The research in this lab, however, suggests that the work of Meinong's student Ernst Mally provides a link between the ideas of Plato and Meinong. Platonic Forms and mathematical objects, on the one hand, and Meinongian objects and fictional objects, on the other hand, can be systematically understood from the point of view of a single metaphysical theory which is based on Mally's distinction between two modes of predication (encoding and exemplification). Forms, mathematical objects, Meinongian objects, and fictions may be species of abstract objects that encode properties. The Forms are abstract objects that encode a single property; mathematical objects are abstracta that encode just the properties attributed to them in their respective mathematical theories; and Meinongian and fictional objects such as the round square, flying horses, unicorns, Zeus, etc., encode their defining properties rather than exemplify them. The notions of encoding and exemplifying a property are fundamental to the theory, and they are explained in more detail in the document The Theory of Abstract Objects.
The connection between the ideas of Plato and Meinong has been documented in a paper coauthored by F. Jeffry Pelletier and Edward N. Zalta entitled ‘How to Say Goodbye to the Third Man’. In this paper, the authors show how to connect the theory of abstract objects with the work of Constance Meinwald, in her book Plato's Parmenides (Oxford: Oxford University Press, 1991) and in her article, ‘Good-bye to the Third Man’ (in the Cambridge Companion to Plato, Cambridge: Cambridge University Press, 1992). Meinwald found evidence that there is a distinction between two kinds of predication in Plato. Meinwald finds support for the idea that when Plato predicates the property P of the Form of P (e.g., in such statements as ‘The Just is just’ and ‘Beauty is beautiful’), he uses a special mode of predication. This is a predication of the form "A is B in relation to itself" (the Greek pros heauto is the phrase Plato uses to mark the predication "in relation to itself"). By contrast, when Plato predicates the property P of ordinary objects (e.g., in such statements as ‘Aristides is just’ and ‘Helen of Troy is beautiful’), he uses the mode of predication "A is B in relation to others" (marked by the Greek pros ta alla). These two kinds of predication are similar, if not identical, to the distinction between encoding a property and exemplifying a property, i.e., the distinction which underlies the theory of abstract objects. This is shown in the paper by Pelletier and Zalta. This paper extends the basic model of Plato's Forms first developed on pp. 41-47 of Edward N. Zalta's book, Abstract Objects: An Introduction to Axiomatic Metaphysics (Dordrecht: D. Reidel, 1983). This material forms Section 5 of the monograph Principia Logico-Metaphysica.