no part of it, perhaps, is more obscure than the story of what is commonly known as the First Sicilian Expedition, which set sail from Athens in the late summer of 427 under Laches, and was reinforced under Pythodorus, Sophocles and Eurymedon in the winter of 426.

Context: Due to its grounding in a simplistic core model, mainstream theoretical work in economics is heavily conditioned by a realist epistemic framework that may be viewed as the “paradogma” – sensu Mitterer – of economics. Problem: The contribution delineates theoretical developments on the basis of a realist epistemology and their problem-laden consequences for the economic sciences. The subsequent critical discussion seeks to clarify whether economic theory formation is a suitable field for the application of Mitterer’s non-dualist ideas. Method: In (...) the context of a review of their historical background, the paper will explore the possibilities and limits of an application of Mitterer’s non-dualist argumentation to the economic sciences, and present a diagnosis of compatibility and a characterisation of necessary steps towards amplification. Results: It can be shown that the economic sciences would gain in expert knowledge and applicability by adopting the alternative of non-dualism, whose potential has been little appreciated so far. The solution to the meta-scientific problems caused by the pre-structuring of economics in terms of a realist epistemology seems at hand. To take up this new meta-scientific perspective, however, theoretical progress in both non-dualism and economics is required, particularly by paying more serious attention to the theoretical component of communication. Implications: Non-dualism can certainly be utilised by the economic sciences to induce radical innovations and conceptional revisions involving higher meta-scientific consistency. In future, pragmatic gaps will increasingly have to be filled conceptually in order to develop more highly-reflected economic theory formation and corresponding scientific practice. Hence the main idea is that economic actions are inevitably, but not exclusively, based on communication. Constructivist content: Theoretical approaches embracing epistemic relativism in the economic sciences will be properly assessed and developed further along the lines of a non-dualist conceptual revision on the basis of an ontology-free understanding of reality. (shrink)

In a previous issue of Philosophical Investigations Professor Radford provides a counterexample to the equation1: a word is on the tip of a man's tongue IFF (a) he can recognize the word and (b1) he believes he may be able to produce It (fairly soon).

In list-method directed forgetting, reexposure to forgotten List 1 items has been shown to reduce directed forgetting. proposed that reexposure to a few List 1 items only during a direct test of memory reinstates the entire List 1 episode. In the present experiments, part-list reexposure in the context of indirect as well as direct memory tests reduced directed forgetting. Directed forgetting was reduced when 50% or more of the items were reexposed, and was intact when only 25% were reexposed. Furthermore, (...) part-list reexposure appeared to reinstate only reexposed items-not the entire List 1 episode. (shrink)

Recovers some of the value in the Wittgensteinian period of philosophy, using certain logical systems: Prior's theory of operators and Hilbert's epsilon calculus. This work applies, discursively, the previous largely technical results published in Prolegomena to Formal Logic (Aldershot, Gower 1989) and Intensional Logic (Aldershot, Ashgate 1994) to resolve matters of current interest in philosophy, logic and linguistics - notably attacking a variety of realisms found in comtemporary cognitive science and the philosophy of mathematics.

I have become more convinced, over the years, by the truth of Wittgenstein’s characterisation of philosophy as arising through misconceptions of grammar. Such a misconception of grammar characterises a very popular approach to indexicality which has been current since the 1970s, stemming from the work of Casteñeda, and Kaplan. Gareth Evans was inclined to allow, for instance, that one could say ‘“To the left (I am hot)” is true, as uttered by x at t iff there is someone moderately near (...) to the left of x such that, if he were to utter the sentence “I am hot” at t, what he would thereby say is true’ (Evans 1985: 358). But not only does this disturb the proper relation between direct and indirect speech, it continues a Fregean tradition which these very cases show to be quite mistaken about the logic of intensions. In this paper, however, I want primarily to point out how this misconception of grammar has distorted our view of people. For some of the above thinkers have tried to make out that human motivation is related to the possession of a certain category of indexical belief, by Lewis called ‘de se beliefs’. I shall look here at how the matter arises in Hugh Mellor’s work on Time. In connection with Time, indexicality arises in McTaggart’s ‘A-series’, and Mellor treats this indexicality in parallel with Evans’ language. First, therefore, I aim to show how Mellor’s discussion of Time grammatically misconceives the situation, and leads to a misrepresentation of the motivation of human action. But a larger conclusion about Fregean intensions is also then immediately available. (shrink)

The Einstein-Podolsky-Rosen paradox as formulated in their original paper is critically examined. Their argument that quantum mechanics is incomplete is shown to be unsatisfactory on two important grounds. (i) The gedanken experiment proposed by Einstein, Podolsky, and Rosen is physically unrealizable, and consequently their argument is invalid as it stands. (ii) The basic assumptions of their argument are equivalent to the assumption that quantum mechanical systems are in fact describable by unique eigenfunctions of the operators corresponding to physical observables, independent (...) of any observation or measurement. Following an argument due to Furry, it is shown that this interpretation of quantum mechanics must lead to some physical predictions at variance with those of conventional quantum mechanics. A decisive experiment has been performed by Freedman and Clauser, which rules out this interpretation, and imposes severe restrictions on any alternative theory which incorporates the Einstein, Podolsky, and Rosen concept of physical reality. (shrink)

The thermodynamics of averaged motion treats the asymptotic spatiotemporal evolution of nonlinear irreversible processes. Dissipative and conservative actions are associated with short and long spatiotemporal scales, respectively. The motion of asymptotically stable systems is slow, monotonic, and continuous, so that the microscopic state variable description of rapid motion can be supplanted by an analysis of the macroscopic variable equations of motion of amplitude and phase. Rapid motion is associated with instability, and the direction of system motion is determined by thermodynamic (...) criteria, in place of an analysis of the microscopic equations of motion. The characteristic structural configurations, deduced from the extremum principles of partial differential equations, are compared with the thermodynamic criteria. As a result of the nature of asymptotic motion, variational principles exist which characterize the asymptotic states of the system. (shrink)

The author has made this treatise on Madhva’s realistic school of Ved?nta philosophy convincing to the modern mind by employing western logical apparatus in substantiating Madhva’s ideas. Following the Indian classical tradition, the author has examined the validity of Advaitaved?nta, the Absolute Monism of ?a?kara and Bh?skara as P?rvapak?a, and logically proved its inconsistencies. He has then established the Dvaitasiddh?nta i.e., the Monotheistic Dualism of Madhva. He has successfully brought out the nuances of the realistic school of Indian philosophical thought (...) in this work. A Modern Introduction to M?dhva Philosophy is Prof B H Kotabagi’s posthumous publication. (shrink)