paradox of expressibility

The paradox of expressibility is quite simple – it involves saying what cannot be said. For Priest, much of twentieth-century philosophy, and especially the best of twentieth-century philosophy, the philosophy and philosophers that have truly plumbed the depths and limits of expression, has for this very reason ended up within the paradox of expressibility, though usually without embracing it if not outright avoiding it (which inevitably leads to another paradox). From Frege to Derrida, and for most of the philosophers in between, this is how things have gone. Take Frege, for instance. In his landmark essays, ‘Function and Concept’, ‘On Sense and Reference’, and ‘On Concept and Object’, Frege modifies the traditional subject-predicate distinction by differentiating instead between a name, which extends beyond the traditional understanding of subject in that it now includes noun-phrases that may appear within the predicate phrase itself; and concept-expression which replaces the traditional use of the term predicate, which is ‘what is left,’ as Priest puts it, ‘when the names are deleted from a sentence.’ Priest gives the example, ‘Oswald was framed for the murder of Kennedy,’ where ‘Oswald’ and ‘the murder of Kennedy’ are names and ‘was framed for’ is a concept-expression. Where difficulties enter the scene is when Frege differentiates between sense (sinn) and reference (bedeutung). The reference or denotation of a sentence or a statement, which includes both a name and a concept-expression, is its truth-value. The reference of a name for Frege is an object, and for a concept-expression it is a concept. The sense is that which enables us to determine which truth-value, object, or concept is the correct referent. The problem arises when we name a concept, using an expression such as ‘the concept “horse”’ to denote the concept we have in mind. Since a concept is not an object, for Frege, but is rather a function which allows us to map an object to a truth-value, the question then is: how can we name a concept? What concept enables us to correctly map our name to the concept named? And so on. Frege was aware of his predicament, and Priest cites Frege on this point:

By a kind of necessity of language, my expressions, taken literally, sometimes miss my thought: I mention an object when I intend a concept. I fully realize that in such cases I was relying on the reader who would be ready to meet me half-way – who does not begrudge a pinch of salt.

It’s game, set, match for Priest at this point, and the pattern is set for the analyses to follow. In his analyses of Wittgenstein (both of the Tractatus and Philosophical Investigations), Quine, Davidson, Heidegger, and Derrida, Priest argues that each in the end will paradoxically tell us a lot about what can not be told. Wittgenstein will say a lot about what we cannot say but can only show; Quine very clearly and with great precision of reference undermines the very notion of reference and determinacy; Davidson argues that ‘true-in-English’ is not expressible in English despite the fact that Davidson expresses it with the phrase ‘true-in-English’; and Derrida, finally, has a lot to say about the inexpressibility of différance.

This quick summary is not meant as a defense of Priest’s arguments. I would be interested to hear what people make of his claims concerning Frege, Heidegger, etc. But as Priest himself admits, he is not interested in an exegesis that will necessarily sway scholars who have devoted their entire professional careers to the study of Heidegger for example. Priest’s point is to highlight the pattern he sees, the paradox that arises at the limit of expression; and the fact that this paradox arises among thinkers as diverse as Frege, Quine, Derrida, Heidegger, and Nagarjuna is evidence for Priest that there is something going on.

What I’m interested in is with the something that is going on, for I take there to be something ontological going on, a paradox at the heart of reality. In Philosophy at the Edge of Chaos and in my earlier book The Problem of Difference I argue much along these lines, adopting Deleuze as my ally for in Deleuze we find one who repeatedly affirms certain paradoxes. One merely need look through the table of contents to Logic of Sense to discover the importance of paradox in Deleuze’s thought – the first two chapters on becoming and surface effects are about the paradoxes of each, and these set the stage for the remaining discussions of the book. This is not to say that Deleuze and Priest are of the same mind. Priest sets out to incorporate the ‘true contradictions’ that arise at the limits of thought and expression into a broader and more encompassing logic, what he calls dialetheism; whereas Deleuze on my view is more interested in affirming the paradox at the ontological level, at the level of becoming and process rather than at the level of logic. It is interesting that Priest ends his book with a chapter on Nagarjuna. Nagarjuna is significant for Priest (and presumably for Jay Garfield with whom Priest wrote this chapter) because he affirmed an ontological paradox. Agreed. This is important and ought to be stressed. But then they argue that what Nagarjuna is doing here in affirming an ontological paradox ‘is quite distinctive, and to our knowledge is found nowhere else.’ (269). Now there are no doubt aspects of Nagarjuna’s thought that are distinctive and are not to be found in the western tradition – such as the use of the tetralemma – but if my reading of Deleuze is correct then Nagarjuna is not alone in affirming an ontological paradox.