The interpretation which I propose for the traditional forms has, then, the following merits: (a) it enables the whole body of the laws of the system to be accepted without inconsistency;

(b) with the reservation noted above, it gives the constants of the system just the sense which they have in a vast group of statements of ordinary speech; (c) it emphasizes an important general feature of statements of that group, viz., that while the existence of members of their subject-classes is not a part of what is asserted in such statement, it is, in the sense we have examined, presupposed by them.

It is this last feature which

makes it unplausible to regard assertions of existence as either the whole, or conjunctive or disjunctive parts, of the sense of such ordinary statements as ' All the men at work on the scaffolding have gone home' or 'Some of the men are still at work'.

This was the reason why we were unhappy about regarding such expressions as '(x)(fx>g) as giving the form of these sentences; and why our uneasiness was not to be removed by the simple addition of positively or negatively existential for mulae.

Even the resemblance between 'There is not a single book in his room which is not by an English author' and the negatively existential form '~(Ix)(fx. ~gx) was deceptive.

The former, as normally used, carries the presupposition ' books-in-his-room ' and is far from being entailed by ' not-a-book-in. his-room'; whereas the latter is entailed by ~(J)(fx)'.

So

it is that if someone, with a solemn face, says ' There is not a single foreign book in his roora 'and then later reveals that there are no books in the room at all, we have the sense, not of having been lied to, but of having been made the victim of a sort of linguistic outrage. Of course he did not say there were any books in the room, so he has not said anything false.

Yet what

he said gave us the right to assume that there were, so he has misled us.

For what he said to be true (or false) it is necessary

(though not sufficient) that there should be books in the room.

Of this subtle sort is the relation between ' There is not a book in his room which is not by an English author ' and ' There are books in his room'. Some will say these points are irrelevaat to logic (are ' merely pragmatic '). If to call them 'irrelevant to logic' is to say that they are not considered in formal systems, then this is a point I should wish not to dispute, but to emphasize. But to logic as concerned with the relations between general classes of statements occurring in ordinary use, with the general conditions under which such statements are correctly called 'true ' or 'false', these points are not irrelevant.

Certainly a 'pragmatic con-aideration, a general rule of linguistic conduct, may perhapa be geen te underile these points: the rule, namely, that one does not make the (logically) lesser, when one could truthfully (and with equal or greater linguistic economy) make the greater, claim. Assume for a moment that the form 'There is not a single . . . which 18 not • ..'were introduced

into ordinary speech with the same sense as '~(Jx)(fx.~gx). Then the operation of this general rule would inhibit the use of this form where one could truly say simply 'There is not a single... or the introduced

orm just those logical presuppositions which 1 have describea; the Iort would tend, if it did not remain otiose, to develop just those ditterences I have emphasized from the logic of the symbolio form it was introduced operation of this .was first pointed

out to me, in a different connexion, by Mr. h. P.. Grice.