The Overturning

After so much time spent on the Sophist, I'm at risk of simply repeating myself if I spend too much more time elaborating our starting point for this Plato section.  The Sophist already overturns Platonism, and we already know how -- the 'fake' things at the end of a chain of division, those furthest removed from the Idea, those Nth level simulacra like the Sophist himself, have a reality of their own.  Their not-Being is also Being.  What seemed a hierarchy turns out to be a circle, and difference, becoming, movement, novelty, etc ... turn out to be built right into the heart of Being.

This can seem awfully abstract though, so I want to consider a concrete image that help me understand the subtle distinction between Platonism and its inversion.  This came up in thinking about the contrast we saw Heidegger draw between the Same and the Identical:

The same never coincides with the equal, not even in the empty indifferent oneness of what is merely identical. The equal or identical always moves toward the absence of difference, so that everything may be reduced to a common denominator. The same, by contrast, is the belonging together of what differs, through a gathering by way of the difference. We can only say 'the same' if we think difference....

Deleuze rephrases this distinction in asking whether Plato's Ideas are the Same or the Identical with respect to all the differences in the lineage they structure.

The four figures of the Platonic dialectic are therefore: the selection of difference, the installation of a mythic circle, the establishment of a foundation, and the position of a question-problem complex. However, difference is still related to the Same or to the One through these figures. No doubt the same should not be confused with the identity of the concept in general: rather, it characterises the Idea as the thing itself. Nevertheless, to the extent that it plays the role of a true ground, it is difficult to see what its effect is if not to make that which is grounded 'identical', to use difference in order to make the identical exist.  In reality, the distinction between the same and the identical bears fruit only if one subjects the Same to a conversion which relates it to the different, while at the same time the things and beings which are distinguished in the different suffer a corresponding radical destruction of their identity. Only on this condition is difference thought in itself, neither represented nor mediated. 

When I first read that Heidegger quote, I wondered how the Same gathering together differences into One was related to the concept of analogy.   In fact, the Same in this Heideggerean sense  is precisely the opposite of the Same in analogy (notice that the use of the term changes from the first quote to the second).  Analogy, like Plato's Ideas, tries to isolate the identical common denominator in a set of differences.  To do this you have to begin by taking each of the differences as having a fixed identity.  Then you compare these to one another to see where they overlap.  Once you establish what their identities share in common, you extract this as the root of the analogy, and can now draw a relationship between each difference and this common central point.  The differences now become 'essentially' just examples of the analogy (albeit ordered examples in the case of Plato's Ideas).  We could sketch  the structure as a set of concentric circles of different sizes, but I was thinking of it like this:

IDENTICAL

The identity of each of the points arrayed around the circle is given, and they all refer to a central Identical that they partake in.  The points themselves are not connected here; their only relationship is through the mediation of the central point.

By contrast, we can redraw this network map to illustrate the Same.  But we have to start with the way the various differences arrayed around the circle differ from one another, rather than taking for granted and comparing their self-identities.  We have to follow the direct connection between the points and see how they lean on and transform into one another.  The connection isn't mediated by a central term in this case.  

SAME

Nevertheless, a central term does appear here, but only as a byproduct of the direct relationship of differences.  The Same emerges as the way we can refer to the whole pattern of connection of difference as one entity.  This entity isn't just the overlap of a set of fixed identities though.  It is only defined through the motion of the circulation of difference.