Cantab. Your theory of descriptions is, indeed, a most valuable contribution to logical theory, and an exemplary specimen of philosophical analysis. But how can you say that the description of a particular (or of a universal, for that matter) is, from the standpoint of a logician, an expression which contain the names of all particulars (or universals) or is the defined equivalent of such an expression? Surely it is clear not only that we can not name all particulars (or universals), our language doesn't even begin to contain such a list of names! Your account of the relation of descriptions to names must be mistaken. Russell. I don't see how it can be mistaken. How can a language have a greater scope than the names it contains? I will grant that we can not utter the names of all particulars in one breath (or in one life-time, for that matter), but the name "x 1 " is not itself an utterance. The name "red" is no more an individual utterance than redness is an individual red patch. In some sense which, as logician, I can not clarify, a language has an existence or reality over and above the utterances which are its tokens. It is humanly necessary to use tokens of "(Ex) fx" rather than tokens of the definitionally equivalent expression, "fx 1 V fx 2 V fx 3 V . . . ." But the language contains the latter expression in its entirety, even though we are unable to token more than an infinitesimal segment of it. I will admit that there is much here that I can not explicate, but as logician I must stand firm. A language can describe no further than it names. I hasten to add, however, in accordance with the distinctions I have drawn above, that a user of language can describe further than he can utter names. Cantab. You logicians are all alike! Adept at manipulating abstractions, you can not see what is before your eyes! Languages are human facts, and like other human facts, they are clumsy, imperfect, and incomplete. French, German, Bantu . . . these are languages. They are historical facts. They are born, they grow, they die. I agree that the English word "red" is not a single utterance. It is, however, a class of utterances, a class which can only be defined in sociological, historical, psychological -- in short, anthropological -- terms. Can you seriously say that English, or German, or Bantu contains names for all particulars and (simple) universals? Furthermore, a language isn't a mere set of utterance-classes. It finds its existence in occasions on which utterances are used as linguistic utterances. Words, to be sure, have meaning, but it is more accurate to say that words have meaning for users of words. Indeed, it is primarily utterances which have meaning, and to say that a word (as utterance-class) has meaning, is to say that each event which is properly an utterance or token of the word (and not a mere parroting) has meaning. Russell. I must admit that I have been thinking of a language as an ideal system, tidy and complete to an immeasurably greater extent than any historical language. Yet I would have said that my analysis applies to French, German, and Bantu, so that in some sense I must have been talking about sociological facts of the kind you have been mentioning. You are a philosopher. Can you resolve my perplexity? Cantab. To the epistemologist, the key to the understanding of the human cognitive enterprise is the concept of the given. In whatever manner knowledge may be said to extend in scope beyond the given, givenness is the fundamental mode, if not of knowledge itself, then of being within the domain or purview of knowledge. Again, in whatever manner meaning may be said to extend in scope beyond the given, givenness is the fundamental mode, if not of meaning itself, then of being within the domain or purview of meaning. Whatever the heights that can be scaled by piling language habit on language habit, whatever, indeed the internal structure of language habits themselves -- a problem we gladly leave to the psychologist -- this much is clear to the epistemologist who is worth his salt:3 the towering edifice of language rests on the confrontation of sign-event with datum in a field of acquaintance. lt is not enough to say that a name isn't a name unless it names something (has a nominatum). This axiom can itself be understood only in terms of the more fundamental principle that only a sign-event whose referent, be it a universal or a particular, is given to the user of the sign-event can be a name. Indeed, name and nominatum must fall together in one field of direct awareness. To the epistemologist who penetrated below the anthropological standpoint I was presenting a moment ago to shake you out of your naive linguistic realism, language is by its nature datum-centric. It is in the given that he finds the cash value of the vast structure of linguistic habits and events which is studied in so many ways by the various sciences of Man. Russell. I find your argument which moves from language as studied by empirical linguistics to its roots and purchase in the given quite persuasive. Unfortunately, however, much your interpretation of language and meaning may appeal to me as a budding epistemologist, as a logician I am puzzled and unhappy. In my unenlightened days I thought of a language as an ideal structure so correlated with the world that (in addition to its specifically logical devices) it contains a name for each basic particular and for each simple universal ingredient in the world. Now I am being driven to hold that a language can contain names for only what is surely a