Game theory, economics, logic, philosophy, mathematics, cognitive science,Ĭryptography, and auction theory, as well as to application specialists usingįormal and mathematical methods and tools. Interdisciplinary: it will be of interest to researchers in the fields ofĪrtificial intelligence, agents, computer science, knowledge representation, The scope of Knowledge, Rationality and Action is The journal includes a section on Knowledge, Rationality and Action as a The journal focuses on the role of mathematical, logical and linguistic methods in the general methodology of science and the foundations of different sciences. The journal explores symbolic logic and foundations of mathematics relevant to the philosophy and methodology of science and those facets of the ethics, history and sociology of science which are important for contemporary topical pursuits. Coverage includes the theory of knowledge general methodological problems of science, of induction and probability, of causation and the role of mathematics, statistics and logic in science and the methodological and foundational problems of different sciences. Synthese spans the topics of Epistemology, Methodology and Philosophy of Science. I argue that Giordano's nilpotents supply the best answer to Zeno's paradox. Lawvere's Smooth Infinitesimal Analysis and the other is inspired by Paolo Giordano's ring of Fermat Reals. One of these solutions is inspired by F.W. After arguing that any solution to the paradox must satisfy certain theoretical requirements, I examine White's solution alongside two nilpotent solutions. in relation to the hyperreal infinitesimals of nonstandard analysis. In this paper, I follow the basic outline of White's solution but argue that his solution suffers from arbitrariness and a related theoretical artificiality in relation to the system of infinitesimals he invokes, viz. Contra Zeno, this allows the arrow to be moving in the present, rather than frozen in place. In "Zeno's Arrow, Divisible Infinitesimals, and Chrysippus," White suggests using an infinitesimal value as the length of the present. Do you ever get the feeling that you are but an infinitesimal speck. Therefore, the arrow is both moving and at rest. Incalculably, exceedingly, or immeasurably minute vanishingly small. However, if the present is a single point in time, then the arrow is frozen in place during that time. Zeno's Arrow goes like this: during the present, a flying arrow is moving in virtue of its being in flight. Nilpotents are nonzero numbers that yield zero when multiplied by themselves a certain number of times. I offer a novel solution to Zeno's paradox of The Arrow by introducing nilpotent infinitesimal lengths of time.
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