AND THE PROBABILITIES OF AUTHORITY AND ARGUMENT. 



407 



The condition of inference expresses itself; in the X^^ , of the conclusion, m must neither be 

 nor negative. The first case gives no Aristotelian syllogism; the middle term never entering 

 universally (of necessity) into any of its forms, under any degree of specification which the usual 

 modes of speaking allow. The other cases divide the old syllogisms among themselves in the fol- 

 lowing manner: they are written so as to show that there is sometimes a little difference of amount 

 of specification between the results of different figures, which amount may change in the reduction 

 from one figure to another. The Roman numerals mark the figures. 



2. t = a, V = b 

 t = a, V = b 

 t < a, V = b 

 t < a, V = b 



3. u = b, V = b 

 u < b, V = h 

 u = b, e < b 



4. t = a, V = b, w = c 

 t = a, V = b, w = c 

 t = a, V = b, w = c 

 t = a, V = b, w = c 



V = b, w = c 



V = b, w = c 

 t — a, V = b, 



5. u = b, V = b, w = c 

 u = b, V = b, w = c 



V = b, w = c 



V = b, w = c 

 u = h, w = c 



Y)Z„,+ ^)r. = A')Z„,„. 

 ^)F„+ Y)Z,„= Z,,.„^ 

 V)Z,^.+ X,Y, = X,Z,„„, 

 .r,F„ + Y)Z,,.= z, „,^, 



Y)X,+ Y)Z,= Z,„,„X,„, 



Y„x, +r)z,„ = z,„„,x,„, 

 Y)x,+ r„z,„=z,,„.Ar,,, 



Y. Z + X)Y„= X. Z 



Z.Y + X)Y,^= X.Z 



X)Y„+ Z . Y = Z . X 



X)Y^+ Y.Z = Z.X 



Y. Z + XtY„ = Xr- Z 



Z.Y + XtY^ = Xr- Z 



X)Y^ + Z,^.:Y= Z,„:X 



Y.Z + Y)Xt= X,^,-Z 

 Z.Y+Y)X,= X,^,:Z 

 Y.Z + Y^X, = X„^,:Z 

 Z.Y + Y^X, = X„_,:Z 

 Y,:Z + r) A-, = X. ,:Z 



Barbara I. 

 Bramantip IV. 

 Darii I. 

 Dimaris IV. 



Darapti III. 

 Disamis III. 

 Datisi III. 



Celarent I. 

 Cenare II. 

 Camestres II. 

 Camenes IV. 

 Ferio I. 

 Festitio II. 

 Baroko II. 



Felapton III. 

 Fesapo IV. 

 Feriso III. 

 Fresison IV. 

 Bokardo III. 



This system is complete in itself, if contraries be excluded. That in the body of this paper is 

 also complete, if all specification be excluded, except which is contained in the usual words some and 

 alt. An attempt to combine the two systems would be useless, because its forms of expression 

 would not be those of common language. For instance, the following must be one form of an 

 affirmative proposition in the combined system " Of t Xs and t' .rs every one is one or other 

 of u Fs and u' y s." It would be useless to investigate the conditions of inference as to forms 

 which are not those of speech in any language. 



But at the same time there is a certain approach to the preceding forms, if we take in not 

 merely the logical force of our common propositions, but also wiiat is usually implied. He who 

 nays, " Some Afs are I's," is generally held to mean that tlic other Xs are not Ks. The complex 

 syllogisms, in which the alternatives left by the common forms are supposed to be definitely settled, 

 are worthy of attention : and their theory is as follows. 



With respect to the name Y, the name X may be of seven different kinds, distinguishable with- 

 out numerical specification. These arc as follows : neither term containing the whole universe. 



