James Smith of Calvin College has an important analysis of Catherine Pickstock’s attempt to conflate Christian incarnation and Platonic participation in his book, Speech and Theology (in the Radical Orthodoxy series). He admits that participation can affirm the material and bodily as instruments for the soul’s salvation, but questions whether Pickstock has done justice to the fact that, for Plato, embodiment is the result of a “fall.” As he says, “On a radically incarnational or creational register, the material does not play a simply ‘remedial’ role in a postlapsarian state of affairs, but rather an integral and essential role for creatures as created.” By contrast, “a participatory ontology only affirms materiality and embodiment as a kind of ‘necessary evil’ based on a prior determination of embodiment as already constituted by a fall” (pp. 176-7).

Much of this depends on what is meant by “participation,” of course, but Smith’s cautions against equating incarnation with participation are beneficial.