"Quantification and Colour in Natural Language"
Dany Jaspers, President of the Center for Research in Syntax, Semantics and Phonology (HUB)
(deelgebied: semantics, logic, cognitive science, analytic philosophy)
Date: April 07, 2011 - 14.30-16.00
Location: Grote Vergaderzaal - 3de verdieping- Blandijnberg 2 - Ghent
In his “Remarks on Colour” (1977: III-46), Ludwig Wittgenstein writes: “Among the colours: Kinship and Contrast. (And that is logic).” In this linguistic talk on colour percepts and concepts, proof will be provided that Wittgenstein’s intuition about the logical nature of colour relations is to be taken literally. Oppositions in logic and colour perception will be shown to be isomorphic and consequences for colour language will be drawn.
First, we shall look at the nature of the oppositions between primary and secondary colours as represented in the colour wheel and the Aristotelian oppositions between quantified propositions as represented in the logical square of oppositions. Algebraic definitions for the logical oppositions – i.e. for entailment, contradiction, contrariety and subcontrariety – will then be shown to carry over to the realm of colour percepts, where they describe very precisely the relations obtaining between the known primary and secondary colours. Next, linguistic evidence for the reality of the resulting isomorphism will be adduced. For example, the operators that resist natural single-item lexicalization in logic (such as not all, for which there is no natural lexicalization *nall) systematically have counterparts in the realm of colour terms which are not naturally lexicalized either.
In the second part of the talk, the consequences of the isomorphism will be explored. From the perspective of the architecture of cognition, the pattern suggests that natural language quantification and negation are much more deeply rooted in the physiological structure of human cognition than standardly assumed. Philosophically speaking, the algebras of logic and colour offer an interesting perspective from which to look at the time-honoured colour incompatibility (or: colour exclusion) problem, i.e. the problem that the statement “this is red and this is green” is felt to be contradictory if this refers to a spatio-temporally single colour spot. Wittgenstein realized that colour incompatibility posed a serious threat to his view in the Tractatus Logico-Philosophicus that “the logical product of two elementary propositions can neither be a tautology nor a contradiction” (§ 6.3751). There being no logical vocabulary in “this is red” or “this is green” to warrant the conclusion that they are non-elementary propositions, how come the logical product is contradictory nonetheless? Many say that it was the lack of a solution to this problem that led Wittgenstein to give up the Tractatus approach. With the considerable advantage of hindsight, it may be suggested that rather than dissolving the problem by rejecting his Tractatus, Wittgenstein could have attempted to solve colour incompatibility in terms of the internal logico-semantic structure of colour concepts (cf. Katz 1998). Such a linguistic approach has the further advantage that it can account for several other undeniably logical intuitions about colour statements, including the fact that this spot is red entails both this spot has a color and this spot is not yellow.
References
Wittgenstein, L. (1977), Remarks on Colour, Ed. G.E.M. Anscombe, Oxford: Basil Blackwell.
KATZ, J.J. (1998), The Problem in Twentieth-Century Philosophy, The Journal of Philosophy XCV, 11, 547-575.