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  1. Philip Ehrlich (forthcoming). An Essay in Honor of Adolf Grünbaum's Ninetieth Birthday: A Reexamination of Zeno's Paradox of Extension. .
    We suggest that, far from establishing an inconsistency in the standard theory of the geometrical linear continuum, Zeno’s Paradox of Extension merely establishes an inconsistency between the standard theory of geometrical magnitude and a misguided system of length measurement. We further suggest that our resolution of Zeno’s paradox is superior to Adolf Grünbaum’s now standard resolution based on Lebesgue measure theory.
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  2. Philip Ehrlich (2012). The Absolute Arithmetic Continuum and the Unification of All Numbers Great and Small. Bulletin of Symbolic Logic 18 (1):1-45.
    In his monograph On Numbers and Games, J. H. Conway introduced a real-closed field containing the reals and the ordinals as well as a great many less familiar numbers including $-\omega, \,\omega/2, \,1/\omega, \sqrt{\omega}$ and $\omega-\pi$ to name only a few. Indeed, this particular real-closed field, which Conway calls No, is so remarkably inclusive that, subject to the proviso that numbers—construed here as members of ordered fields—be individually definable in terms of sets of NBG (von Neumann—Bernays—Gödel set theory with global (...)
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  3. Kenneth Easwaran, Philip Ehrlich, David Ross, Christopher Hitchcock, Peter Spirtes, Roy T. Cook, Jean-Pierre Marquis, Stewart Shapiro & Royt Cook (2010). The Palmer House Hilton Hotel, Chicago, Illinois February 18–20, 2010. Bulletin of Symbolic Logic 16 (3).
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  4. Philip Ehrlich (2007). JL Bell, The Continuous and the Infinitesimal in Mathematics and Philosophy. Bulletin of Symbolic Logic 13 (3):361-362.
     
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  5. Philip Ehrlich (2005). Continuity. In Donald M. Borchert (ed.), The Encyclopedia of Philosophy, 2nd Ed.
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  6. Philip Ehrlich (2005). Corrigendum to "Number Systems with Simplicity Hierarchies: A Generalization of Conway's Theory of Surreal Numbers". Journal of Symbolic Logic 70 (3):1022.
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  7. Philip Ehrlich (2001). Number Systems with Simplicity Hierarchies: A Generalization of Conway's Theory of Surreal Numbers. Journal of Symbolic Logic 66 (3):1231-1258.
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  8. Philip Ehrlich (1997). From Completeness to Archimedean Completenes. Synthese 110 (1):57-76.
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  9. Philip Ehrlich & Moshe Machover (1996). Real Numbers, Generalizations of the Reals and Theories of Continua (Synthese Library, Vol. 242). British Journal for the Philosophy of Science 47 (2):320-324.
     
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  10. Philip Ehrlich (1986). The Absolute Arithmetic and Geometric Continua. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1986:237 - 246.
    Novel (categorical) axiomatizations of the classical arithmetic and geometric continua are provided and it is noted that by simply deleting the Archimedean condition one obtains (categorical) axiomatizations of J.H. Conway's ordered field No and its elementary n-dimensional metric Euclidean, hyperbolic and elliptic geometric counterparts. On the basis of this and related considerations it is suggested that whereas the classical arithmetic and geometric continua should merely be regarded as arithmetic and geometric continua modulo the Archimedean condition, No and its geometric counterparts (...)
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  11. Philip Ehrlich (1982). Negative, Infinite, and Hotter Than Infinite Temperatures. Synthese 50 (2):233 - 277.
    We examine the notions of negative, infinite and hotter than infinite temperatures and show how these unusual concepts gain legitimacy in quantum statistical mechanics. We ask if the existence of an infinite temperature implies the existence of an actual infinity and argue that it does not. Since one can sensibly talk about hotter than infinite temperatures, we ask if one could legitimately speak of other physical quantities, such as length and duration, in analogous terms. That is, could there be longer (...)
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