mB 



Mr DE morgan, on the syllogism, No. Ill, 



and collative only, upon the ideas of class and attribute considered as philosophical units. 

 They number, then, but the numerical total is of no interest, or only of infrequent and acci- 

 dental interest, in the form of thought : just as in common life, the junction in thought of 

 a general, a battle, a site, a result, and a despatch, offers no interest in its quinary character. 

 The mathematical whole, or whole of class, thinks, most frequently, of class aggregated 

 of classes; less frequently, rarely in comparison, of class compounded of classes. The meta- 

 physical whole, or whole of attribute, thinks, almost always, of attribute compounded of attri- 

 butes : sometimes, but very rarely, of attribute aggregated of attributes. Extension, then, 

 predominates in the mathematical whole ; intension in the metaphysical. 



Every proposition, at least of the onymatic character, may be thought in either whole: 

 and practical logic slips out of one into the other, as facility will require. All consequences 

 which spring out of onymatic relations may be obtained in any whole. To insist that all 

 thought is in one whole, is a mistake : that it ought to be, an absurdity. 



Each onymatic proposition has two terms, and each term may be thought in either of the 

 two ways. This gives four readings: — 



Logico 



On these see ^ X, I shall here specially consider the first and third, from which all that 

 is peculiar to the second and fourth easily follows. 



In the relation of containing and contained, there may be terminal precision, or terminal 

 ambiguity. If, when X is contained in Y, we mean that X is part only, leaving another part, 

 there is terminal precision ; but if we mean that possibly X may be as large as Y, there is 

 terminal ambiguity. The distinction is that of part-not-whole, and part-or-whole. (§ XI.) 



The first table following contains the various relations which may exist between the classes 

 X and Y, as to inclusion or exclusion, under terminal ambiguity, with the readings in the 

 arithmetical whole, and the notation of my last paper, presently noticed further. This is all 

 condensed in the heading : and the other tables are as described. 



XXVI. Logico-mathematicnl Reading. Terminal Ambiguity. (§§ XIII, XVII.) 



Proposition of assertion or denial. 



Assertion of X contained in Y 

 Denial of X contained in Y 



Assertion of X excluded from Y 

 Denial of X excluded from Y 



Assertion of x contained in Y 

 Denial of x contained in Y 



Assertion of x excluded from Y 

 Denial of x excluded from Y 



X subjected to 

 Y as 



Species 

 Exient 



Coexternal 

 Copartient 



Complement 

 Coinadequate 



Genus 

 Deficient 



Y predicated of i „ , , , „ 



X as Reading in anthmetical whole. I Notation. 



Genus Every X is Y j X))Y 



Deficient Some Xs are not Ys X(-(Y 



Coexternal No X is Y X)-(Y 



Copartient Some Xs are Ys XQY 



Complement Everything is either X or Y i X(-)Y 



Coinadequate Some things are neither Xs nor Ys , X)( Y 



Species Some Xs are every Y X((Y 



Exient No Xs are some Ys ' X)'»)Y 



