Misinterpretations of Quantifiers

Abstract

Professor Geach has frequently engaged in polemic against 'Oxford philosophers' who make use of the term of art 'referring expression'. It would be equally appropriate to the principles Geach has set out for identifying a sentence as a singular proposition to criticize 'Harvard philosophers' for their uncritical use of the expression 'singular term'. Just as not all 'Oxford philosophy' comes from Oxford, so not all 'Harvard philosophy' emanates directly from Harvard; so one is not surprised to find the ill-effects of the 'singular term' terminology appearing in a recent paper by Dr. T. R. Baldwin.' Baldwin makes crucial use of the notion of a 'context-dependent singular term', and gives as examples of this category 'This man', and 'He' in 'He smokes' (p. 225). Thus he talks of a sentence 'He smokes' being true in a certain context, c. Presumably, what this means is that someone could utter the sentence 'He smokes' in a situation where, by pointing or by relying on previous conversation, it was clear that 'He' here indicated a particular man. Armed with this device, Baldwin produces a truth-theoretical definition of '(3x) (x smokes)', which, he claims, is a 'substitutional' interpretation which, despite being substitutional, allows the proposition to be verified by a nameless smoker. One of the features which distinguish 'substitutional' from 'objectual' interpretations of quantification is that the former operate with the notion of truth, whereas the latter operate with the notion of satisfaction. This distinction is less apparent in Baldwin's paper than it usually is. This is because his version of the 'objectual' truth definition of the existential quantifier, (5), on page 222, uses the terminology of an open sentence's being 'true of' a sequence, s, rather than a sequence's 'satisfying' an open sentence, whilst his modified 'substitutional' interpretation uses the terminology of a sentence's being 'true in' a context, c. To make matters worse, Baldwin introduces a modified 'objectual' interpretation which uses the notion of context-dependent variables, where a context for a variable is a function from variables to members of the domain (p. 230). Thus, as well as 'true of s', which is a predicate of open sentences, we have 'true in c', which is a predicate of closed sentences, and 'true in d', where 'd' takes as values contexts for variables, which is a predicate of open sentences again. Baldwin is clearly committed to these distinctions: he says 'truth in c is not defined for expressions with free variables, and truth in d is not defined for expressions with singular terms' (ibid.). By 'expressions with singular terms' Baldwin presumably means