In discussing propositional quantifiers we have considered two kinds of variables: variables occupying the argument places of connectives, and variables occupying the argument places of predicates.
We began with languages which contained the first kind of variable, i.e., variables taking sentences as substituends. Our first point was that there appear to be no sentences in English that serve as adequate readings of formulas containing propositional quantifiers. Then we showed how a certain natural and illuminating extension of English by prosentences did provide perspicuous readings. The point of introducing prosentences was to provide a way of making clear the grammar of propositional variables: propositional variables have a prosentential character — not a pronominal character. Given this information we were able to show, on the assumption that the grammar of propositional variables in philosopher's English should be determined by their grammar in formal languages (unless a separate account of their grammar is provided), that propositional variables can be used in a grammatically and philosophically acceptable way in philosophers' English. According to our criteria of well-formedness Carnap's semantic definition of truth does not lack an ‘essential’ predicate - despite arguments to the contrary. It also followed from our account of the prosentential character of bound propositional variables that in explaining propositional quantification, sentences should not be construed as names.
One matter we have not discussed is whether such quantification should be called ‘propositional’, ‘sentential’, or something else. As our variables do not range over (they are not terms) either propositions, or sentences, each name is inappropriate, given the usual picture of quantification. But we think the relevant question in this context is, are we obtaining generality with respect to propositions, sentences, or something else?
Because people have argued that all bound variables must have a pronominal character, we presented and discussed in the third section languages in which the variables take propositional terms as substituends. In our case we included names of propositions, that-clauses, and names of sentences in the set of propositional terms. We made a few comparisons with the languages discussed in the second section. We showed among other things how a truth predicate could be used to obtain generality. In contrast, the languages of the second section, using propositional variables, obtain generality without the use of a truth predicate.
KeywordsFormal Language Relevant Question Propositional Variable Truth Predicate Separate Account
Unable to display preview. Download preview PDF.
- BelnapN. D., 1967, ‘Intensional Models for First Degree Formulas’,The Journal of Symbolic Logic 32, 1–22.Google Scholar
- CarnapR., 1946,Introduction to Semantics, Harvard University Press, Cambridge, Mass.Google Scholar
- CurryH. B., 1963,Foundations of Mathematical Logic, McGraw-Hill Book Company, New York.Google Scholar
- HeidelbergerH., 1968, ‘The Indispensibility of Truth’,American Philosophical Quarterly 5, 212–17.Google Scholar
- QuineW. V., 1962,Mathematical Logic, Harper and Row, New York, revised edition.Google Scholar
- QuineW. V., 1970,Philosophy of Logic, Prentice-Hall, Englewood Cliffs, New Jersey.Google Scholar
- RamseyF. R., 1927, ‘Facts and Propositions’,Aristotelian Society Suppl. Vol. 7, 153–70.Google Scholar
- SellarsW. F., 1963,Science, Perception and Reality, Routledge and Kegan Paul, London.Google Scholar
- SuppesP., 1957,Introduction to Logic, D. Van Nostrand Company, Inc., Princeton, New Jersey.Google Scholar