Penalty functions over a cartesian product of lattices

In this work we present the concept of penalty function over a Cartesian product of lattices. To build these mappings, we make use of restricted dissimilarity functions and distances between fuzzy sets. We also present an algorithm that extends the weighted voting method for a fuzzy preference relation.

Schwinger and Pegg-Barnett approaches and a relationship between angular and Cartesian quantum descriptions: II. Phase spaces

Following the discussion-in state-space language-presented in a preceding paper, we work on the passage from the phase-space description of a degree of freedom described by a finite number of states (without classical counterpart) to one described by an infinite (and continuously labelled) number of states. With this it is possible to relate an original Schwinger idea to the Pegg-Barnett approach to the phase problem. In phase-space language, this discussion shows that one can obtain the Weyl-Wigner formalism, for both Cartesian and angular coordinates, as limiting elements of the discrete phase-space formalism.

The Dirac-Hestenes equation for spherical symmetric potentials in the spherical and Cartesian gauges

In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space-time the Dirac-Hestenes equation - which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation - by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac-Hestenes equation in both gauges has exactly the same mathematical difficulty. © World Scientific Publishing Company.

Is global workspace a cartesian theater? How the neuro-astroglial interaction model solves conceptual issues

The Global Workspace Theory (GWT) proposed by Bernard Baars (1988) along with Daniel Dennett’s (1991) Multiple Drafts Model (MDM) of consciousness are renowned cognitive theories of consciousness bearing similarities and differences. Although Dennett displays sympathy for GWT, his own MDM does not seem to be fully compatible with it. This work discusses this compatibility, by asking if GWT suffers from Daniel Dennett’s criticism of what he calls a “Cartesian Theater”. We identified in Dennett 10 requirements for avoiding the Cartesian Theater. We believe that some of these requirements are violated by GWT, but not all, hence there is partial incompatibility with MDM, and it is nonsense to answer if GWT is or is not a Cartesian Theater. However, by asking such question we conclude that the issues around this discussion involve fuzzy claims about degrees of consciousness and we show how the Neuro-Astroglial Interaction Model (NAIM) is fit for solving such conceptual issues.

Alternative Formulations for Angular Momentum Operators, Cartesian and Spherical Polar Forms

The conversion between representations of angular momentum in spherical polar and cartesian form is discussed.

Principles of natural and metaphysical philosophy : intended on a more ancient, common-sense, and popular plan, and more consistent also with later improvements that the Cartesian or Newtonian : comprimising a review of prevailing systems now taught ...

Errata: p. [vii]

Studies in the Cartesian philosophy

The problem of Descartes -- The method of Descartes -- The metaphysics of Descartes -- The Cartesian principles in Spinoza and Leibniz -- The Cartesian principles in Locke -- Hume's criticism of the Cartesian principles -- The transition to Kant.

The body, the device, the sleepwalkers. On the spinozian uses of experience as a critics of the cartesian concept of freedom

In this paper I discuss one of the most significant strategies in Spinoza’s theoretical approach against those that entrave its understanding in a very powerful way. As well as Descartes, Spinoza uses the inmediate or unreflexive experience for developing his conception of free will or the distinction between body and soul, but he does so in order to prove that the experience is useful to demonstrate some purely anti-Cartesian thesis that express the core principles of Spinozism.