The universal force of free choice any

This paper adds to the ongoing debate about the quantificational status of English FC any. It argues that any is a universal, though its universality is such that it can be conjoined with an existential statement. This is established by showing, first of all, that various properties that are amenable to a universal account of FC any remain elusive in recent accounts that treat it as an indefinite. Secondly, it presents a detailed description of supplementary/numeral any, cases in which any occurs with an indefinite. Such cases have been assumed to provide evidence for the indefinite-any view but an explicit semantics for the constructions is given, showing that any invariably contributes universal quantificational force. Existential force always comes from other elements. The paper also discusses alternative formulations that preserve the key insights of the universalist position and the role of cross-linguistic variation in the study of FC items.

God and Factual Necessity

Many philosophers and philosophically oriented theologians hold that it is unreasonable to treat the statement ‘There is a God’ as analytic or logically true. As an existential statement, they argue, it is no different from any statement of its kind. Existential statements cannot be analytic, because contra-existential statements cannot be contradictory. (Notice, however, that existential statements can be contradictory, and contra-existential statements can be analytic.) To say, for example, that unicorns do not exist is simply to say that no entity satisfies the description ‘unicorn’. But this cannot be complex in the sense of entailing two contradictory statements. If so, then the existential statement corresponding to it cannot be analytic. In general, since no contra-existential statement can be contradictory, no existential statement can be analytic.

Testing singly quantified tautologies

An effective method for testing arguments consisting of singly quantified expressions has recourse to Parry's trapezoid symbolism.1 The procedure entails representing in that symbolism each premise of the argument and the negation of the conclusion. Variables are disregarded. After clearing away any negated quantifiers, the universal statements, including a denied existential conclusion, are first set down and their conjunction (KU) derived. Existential statements, including a denied universal conclusion, are then listed. The argument is valid if and only if some contradiction appears, whether as some premise empty of lines, as a KU empty of lines, or as some existential statement having no lines in common with the KU.

On the interpretation of intuitionistic number theory

The purpose of this article is to introduce the notion of “recursive realizability.”Let P be some property of natural numbers. Consider the existential statement, “There exists a number n having the property P.” To explain the meaning which this has for a constructivist or intuitionist, it has been described as a partial judgement, or incomplete communication of a more specific statement which says that a certain given number n, or the number n obtainable by a certain given method, has the property P. The meaning of the existential statement thus resides in a reference to certain information, which it implies could be stated in detail, though the trouble is not taken to do so. Perhaps the detail is suppressed in order to convey a general view of some fact.The information to which reference is made should be thought of as possibly comprising other items besides the value of n or method for obtaining it, namely such items as may be necessary to complete the communication that that n has the property P.