Existence and the Variable
Existence and the Variable
We are all familiar with Quine’s meme-like dictum, “To be is to be the value of a variable”, with its repetition of “to be” (redolent of Hamlet) and its hypnotic alliteration over “v”. We descend from the commanding heights of Being to the arid lowlands of the logical formula, savoring the exciting bathos (there is such a thing): is that all that being comes to? We have been handed the key to penetrating the obscurities of existence: just attend to the mechanics of quantification—the bound variable in its pristine rigor, its sleek minimalism. But is the view plausible? Is this a convincing analysis of the concept of existence? Methinks it not to be, Horatio: its charms are illusory, its promise empty. Existence is not to be elucidated by the variable.
Point number one: the dictum locates existence in a meta-linguistic fact—the having of a value by a variable. The value is an object, the variable a sign, typically an x or y (excuse my use-mention sloppiness). The object is assigned to the sign, in an act of momentary reference, the latter “ranging over” the former. It is like reference proper; and indeed we can conjure an alternative dictum as follows: To be is to be the reference of a singular term. That proposal too is meta-linguistic in form: it locates existence in a fact about language—the having of reference by a singular term. Both theories make existence depend on language: no words no existence. But that is clearly wrong: being is not hostage to speaking. Things can exist without signs existing—for example, the Sun existed long before symbols did. The Sun looks at the Earth and wonders how its existence could depend on what is going on linguistically on that planet’s surface. The variable, remember, is really just a smartened up pronoun: and the Sun does not owe its existence to the activities of pronouns. Intuitively, variables (pronouns, singular terms) are extrinsic to existential facts; they don’t inhabit the same space as the existent entities they distantly designate. Variables didn’t come along with the Big Bang; they are not inherent in being.
Point two: the value of a variable needs to exist if it is to suffice for the existence of objects. It is no use ranging lustily over fictional entities, fantasies, and fairies; the assigned value must be an existent value. You will not bring the Sun into existence by assigning a nonexistent star to the variable x in “For some x, x is a star that lights up the Earth”; nor will you magic unicorns into existence by allowing them to operate as values of variables. Thus the dictum must read, “To be is to be the existent value of a variable”. Similarly for the variable itself: it too must not be merely fictional. So we must be understood to mean: existence consists in an existent object being the value of an existent variable. A double circularity therefore lurks within Quine’s dictum, just waiting to sprout an infinite regress. For how are we to analyze the existence of variables (letters of the alphabet) except by declaring them values of other variables? Variables ranging over variables are our only recourse–and so on till the variables comprise an infinite list. We can’t analyze the existence of one thing by invoking the existence of another thing that calls for the same analysis.
Point three: which variable is it that existence consists in? There are many variables—in practice arbitrarily limited to x, y, and z. Does the existence of the Sun depend upon one of these letters but not the others? That seems arbitrary: why choose x and not y? Indeed, why limit ourselves to the conventions of logic texts, or English pronouns? Perhaps the Sun depends for its existence on x, the Earth on y, and Pluto on (say) r. This is like saying that Venus depends for its existence on the name “Hesperus” but not the name “Phosphorus”. This is nonsense: existence is the same thing no matter how the existent object is designated. Variables are conventional, unlike existence itself. This is what comes of trying to tie existence to language: all the conventionality and arbitrariness of language infects existence itself. If existence is meta-linguistic, then it must inherit the properties of human languages; but it resolutely shuns those properties. To be is not to be conventionally designated thus and so.
A final point: presumably the sentences in which the variables occur must be true in order for existence to be assured. So Quine’s dictum must be expanded to assert that existence is equivalent to the truth of a sentence containing a bound variable. But then we are analyzing existence by means of truth: is that what we really want? Not that truth is somehow suspect or tacitly committed to existence, but it does seem extrinsic to existence as such. Truth belongs with the proposition, but existence is pre-propositional—a matter of reality in its primordial form. We would not wish to analyze being red, say, by invoking the truth of certain sentences (for an object to be red is for the sentence “This is red” to be true), so why do that for existence? Keep language out of it: eschew (another Quinean word) linguistic idealism! Existence as such has nothing intrinsically to do with variables and their values, pronouns and their denotations, or singular terms and their references; existence is what reality gets up to when left to its own devices. The variable is no doubt a fine invention, a valuable device of (formal) language, but let’s not confuse it with basic non-linguistic being. To be is to be completely independent of the variable and its values. 
 Similarly, not to be is independent of a variable lacking a value. Hamlet would never have said, “To be the value of a variable or not to be the value of a variable, that is the question”: that is not the question. The word “exists” simply doesn’t mean, “to be the value of a variable”.
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