What numbers are

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43823/1/11229_2004_Article_BF00660892.pd

Mind and body, form and content: how not to do petitio principii analysis

Few theoretical insights have emerged from the extensive literature discussions of petitio principii argument. In particular, the pattern of petitio analysis has largely been one of movement between the two sides of a dichotomy, that of form and content. In this paper, I trace the basis of this dichotomy to a dualist conception of mind and world. I argue for the rejection of the form/content dichotomy on the ground that its dualist presuppositions generate a reductionist analysis of certain concepts which are central to the analysis of petitio argument. I contend, for example, that no syntactic relation can assimilate within its analysis the essentially holistic nature of a notion like justification. In this regard, I expound a form of dialectical criticism which has been frequently employed in the philosophical arguments of Hilary Putnam. Here the focus of analysis is upon the way in which the proponent of a position proceeds to explain or argue for his/her own particular theses. My conclusion points to the use of such dialectic within future analyses of petitio principii

A new revisability paradox

In a recent article, Mark Colyvan has criticized Jerrold Katz's attempt to show that Quinean holism is self-refuting. Katz argued that a Quinean epistemology incorporating a principle of the universal revisability of beliefs would have to hold that that and other principles of the system were both revisable and unrevisable. Colyvan rejects Katz's argument for failing to take into account the logic of belief revision. But granting the terms of debate laid down by Colyvan, the universal revisability principle still commits Quineans to holding that one belief is both revisable and unrevisable: the belief that some beliefs are revisabl

Choosing the realist framework

There has been an empiricist tradition in the core of Logical Positivism/Empiricism, starting with Moritz Schlick and ending in Herbert Feigl (via Hans Reichenbach), according to which the world of empiricism need not be a barren place devoid of all the explanatory entities posited by scientific theories. The aim of this paper is to articulate this tradition and to explore ways in which its key elements can find a place in the contemporary debate over scientific realism. It presents a way empiricism can go for scientific realism without metaphysical anxiety, by developing an indispensability argument for the adoption of the realist framework. This argument, unlike current realist arguments, has a pragmatic ring to it: there is no ultimate argument for the adoption of the realist framework. © 2009 Springer Science+Business Media B.V

The Wonder of Colors and the Principle of Ariadne

The Principle of Ariadne, formulated in 1988 ago by Walter Carnielli and Carlos Di Prisco and later published in 1993, is an infinitary principle that is independent of the Axiom of Choice in ZF, although it can be consistently added to the remaining ZF axioms. The present paper surveys, and motivates, the foundational importance of the Principle of Ariadne and proposes the Ariadne Game, showing that the Principle of Ariadne, corresponds precisely to a winning strategy for the Ariadne Game. Some relations to other alternative. set-theoretical principles are also briefly discussed

On the existence of a modal antinomy

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43821/1/11229_2004_Article_BF00636296.pd

Slim Epistemology with a Thick Skin

The distinction between ‘thick’ and ‘thin’ value concepts, and its importance to ethical theory, has been an active topic in recent meta-ethics. This paper defends three claims regarding the parallel issue about thick and thin epistemic concepts. (1) Analogy with ethics offers no straightforward way to establish a good, clear distinction between thick and thin epistemic concepts. (2) Assuming there is such a distinction, there are no semantic grounds for assigning thick epistemic concepts priority over the thin. (3) Nor does the structure of substantive epistemological theory establish that thick epistemic concepts enjoy systematic theoretical priority over the thin. In sum, a good case has yet to be made for any radical theoretical turn to thicker epistemology

An exact solution method for 1D polynomial Schr\"odinger equations

Stationary 1D Schr\"odinger equations with polynomial potentials are reduced to explicit countable closed systems of exact quantization conditions, which are selfconsistent constraints upon the zeros of zeta-regularized spectral determinants, complementing the usual asymptotic (Bohr--Sommerfeld) constraints. (This reduction is currently completed under a certain vanishing condition.) In particular, the symmetric quartic oscillators are admissible systems, and the formalism is tested upon them. Enforcing the exact and asymptotic constraints by suitable iterative schemes, we numerically observe geometric convergence to the correct eigenvalues/functions in some test cases, suggesting that the output of the reduction should define a contractive fixed-point problem (at least in some vicinity of the pure $q^4$ case).Comment: flatex text.tex, 4 file