AND THE PROBABILITIES OF AUTHORITY AND ARGUMENT. 



381 



I shall use, as is usual, the letters A and E to signify positive and negative universals : and 

 / and for the corresponding particulars : but with a modification presently noticed. I shall also 

 use the following notation, without which I should hardly iiave liad patience for the many hundreds 

 of cases which this paper has required. 



P) Q signifies Every P is Q. 



P . Q No P is Q. 



PQ Some Ps are Qs. 



P : Q Some Ps are not Qs. 



I have taken for tlie convertible propositions, the symbols P. Q and PQ, whicli the algebraist is 

 accustomed to consider as identical with Q.P and QP: the same thing is true under these 

 meanings. But P ) Q and P : Q, which are also used in arithmetic and algebra, convey no idea of 

 convertibility. 



All expressions that have any meaning can of course be reduced to one of these forms. 

 Aristotle denies tiiis, and divides all expression into significative and enunciative, meaning by tlie 

 latter that in which there is truth or falsehood. Thus prayer, he says, is speech, but neitlier true 

 nor false. This is surely not correct ; — Deliver jis from evil may be either " To be delivered 

 from evil is our prayer," or " We are of those who pray to be delivered from evil," or " Evil is a 

 thing we pray to be delivered from." Or, as the text, it would be " Deliver us from evil, is the 

 passage on which I mean to comment :" and the sermon would probably give all the enunciations 

 above. In a request, command, inquiry, or announcement, the tone* of voice predicates. 



In classifying all possible predications -by means of two names V and ^V, their contraries must 

 be included. AVe must therefore consider all the relations that may exist between Y and ^Y, 

 JT and y, y and x, x and }'. Between each of these there are six modes of enunciation : thus 

 between P and Q we have 



P)Q, Q)P, P.Q^Q.P, PQ = QP, P:Q, Q.P. 



12 3 4 5 6 



But it will be best to arrange these by contradictories, or propositions one of which must be true 

 and the other false: as P ) Q and"P:Q, Q)P and Q: P, P.Q and PQ. These six modes 

 applied to each of the four variations of subjects, give twenty-four varieties, which are reducible 

 to eight, being identical three and three, as follows: 



J^)y=X.y = y),v 

 X:Y=Xy =y:^v. 



Y) X = Y ..V = .v)y. 

 Y:X=Yx =a:y. 



Though the use of the great and small letters may suit the eye, these lines should be read tliu.s: 

 " Every A' is F" is identical with " no X is not-F," and "every not-K is not-A'," and so on. These 

 eight modes may all be derived from the four Aristotelian modes by changing both terms into 

 contraries ; which suggests the following notation : 



(A) X)Y ; .v)y=Y)X 



(O) X:Y a::y=Y:X 



X.Y= X)y= Y)w. 



XY=X -.y =^ Y:.v. 



a,.y=.l)Y = y) X. 



xy = x : Y = y : X. 





X. Y 

 XY 



,v .y 

 wy 



(i). 



• To call H i>LT>von hy hi.s tiiinic \n a propohiiinn, perliapH more. [ John ; tliertf'orc, you are ihe person I want lo speak to." The 



Then- In certainly the full nic.inin^ of a .tylloj^isin in it. \\'hen a leiist tliat can he siiid is, that he states the premisut*, and U-ave-. 



pmon calli — John ! no one can Hay that any part of the following \ John lo draw the conclusion. 

 ti not implied : '* John in the pereon I want to speak to ; you arc 



