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On What Exists Mathematically: Indispensability without Platonism
indispensability ontological commitment Quine Armstrong
2009/9/17
According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitme...
Platonism in classical logic versus formalism in the proposed non-Aristotelian finitary logic
foundations of mathematics foundations of quantum mechanics
2008/4/22
The main thesis of this paper is that Platonism is inherent in classical infinitary reasoning and that strict formalism inevitably leads one to the author's non-Aristotelian finitary logic (NAFL) prop...
On the logical consistency of special relativity theory and non-Euclidean geometries: Platonism versus formalism
relativistic determinism relativity of simultaneity
2008/4/15
The Lorentz transformations in the theory of special relativity~(SR) lead to a little-investigated phenomenon called relativistic determinism. When two relatively moving inertial observers A and B coi...
Comment on "On the logical consistency of special relativity theory and non-Euclidean geometries: Platonism versus formalism"
special theory of relativity undecidable propositions
2008/4/10
As observed in the PhilSci preprint ID Code 1255 [1], consistency in the author's proposed non-Aristotelian finitary logic (NAFL) demands that Euclid's fifth postulate must necessarily be provable fro...