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  1. Toshio Ishigaki (2000). Model-Theoretic Nature of the Laws of Motion in Newton's Principia. Annals of the Japan Association for Philosophy of Science 10 (1):1-17.
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  2. Toshio Ishigaki (1995). A Formal System for Classical Particle Mechanics, its Model-Theoretic Applications and Space-Time Structure. Synthese 102 (2):267 - 292.
    In the history of Newtonian Mechanics physicists and astronomers did not rely on so-called inertial frames, indeed they were not able to identify such frames. So the usual neo-Newtonian formalism of Newtonian Mechanics contains some superfluous components. In the present paper I will formulate a formal system for classical particle mechanics in Leibnizian space-time, where a relation, a counterpart of the second law of motion, between force on bodies and derivative of their momentum will be defined relative to every, inertial (...)
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  3. Toshio Ishigaki (1994). Newton's Principia From a Logical Point of View'. Annals of the Japan Association for Philosophy of Science 8 (4):221-36.
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  4. Toshio Ishigaki (1991). Four Mathematical Expressions of the Uncertainty Relation. Foundations of Physics 21 (9):1089-1105.
    The uncertainty relation in quantum mechanics has been explicated sometimes as a statistical relation and at other times as a relation concerning precision of simultaneous measurements. In the present paper, taking the indefiniteness of individual experiments as represented by diameters of Borel sets in projection-valued measure, we mathematically distinguish four expressions, two statistical and two concerning simultaneous measurements, of the uncertainty relation, study their interrelations, and prove that they are nonequivalent to each other and to the eigenvector condition (EV) in (...)
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