To non-logicians this heading may suggest a certain sort of moral (or quasi-moral) seriousness; but, to a logician, the phrase means roughly ‘implication of exemplification’. That is, there is an existential commitment when there is an implication that a predicate is exemplified or that a certain thing or kind of thing exists.
A there-is sentence is probably the most explicit way of taking on an existential commitment in the logician’s sense. And it might be doubted that we have shown proper respect to this sort of sentence and to other existentials. The problem can be sharpened by thinking about the name Santa Claus. The analysis of the sentence There is a Santa Claus raises issues that would be distracting at this point, but enough has been said already to suggest that we might analyze There is something that is Santa Claus as ∃x x = s (with s abbreviating Santa Claus). But is this analysis right? The sentence ∃x x = s is a tautology, for it says that there is some referential value that is identical to the value of s, and that is bound to be true, even if s is undefined. So on this analysis, we end up saying that the sentence There is something that is Santa Claus is indubitably true (but we also say it is empty of content, so we have no genuine reassurance to offer small children).
This empty existential commitment is not as crazy as it may seem. We have interpreted the existential quantifier as claiming the existence of examples among referential values, and the nil value—the reference value of non-referring terms—is a genuine referential value. Since this interpretation of the existential quantifier is just a stipulation of the meaning of the sign ∃, there is really no way to quarrel with it. But things may heat up when we use this special sign to render the English there-is form and other existential sentences. That is, it can still be asked whether English existentials claim merely that examples may be found among reference values or make the stronger claim that examples can be found among non-nil values. Let us refer to the latter, more specific sort of claim as a substantive existential commitment.
Looking at bare there-is existentials may sharpen the issue in the wrong way so let us look at other cases. We can attribute a substantive existential commitment to a form (∃x: ρx) θx if ρ is necessarily false of the nil value; for then any example in the extension of ρ must then be a non-nil value. And the same is true of the form ∃x θx if the extension of θ is necessarily limited to objects. The difficulty with ∃x (x = s) is that there seems to be nothing to force a similar limitation since we have already stipulated the extension of =; it is the only predicate in this sentence, and we have stipulated that it holds of the nil value and itself. However, we may have placed too simple an interpretation on the question of whether there is a Santa Claus; perhaps a child is really asking whether there was some person who is Santa Claus. We can analyze the sentence There is someone who is Santa Claus as ∃x (Px ∧ x = s) [P: λx (x is a person); s: Santa Claus], and this is not a tautology. The substantive existential commitment here is imposed by the predicate P.
These are controversial matters; and, although the approach we have taken to there-is existentials is a viable one, it is not the only viable one. Accordingly, it is worth noting that we have the resources available to take a different approach. If we wish to attribute substantive existential commitment through purely logical vocabulary, we could introduce a logical constant to capture the predicate λx (x is non-nil), and we would stipulate that the extension of such a constant on any range R consist of all non-nil values. One alternative to the analyses of claims of exemplification that we have been giving is then that real
claims of exemplification (and real
generalizations) always have such predicate as part of their restrictions. Another way of formulating this alternative approach would be to introduce an individual term that is stipulated to refer to the nil value—i.e., one whose reference is stipulated to be undefined. Substantial existential commitment could then be expressed by denying identity with this term. (In fact, such a term will be a by-product of the approach to definite descriptions we consider in 8.4.2, but we will not make it part of our analysis of claims of exemplification.)