vanishingly small portion of the ingredients of the world, namely, the elements of someone's field of acquaintance -- including universals as well as particulars -- at a time; the language itself being a set of sign-events within that same field of acquaintance. But if the names a language contains are as limited as this, how can the user of the language refer to items (universals as well as particulars) which fall beyond the scope of this momentary field of acquaintance? Does not your theory of names commit you to a semantic solipsism of the present moment? Indeed, how could one entertain such a meaning as now? for surely this meaning intrinsically involves the contrast meaning then! Cantab. (Startled) But surely it is you who gave us the answer to this question! It was your distinction between names and descriptions which enabled the epistemologist to draw the distinction between knowledge by acquaintance and knowledge by description which disposes of the pseudo-problem into which you have talked yourself! We refer to objects which are not given by means of descriptive phrases, thus: "the object which I shall see a moment later than this." It is by the use of descriptions that we refer to the world of which our data constitute such a vanishingly small part. Russell. No! That won't do at all. We are going around in a circle. The theory of descriptions as I formulated it above rested on the very conception of language of which you have so vigorously tried to disabuse me. You will remember that I claimed that a sentence involving a description is logical shorthand for a set of sentences involving the names of all items of the type to which the descriptum belongs. Thus, we saw that, of the two sentences which explicate the meaning of "the f exists," the first, namely, (Ex) fx is the defined equivalent of fx 1 V fx 2 V fx 3 V . . . which is a sentence of which I have tokened only the first three alternants. Indeed, if we suppose that the world consists of a finite set of particulars whose number is t, then the sentence, "The f exists," is equivalent to the following expression: fx 1 & ~fx 2 & ~fx 3 & . . . ~fx t or ~fx 1 & fx 2 & ~fx 3 & . . . ~ fx t or ~fx 1 & ~fx 2 & fx 3 & . . . ~fx t .................................................. or ~fx 1 & ~fx 2 & ~fx 3 & . . . fx t It surely follows from this analysis that if all nominata are data-here-now, then descriptive phrases can not possibly enable one to refer to what is not a datum-here-now. That would indeed be to pull from a top-hat a rabbit that wasn't there! That is the business of magicians, not logicians, and, alas! even magicians only seem to do it. Cantab. Can it really be that your theory of descriptions is infected with this naive conception of a language as an ideal structure which covers the world like a metaphysical blanket? But wait! Surely the theory of descriptions says only that "The f exists" is equivalent to "(Ex) fx & (y) fy --> y = x." It is your interpretation of the latter as the defined equivalent of an expression which involves all the names of the language which is at fault. In short, the trouble lies in your account of the existential operator. It may be helpful nonsense to say that to an angel whose world was present in one field of acquaintance, "(Ex) fx" would be logically equivalent to an alternation of atomic sentences whose constituents were names. But for us there can be no such equivalence. In our language, "(Ex) fx" is not an abbreviation. It -- or "(x) fx," whichever one takes as primitive -- is a basic logical expression. More accurately, &(E_) --_" represents a primitive logical operation, for, to put it bluntly, variables are not logical constructions out of names, as you suggest. They are blanks. The logical meaning of general operators lies in the role they play in rules relating to the filling of blanks and in rules relating expressions involving blanks to one another. Russell. This is an interesting suggestion, though I am not quite sure that I grasp what you are driving at. Perhaps if you were to explain how it enables you to dissolve my puzzle as to how we can mean further than we can name. . . . Cantab. Yes, I think that I can exorcise your puzzle now, though I must confess that before I thought of this new approach to the existential operator, you had me worried. I now see that we must distinguish between two modes of empirical meaning. (1) The mode characteristic of names. Here there is a direct tie between the linguistic and the non-linguistic. Both names (sign-events) and nominata fall within one field of empirical givenness. (2) A mode of meaning built on the former, but not reducible to it. This mode of meaning consists in the employment of general operators and variables. The empirical significance of expressions belonging at this level of language lies in the rules relating it to the first mode of meaning. Thus, we can go from "(x) fx" to "fa" where "a" is a name and thus has empirical meaning of the first mode. On the other hand, the unique contribution of this second mode of meaning lies in the fact that the use of expressions on this level constitutes, subject to an anchoring in the first mode of meaning, "a reference to the world as including but extending beyond the given." Empirical meaning proper is a matter of givenness. Reference to the world is a purely formal matter of the logical structure of our language. It has empirical significance or "cash value" only by virtue of the rules which tie general operators and variables up with names, and hence with empirical meaning proper.