Arithmetic, Logicism, and Frege’s Definitions

2021 ◽  
Vol 61 (1) ◽  
pp. 5-25
Author(s):  
Timothy Perrine ◽  
Keyword(s):  
Michael Dummett ◽  
Full Solution

This paper describes an exegetical puzzle that lies at the heart of Frege’s writings—how to reconcile his logicism with his definitions and claims about his definitions. It also reviews two interpretations that try to resolve this puzzle: the “explicative interpretation” and the “analysis interpretation.” This paper defends the explicative interpretation and critiques the careful and sophisticated defenses of the analysis interpretation given by Michael Dummett and Patricia Blanchette. Specifically, I argue that Frege’s texts either are inconsistent with the analysis interpretation or do not support it. I also defend the explicative interpretation from the recent charge that it cannot make sense of Frege’s logicism. While I do not provide the explicative interpretation’s full solution to the puzzle, I show that its main competitor is seriously problematic.

Some Explicit Results for the Mean Spherical Approximation for Mixtures of Yukawa Fluids

2008 ◽  
Vol 73 (3) ◽  
pp. 424-438 ◽  
Author(s):  
Douglas J. Henderson ◽  
Osvaldo H. Scalise
Keyword(s):  
Integral Equation ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Inverse Temperature ◽  
Temperature Expansion ◽  
Yukawa Fluid ◽  
The Mean ◽  
Full Solution ◽  
Insight Into ◽  
Reasonable Model

The mean spherical approximation (MSA) is of interest because it produces an integral equation that yields useful analytical results for a number of fluids. One such case is the Yukawa fluid, which is a reasonable model for a simple fluid. The original MSA solution for this fluid, due to Waisman, is analytic but not explicit. Ginoza has simplified this solution. However, Ginoza's result is not quite explicit. Some years ago, Henderson, Blum, and Noworyta obtained explicit results for the thermodynamic functions of a single-component Yukawa fluid that have proven useful. They expanded Ginoza's result in an inverse-temperature expansion. Even when this expansion is truncated at fifth, or even lower, order, this expansion is nearly as accurate as the full solution and provides insight into the form of the higher-order coefficients in this expansion. In this paper Ginoza's implicit result for the case of a rather special mixture of Yukawa fluids is considered. Explicit results are obtained, again using an inverse-temperature expansion. Numerical results are given for the coefficients in this expansion. Some thoughts concerning the generalization of these results to a general mixture of Yukawa fluids are presented.

Extreme-point solutions in Markov decision processes

1983 ◽  
Vol 20 (04) ◽  
pp. 835-842
Author(s):  
David Assaf
Keyword(s):  
Convex Function ◽  
Extreme Point ◽  
Markov Decision Processes ◽  
Convex Functions ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
Markov Decision ◽  
Full Solution

The paper presents sufficient conditions for certain functions to be convex. Functions of this type often appear in Markov decision processes, where their maximum is the solution of the problem. Since a convex function takes its maximum at an extreme point, the conditions may greatly simplify a problem. In some cases a full solution may be obtained after the reduction is made. Some illustrative examples are discussed.

Semantic Realism, Actually

Metaphysica ◽  
2020 ◽  
Vol 21 (2) ◽  
pp. 237-254
Author(s):  
Simon Hewitt
Keyword(s):  
Philosophy Of Language ◽  
Semantic Realism ◽  
Michael Dummett

AbstractMichael Dummett offered a semantic characterisation of a variety of realism-antirealism debates. This approach has fallen out of fashion. This has been to the detriment of metaphysics. This paper offers an accurate characterisation of Dummett’s view, often lacking in the literature, and then defends it against a range of attacks (from Devitt, Miller and Williamson). This understanding of realism debates is resilient, and if we take it seriously the philosophical terrain looks importantly different. In particular, the philosophy of language has a foundational role with respect to metaphysics.

scholarly journals Nonlocal Transport Processes and the Fractional Cattaneo-Vernotte Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
J. F. Gómez Aguilar ◽  
T. Córdova-Fraga ◽  
J. Tórres-Jiménez ◽  
R. F. Escobar-Jiménez ◽  
V. H. Olivares-Peregrino ◽  
...  
Keyword(s):  
Fractional Calculus ◽  
Disordered Systems ◽  
Fourier Method ◽  
Mean Square Displacement ◽  
Fractional Power ◽  
Transport Processes ◽  
Diffusion Equations ◽  
Alternative Representation ◽  
Dimensional Parameters ◽  
Full Solution

The Cattaneo-Vernotte equation is a generalization of the heat and particle diffusion equations; this mathematical model combines waves and diffusion with a finite velocity of propagation. In disordered systems the diffusion can be anomalous. In these kinds of systems, the mean-square displacement is proportional to a fractional power of time not equal to one. The anomalous diffusion concept is naturally obtained from diffusion equations using the fractional calculus approach. In this paper we present an alternative representation of the Cattaneo-Vernotte equation using the fractional calculus approach; the spatial-time derivatives of fractional order are approximated using the Caputo-type derivative in the range(0,2]. In this alternative representation we introduce the appropriate fractional dimensional parameters which characterize consistently the existence of the fractional space-time derivatives into the fractional Cattaneo-Vernotte equation. Finally, consider the Dirichlet conditions, the Fourier method was used to find the full solution of the fractional Cattaneo-Vernotte equation in analytic way, and Caputo and Riesz fractional derivatives are considered. The advantage of our representation appears according to the comparison between our model and models presented in the literature, which are not acceptable physically due to the dimensional incompatibility of the solutions. The classical cases are recovered when the fractional derivative exponents are equal to1.

scholarly journals Interferometric Investigations of Eclipsing Binaries as a Key to an Improved Distance Scale

2006 ◽  
Vol 2 (S240) ◽  
pp. 496-498
Author(s):  
K. Shabun ◽  
A. Richichi ◽  
U. Munari ◽  
A. Siviero ◽  
B. Pacsysnki
Keyword(s):  
Spectral Type ◽  
Effective Temperature ◽  
Binary Systems ◽  
Angular Separation ◽  
Eclipsing Binaries ◽  
Multiple Systems ◽  
Long Baseline ◽  
Global Calibration ◽  
Empirical Calibration ◽  
Full Solution

AbstractBinary and multiple systems constitute one of the main tools for obtaining fundamental stellar parameters, such as masses, radii, effective temperatures and distances. One especially fortunate, and at the same time rare, occurrence is that of double-lined eclipsing binaries with well-detached components. In this special case, it is possible to obtain a full solution of all orbital and stellar parameters, with the exception of the effective temperature of one star, which is normally estimated from spectral type or derived from atmospheric analysis of the spectrum. Long-baseline interferometry at facilities such as the ESO VLTI is beginning to have the capability to measure directly the angular separation and the angular diameter of some selected eclipsing binary systems, and we have proposed such observations with the AMBER instrument. In particular, we aim at deriving directly the effective temperature of at least one of the components in the proposed system, thereby avoiding any assumptions in the global solution through the Wilson–Devinney method. We will also obtain an independent check of the results of this latter method for the distance to the system. This represents the first step towards a global calibration of eclipsing binaries as distance indicators. Our results will also contribute to the effective temperature scale for hot stars. The extension of this approach to a wider sample of eclipsing binaries could provide an independent method to assess the distance to the LMC. The observations will extend accurate empirical calibration to spectral type O9 – B0.

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