as to the facts that are true of that particular would enable you to have a fuller understanding of the meaning of the

name.

BERTRAND RUSSELL.

LONDON, ENGLAND.

DISCUSSION.

Mr. Carr: You think there are simple facts that are not complex. Are complexes all composed of simples? Are not the simples that go into complexes themselves complex?

Mr. Russell: No facts are simple. As to your second question, that is, of course, a question that might be argued whether when a thing is complex it is necessary that it should in analysis have constituents that are simple. I think it is perfectly possible to suppose that complex things are capable of analysis ad infinitum, and that you never reach the simple. I do not think it is true, but it is a thing that one might argue, certainly. I do myself think that complexes-I do not like to talk of complexes—but that facts are composed of simples, but I admit that that is a difficult argument, and it might be that analysis could go on forever.

Mr. Carr: You do not mean that in calling the thing complex, you have asserted that there really are simples?

Mr. Russell: No, I do not think that is necessarily implied.

Mr. Neville: I do not feel clear that the proposition "This is white" is in any case a simpler proposition than the proposition “This and that have the same color."

Mr. Russell: That is one of the things I have not had time for. It may be the same as the proposition "This and that have the same color." It may be that white is defined as the color of "this," or rather that the proposition "This is white" means "This is identical in color with that," the color of "that" being, so to speak, the definition of white. That may be, but there is no special reason to think that it is.

Mr. Neville: Are there any monadic relations which would be better examples?

Mr. Russell: I think not. It is perfectly obvious a priori that you can get rid of all monadic relations by that trick. One of the things I was going to say if I had had time was that you can get rid of dyadic and reduce to triadic, and so on. But there is no particular reason to suppose that that is the way the world begins, that it begins with relations of order n instead of relations of order 1. You cannot reduce them downward, but you can reduce them upward.

If the proper name of a thing, a "this," varies from instant to instant, how is it possible to make any argument?

Mr. Russell: You can keep "this" going for about a minute or two. I made that dot and talked about it for some little time. I mean it varies often. If you argue quickly, you can get some little way before it is finished. I think things last for a finite time, a matter of some seconds or minutes or whatever it may happen to be.

You do not think that air is acting on that and changing it?

Mr. Russell: It does not matter about that if it does not alter its appearance enough for you to have a different sense-datum.

THE WASHINGTON MANUSCRIPT AND THE

TH

RESURRECTION IN MARK.

'HE discovery of the Washington MS. will materially alter the critical apparatus of the next editor of the Greek New Testament. Soden has not observed the fact that this manuscript contains a reading of primary import, in agreement with the lost manuscripts of Eusebius. Westcott and Hort give λdovoa as a marginal reading at έλθουσαι Mark xvi. 5, but they omit its correlative, dxovoɑoɑi, at xvi. 8, a reading already known to John Mill of Oxford, in 1707. Westcott and Hort's oversight was due to the fact that no Greek manuscript, used in 1881, contained the reading (except the ungrammatical άxovoavτes of Gregory's No. 565). Moreover, they had also failed to observe that lost manuscripts quoted by Eusebius read ἀκουσασαι:

και άκουσασαι ἐφυγον, και οὐδενι οὐδεν εἶπον· ἐφοβουντο yao. (Ad Marin. Quaest. 1.)

The critical apparatus of the future will read thus:

Mark xvi. 5.

Corrupted text: eioehdovoal, from the parallel in Luke.

Primitive text: Edovoal, with Evv. Matth., Johann., Petri; Codd. B, 127.1

1 In my article in The Monist, April, 1917, pp. 173f, I adduced the Gothic version here, on the authority of Tischendorf and Massmann; but a study of the Gothic has convinced me that Soden is right in ignoring it.

Mark xvi. 8.

Corrupted text: ehdovoa, inserted as a correlative to εἰσελθουσαι.

Primitive text: ȧxovoaσaι, with lost manuscripts of Sæcc. II-III, apud Euseb. ad Marin., Quaest. I; Codex W, Sinai Syriac, Armenian, and Sahidic versions.

The Washington MS. exhibits the first stage of corruption:

και άκουσασαι ἐξηλθον και έφυγον.

The ἐξελθουσαι or ἐξηλθον was then being added before the deletion of the ἀκουσασαι. The Vatican and Sinaitic MSS. betray the last and complete stage of corruption, wherein the axovoaσaι is dropped altogether:

και ἐξελθουσαι έφυγον ἀπο του μνημείου.

Contrast with this the simplicity of Eusebius's early manuscripts which say nothing about the women going out of the sepulcher (because they had never been in it). The Armenian version omits the Dovoa, and the Sinai Syriac omits the ἀπο του μνημείου. Thus do these two ancient witnesses, based upon lost Greek manuscripts of the same age as those used by Eusebius, furnish complete support to the reading of that Father. The translator of the future will end Mark thus:

And when they heard, they fled, and said nothing to any one, for they were afraid of.....

Here endeth the Gospel according to Mark.

ALBERT J. EDMUNDS.

PHILADELPHIA, PA.

IN

LEIBNIZ AND PASCAL.1*

N the History of Mathematics it is generally stated that the higher analysis took its rise in the method of indivisibles of Cavalieri (1635). This assertion, at least as far as the invention3 of the algorithm of the higher analysis is concerned, is erroneous. In what follows it will be shown, by argument founded on the work of the French mathematicians of the seventeenth century and on the manuscripts of Leibniz, that Leibniz was led to his invention of the algorithm of the higher analysis by a study of the writings of Pascal, more than by anything else.*

With regard to the manuscripts of Leibniz, the first letters of the correspondence between Leibniz and Tschirnhaus are weighty; they contain the further discussion of their joint labor during the time that they lived together in Paris (September, 1675, to November, 1676); it is well known that it was during this time that Leibniz invented the algorithm of the higher analysis. Among these letters, one from Leibniz, not hitherto published, which closes the first part of the correspondence between Leibniz and Tschirnhaus, contains a very detailed statement of the studies of Leibniz during his sojourn in Paris; it is beyond dispute of the utmost importance, since it was written only four years afterward and recalls particulars in a most vivid manner."

Next, we have to consider the works of the French mathematicians about the middle of the seventeenth cen* For footnotes of both author and translator see infra, pp. 550-560.