On diagonal argument, Russell absurdities and an uncountable notion of lingua characterica
King, James Douglass
University of Lethbridge. Faculty of Arts and Science
Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2004
There is an interesting connection between cardinality of language and the distinction of lingua characterica from calculus rationator. Calculus-type languages have only a countable number of sentences, and only a single semantic valuation per sentence. By contrast, some of the sentences, and only a single semantic valuation per sentence. By contrast, some of the sentences of a lingua have available an uncountable number of semantic valuations. Thus, the lingua-type of language appears to have a greater degree of semantic universality than that of a calculus. It is suggested that the present notion of lingua provides a platform for a theory of ambiguity, whereby single sentences may have multiply - indeed, uncountably - many semantic valuations. It is further suggested that this might lead to a pacification of paradox. This thesis involves Peter Aczel's notion of a universal syntax, Russell's question, Keith Simmons' theory of diagonal argument, Curry's paradox, and a 'Leibnizian' notion of language.
vii, 111 leaves ; 29 cm.
Dissertations, Academic , Language and logic , Language and languages -- Philosophy , Logic , Reasoning