Determinate Negation

Something actually means something to the extent that it actually rules out something else. Brandom calls this material incompatibility. I think he is right that this has more to do with contrariety in Aristotle than with so-called “contradiction”, about which a tremendous amount of nonsense has been written in purported reference to Hegel. Hegel’s wording was not always clear, to put it mildly, but I think it is clear that he never meant to talk logical nonsense.

Brandom’s examples (e.g., triangular vs. circular) make it clear that he has in mind a sort of n-ary contrariety, as distinct from the binary kind Aristotle talks about in the Physics (e.g., triangular vs. non-triangular). However, Aristotle’s own argument for distinction based on n-ary rather than binary division in Parts of Animals Book 1 supports Brandom’s extension of Aristotelian contrariety to an n-ary form.

Aristotle also in many places speaks of difference in ways that resemble Brandom’s n-ary contrariety. Aristotle and Hegel and Brandom all laudably direct our attention to conceptual difference. Brandom argues that for Hegel, this also explicitly includes differences in inferential consequence.

There is an important contrast between this “determinate” negation and “infinite” negation or simple polar opposition, in which each of a pair of terms is the simple negation of the other. This latter kind has been called “infinite”, because it does nothing to specify what the difference is between the two terms. (See also Conceptual, Representational; Material Inference; Material Consequence.)