Names of Names

By Arthur N. Prior

(Edited by Jakobsen. Notes by Prior, and Jakobsen. First published Tuesday Oct 18, 2011)

It seems to have been a common doctrine among late medieval writer on Logic that, where we have such a pair of statements as ’”Socrates” has three syllables’ and ”Socrates is wise”, the subject-term of the first statement is the word ”Socrates” used ”non-significatively”, or with ”material supposition”, while the subject-term of the second statement is the same word used ”significatively”, or with ”formal supposition.” The current manner of speaking about such statements is a little different. What would be generally said now is that the two statements have different subject-terms, the subject-term of the first being the name of the subject-term of the second. The word ”Socrates”, it would be said, is ”used” in the second statement, while in the first this word is not ”used” at all, but a quite different word is ”used” to ”mention” it. (1) What I wish to suggest here is that while this new manner of speaking has much to be said for it, there is also something to be said for the old. That what is to be said in favour of the older locution may be made a little clearer, let us turn for a moment to something said some years ago by H.W.B. Joseph (2) in criticism of Stebbing’s rendering of ”A unicorn exists” as ”There is an object c which is such that Φx is true when c is substituted for x.” (3) Joseph remarks on this, ”It will be admitted that the object c would have to be a quadruped, that could beat the ground with its hoofs. But the c which I could substitute for x in the ‘propositional function’ Φx, and so obtain something (viz. A proposition) that is true, could not be a quadruped. I cannot put a quadruped into a proposition. Hence we ought to write ‘There is an object called c which is such that .....’” The sentence on which I wish to concentrate is the penultimate one; and I wish to suggest that it is possible to reply to this that in a very real sense we can “put a quadruped into a proposition,” if there are any quadrupeds about; it being precisely this feat, and others like it, which demonstrative pronouns are designed to accomplish. For a word like ‘This’ or ‘That’, say in ‘That is a unicorn’, has no meaning unless the object to which it is applied is actually present and in some way indicated while the word is being used. The purpose of the word is not so much to function as a subject on its own, “representing” the thing (as words are sometimes said to do); it is rather as it were to bring the thing bodily into the sentence, so that the predicate is attached not so much to another word as to the thing itself. “The shallowness of syntax”, C.S. Peirce has said, “is manifest in it’s failing to recognise the importance of mere words ... to fulfil the function of a grammatical subject.” (4)

With this preliminary, let us turn to the subject of so-called names of names. It may be admitted that there is a sense in which the word “’Socrates’” is the name of the word “Socrates”; but it must be insisted that this is not quite the same sense as that in which the word “Socrates” is the name of the son of Sophroniscus. The addition of the quotation-marks is not merely like the addition of two new letters to produce a totally new word. The case is not as if we had arbitrarily chosen to make the word “Asocratesa” the name of the word “Socrates”,(5) though “Ginger” would have served the purpose just as well. This misunderstanding is not uncommon; it is suggested, e.g., by Quine’s remark (6) that “the personal name buried within the first word of the statement ‘”Cicero” has six letters’... is logically no more germane to the statement than is the verb ‘let’ which is buried within the last word.” The true force of the quotation-marks is that of a demonstrative, and the word between them really is the word indicated – in the given example, it really is the word “Socrates”, the name of the son of Sophroniscus; which does occur in the proposition” ‘Socrates’ has three syllables”, though not in the way in which a quadruped, “beating the ground with its hoofs”, may be said to occur in the proposition formed by pointing to the animal and saying (quite falsely, no doubt, but that is immaterial), “That is a unicorn.” And this, it seems to me, is just what the medieval logicians meant when they said that the statements “’Socrates’ has three syllables” and “Socrates is wise” have the same subject-term, though they are not about the same subject, the common subject-term having a different sort of “supposition” in the two cases. The medieval view, one might say, was that to “mention” a word is one way of “using” it – to be distinguished, certainly, from other ways, but not from “use” altogether.

