Prof. Greg Lavers Publishes "Did Frege Solve One of Zeno’s Paradoxes?"
Greg Lavers publishes "Did Frege Solve One of Zeno’s Paradoxes?" in a new volume on research in history and philosophy of mathematics. The volume contains ten papers collected by the Canadian Society for History and Philosophy of Mathematics.
Abstract: Of Zeno’s book of forty paradoxes, it was the first that attracted Socrates’ attention. This is the paradox of the like and the unlike. On contemporary assessments, this paradox is largely considered to be Zeno’s weakest surviving paradox. All of these assessments, however, rely heavily on reconstructions of the paradox. It is only relative to these reconstructions that there is nothing paradoxical involved, or that there is some rather obvious mistake being made. This paper puts forward and defends a novel interpretation of this paradox, according to which the concept of a unit plays a central role. There is every reason to think the paradox turns on the concept of a unit: after the presentation of the paradox the text of the Parmenides immediately turns to a discussion of units, and the concept of a unit is also central to the Greek conception of a plurality. If this interpretation is correct then the paradox that Zeno presented was the same as one discussed and solved in Frege’s Grundlagen.
Greg Lavers is Associate Professor of Philosophy at Concordia University.