[FOM] The influence of Leibniz on Russell

Verelst Karin kverelst at vub.ac.be
Mon May 7 20:17:30 EDT 2007

Interestingly enough, a similar difference on the nature of relational facts opposes Plato and Aristotle. Plato's relationalism is much more radical than Aristotle's because for Plato, obviously, properties are themselves substantial up to a certain degree. The relational logic which follows from this point of view was set forth by him in the Phaedo, e.g., in the discussion on Simmias's simultaneous being-greater and being-smaller by virtue of the same something, but with respect to something different. Many of the logical fallacies which have been cast upon Plato's metaphysics at first by the Stagirite and by many of his followers afterwards, disappear when this fact is taken into account, as has been noted by H-N Castaneda:

"Contrary to the monolithic consensus among Plato scholars, in the
Phaedo Plato did distinguish, and soundly, between relations and qualities, and dealt with genuine puzzles that arise in attempting to understand the nature of relational facts. The reason why Plato's theory of relations has hitherto remained hidden to his commentators is this: his commentators have either not understood the nature of relations, or, more recently, they have adopted the dogma that a primary or simple relation is just one atomic or indivisible entity that generates facts by being instantiated at once by an ordered
n-tuple. (...) It might be suggested at this juncture that a nominalist must,
nevertheless, distinguish between a thing A being longer than another thing B, and the former being heavier than the second, and this distinction must lie in facts themselves, in nature."

See H. N. Casta\~{n}neda, ``Plato's theory of relations'', in {\em Exact
Philosophy}, Mario Bunge ed., Reidel Publishing Company, Dordrecht, 1973. 

Castaneda gives a formal representation for Plato's relational logic; it would be interesting to compare it to logics such as Church's STT, which I never studied myself. I did show, however, that the logic underlying Plato's system, when formulated within the confines of the subject-praedicate scheme, is not classical but paraconsistent (I will post the link to the preprint of my paper as soon as it is submitted). 

Karin Verelst

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