The only legitimate alternative to this is, I think, to say that the word “Socrates”, though it must be present to the reader for the proposition to be understood (as some object must be present when we utter it for the proposition “That is a unicorn” to be understood), is not itself part of (what we generally describe as) the proposition “’Socrates’ has three syllables”, this latter consisting only of the fragment” ‘ ‘ has three syllables”, in which the quotation-marks are understood as pointing to the word within them (as our finger points to the object in the other case), and so have their meaning unambiguously fixed by the object to which we point as we say it).(7) Common conventions are not quite consistent here. We are normally inclined to say that “’Socrates’”, rather than “’ ‘” (with its meaning fixed by the presence of the word “Socrates” in the place to which it points), is the subject-term of the proposition about the name; but on the other hand we are normally inclined to say that the subject-term of “That is a unicorn” is just the word “That”, or at most the word “That” and the pointing of the finger, in the presence of the object we do not normally include the object itself in the subject-term (although this is defensible, we feel that it is bizarre), as we do include the name in the other case. Again, those who use the language of Ockham do not normally say that the object we indicate as we say “That is a unicorn” is being “used non-significatively”, or that it has suppositio materialis, even though exactly the same thing is being done with it as is being done with such a word as “Socrates” when we “use it non-significatively”, and it has suppositio materialis. Nor do those who prefer the language of Quine normally say that the object, the “That” and the pointing finger together constitute it in the only sense in which “’Socrates’” constitute the name of the name “Socrates.” Nor, I think, is a rigorously consistent usage really to be demanded at this point; but it is as well that the inconsistency of our ordinary usage should not pass without notice, or be allowed to bemuse us.

There is, indeed, one point at which the parallel which I have drawn above involves an artificially simplification; but my central contention is not, I think, affected by its removal. What I have ignored is the difference between “That is a unicorn”, understood as being purely about the object indicated as it is uttered, and “’Socrates’ has three syllables”, understood as referring not merely to the “token” actually enclosed by the inner quotation-marks in any given occurrence of this sentence, but to the word “Socrates” considered as a “type” occurring in other sentences also. This difference may be ignored because the sentence thus understood equivalent to another which really is about the token, namely the sentence “Any token of the same design as the token ‘Socrates’ has three syllables”, and although the strict parallel to this is not “That is a unicorn”, but rather “Any animal like that animal” – pointing to one “is a unicorn”, this parallel, equally with the other, makes it plain that the force of the quotation-marks is that of a demonstrative plus the pointing hand, and not merely that of the first and last letters of a proper name. Quite often, moreover, the phrase “That animal”, accompanied by an indicative gesture, is used to mean “That sort of animal”, as when we go to the Zoo, point to an animal, and say “That animal inhabits South Africa”, though we know perfectly well that the individual beast to which we are pointing inhabits not South Africa but Regent’s Park or Whipsnade. Our linguistic behaviour is precisely the same when we say “’Socrates’ is the subject-term of ‘Socrates is wise’”, though we know perfectly well that the token directly indicated by the first pair of inner quotation-marks is not an “inhabitant” of the propositional token indicated by the second pair, but stands on its own. In both cases, we point to the “token” but understand the “type”; but in both cases the “token” itself must be present if we are to understand anything at all.
A. N. Prior

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(1) So, notably, W.V. Quine, Mathematical Logic $4. This disctinction is used (though not mentioned) in the White Knight’s conversations with Alice in Through the Looking-Glass:
”’…. The name of the song is called ”Haddocs’ Eyes.”’
’Oh, that’s the name of the song, is it?’ Alice said ….
’No, you don’t understand’ the Knight said, looking a little vexed. ’That’s what the name is called. The name really is ”The Aged Aged Man.”’” (H.W.B. Joseph, in Mind 1932, p. 424, shamelessly robs the White Knights of all credit for this subtlety by attributing the remarks to Humpty Dumpty).
(2) Op. Cit.

(3) Underlined words in Prior’s MS are all made into cursive in the text. [Editors note]

(4) The Collected Papers of C.S. Peirce, 3.419.

(5) As the White Knight chooses to make the phrase ”Haddocks’ Eyes” the name of the set of words ”The Aged Aged Man.”

(6) Op. Cit.

(7) I understand from conversation with Professor Donald Davidson that this is the view which he would be inclined to take.