Unnameable but not ineffable

John Bigelow (Monash Philosophy)

I will sketch a theory concerning a cumulative hierarchy of Platonic universals, which are unnameable but not ineffable. I will call this an Eleatic theory in memory of a character called ‘The Eleatic Stranger’ in Plato’s dialogue, The Sophist. I think of this theory as ‘higher-orderism’. There is little reason to think this theory to be complete: there may well be some important universals that lie outside the cumulative hierarchy. But there is reason to hope that the theory is internally consistent; and the cumulative hierarchy does offer explanatory potential that makes it worth exploring.  

Universals are important. Yet as Russell said: ‘Seeing that nearly all the words to be found in the dictionary stand for universals, it is strange that hardly anybody except students of philosophy ever realizes that there are such entities as universals’ (Russell, 1912, pp. 93-94). And when we try to talk about universals in flat-footedly literal language we often quickly tie ourselves in knots. This happens because our attempts to describe universals characteristically resort to figures of speech that need to be taken with what Frege (1892/1952, pp.43, 45) called a pinch of salt; see also Green (2006). 

The Eleatic theory aims to explain how to frame literally true descriptions of universals, using what are called lambda-categorial languages; but the theory also aims to explain why universals are almost always described not literally but obliquely, using figures of speech. One such figure of speech is personification, which is found for instance in Greek mythology; and another is the reification that is found, for instance, in modern mathematical set theory, and in philosophical discourse of the kind I have been writing in these opening paragraphs of this paper, and to which I will continue to resort throughout all the rest of this paper. It is only when you fully understand this figure of speech that you see that it is nonsense, taken literally; it is like a ladder that you throw aside after you have climbed up it.