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  1.  76
    Joseph S. Alper & Mark Bridger (1998). Newtonian Supertasks: A Critical Analysis. Synthese 114 (2):355-369.
    In two recent papers Perez Laraudogoitia has described a variety of supertasks involving elastic collisions in Newtonian systems containing a denumerably infinite set of particles. He maintains that these various supertasks give examples of systems in which energy is not conserved, particles at rest begin to move spontaneously, particles disappear from a system, and particles are created ex nihilo. An analysis of these supertasks suggests that they involve systems that do not satisfy the mathematical conditions required of Newtonian systems at (...)
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  2.  61
    Joseph S. Alper & Mark Bridger (1997). Mathematics, Models and Zeno's Paradoxes. Synthese 110 (1):143-166.
    A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms of rational intervals does provide a formalism for understanding the paradoxes. This model suggests that in (...)
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  3.  26
    Jon Pérez Laaraudogoitia, Mark Bridger & Joseph S. Alper (2002). Two Ways of Looking at a Newtonian Supertask. Synthese 131 (2):173 - 189.
    A supertask is a process in which an infinite number of individuated actions are performed in a finite time. A Newtonian supertask is one that obeys Newton''s laws of motion. Such supertasks can violate energy and momentum conservation and can exhibit indeterministic behavior. Perez Laraudogoitia, who proposed several Newtonian supertasks, uses a local, i.e., particle-by-particle, analysis to obtain these and other paradoxical properties of Newtonian supertasks. Alper and Bridger use a global analysis, embedding the system of particles in a Banach (...)
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    Jon Pérez Laaraudogoitia, Mark Bridger & Joseph Alper (2004). Two Ways Of Looking At A Newtonian Supertask. Synthese 131 (2):173-189.
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  5.  12
    Mark Bridger & Joseph S. Alper (1999). On the Dynamics of Perez Lauraudogoitia's Supertask. Synthese 119 (3):325-337.
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    Joseph S. Alper & Mark Bridger (1997). Mathematics, Models and Zeno's Paradoxes. Synthese 110 (1):143-166.
    A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms of rational intervals does provide a formalism for understanding the paradoxes. This model suggests that in (...)
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