In his celebrated analysis of the piece of wax, Descartes is not at all looking for that which was dwelling in the wax–this problem is not even formulated in this text; rather, he shows how the I, manifest in the Cogito, grounds the judgment of denotation by which the wax is identified. (LOS 14)
Thus states Deleuze in the “Third Series of the Proposition” in The Logic of Sense. We are still talking about the role of language in philosophical reality here. The first question that comes to my mind is: What does Deleuze mean by denotation? First, we have the “proposition.” An example of a famous proposition is ”the cat is on the mat.” Denotation is a relation. Individuated external states of affairs and propositions must be related in some way. The cat’s being on the mat must be able to be said somehow. Second, we have words and and particular representational “images.” Some words function differently than others. Indexicals like “it, that, this, etc” function at an intuitive level when it comes to denotation. ‘The denotating intuition is then expressed by the form: “it is that,” or “it is not that”‘ (LOS 12). What is important to note here is that the indexicals in the intuition are empty; the actual state of affairs is what is full. The gap must be bridged. But is there really a gap? Hold that thought. At this stage it is right to assert that propositions can be either true or false. Do the states of affairs (in all their gritty material existences) truely or falsely ”match-up” with the words that are used to describe the images of those states of affairs in a representational sense?
We are now in search of a higher ground. Does this come as a surprise? Well, we might as well just get it out in the open. We’re dealing with full blown subjectivity here. We are at the crossroads between the proposition and whoever or whatever expresses it. Deleuze calls this relation of the proposition “manifestation.” ‘[M]anifesters, beginning with the “I,” constitute the domain of the personal, which functions as the principle of all possible denotation’ (LOS 13). As long as you exist as inferred by the act of your thinking, there is the possibility that you could be right or wrong, have a true belief or have an illusion, about some proposition’s own standing in the world. Cogito grounds that ‘judgment of denotation’ (LOS 14).
