132 EEASONING. 



§ 2. On examining, then, these two general formulae, we find that in 

 both of them, one premise, the major, is a universal proposition; and ac- 



pend, either for purposes of speculation or of practice, do not, except in a few peculiar cases, 

 admit of any numerical precision ; common reasoning can not be translated into Mr. De 

 Morgan's forms, which therefore can not serve any purpose as a test of it. 



Sir William Hamilton's theory of the " quantification of the predicate " may be described as 

 follows : 



"Logically" (I quote his words) "we ought to take into account the quantity, always un- 

 derstood in thought, but usually, for manifest reasons, elided in its expression, not only of the 

 subject, but also of the predicate of a judgment." All A is B, is equivalent to all A is some 

 B. No A is B, to No A is any B. Some A is B, is tantamount to some A is some B. 

 Some A is not B, to Some A is not any B. As in these forms of assertion the predicate is 

 exactly co-extensive with the subject, they all admit of simple conversion ; and by this we 

 obtain two additional forms — Some B is all A, and No B is some A. We may also make 

 the assertion All A is all B, which will be true if the classes A and B are exactly co-extensive. 

 The last three forms, though conveying real assertions, have no place in the ordinary classifi- 

 cation of Propositions. All propositions, then, being supposed to be translated into this lan- 

 guage, and written each in that one of the preceding forms which answers to its signification, 

 there emerges a new set of syllogistic rules, materially different from the common ones. A 

 general view of the points of difference may be given in the words of Sir W. Hamilton (^Dis- 

 cussions, 2d ed., p. 651) : 



"The revocation of the two terms of a Proposition to their true relation ; a proposition be- 

 ing always an equation of its subject and its predicate. 



"The consequent reduction of the Conversion of Propositions from three species to one — 

 that of Simple Conversion. 



" The reduction of all the General Laws of Categorical Syllogisms to a single Canon. 



"The evolution from that one canon of all the Species and varieties of Syllogisms. 



"The abrogation of all the Special Laws of Syllogism. 



"A demonstration of the exclusive possibility of Three Syllogistic Figures; and (on new 

 grounds) the scientific and final abolition of the Fourth. 



"A manifestation that Figure is an unessential variation in syllogistic form; and the con- 

 sequent absurdity of Reducing the syllogisms of the other figures to the first. 



"An enouncement of one Organic Principle for each Figure. 



"A determination of the true number of the Legitimate Moods ; with 



"Their amplification in number (thirty-six); 



"Their numerical equality under all the figures ; and 



"Their relative equivalence, or virtual identity, throughout every schematic difference. 



"That, in the second and third figures, the extremes holding both the same relation to the 

 middle term, there is not, as in the first, an opposition and subordination between a term ma- 

 jor and a term minor, mutually containing and contained, in the counter wholes of Extension 

 and Comprehension. 



"Consequently, in the second and third figures, there is no determinate major and minor 

 premises, and there are two indifferent conclusions : whereas in the first the premises are de- 

 terminate, and there is a single proximate conclusion." 



This doctrine, like that of Mr. De Morgan previously noticed, is a real addition to the syl- 

 logistic theory ; and has moreover this advantage over Mr. De Morgan's "numerically definite 

 Syllogism," that the forms it supplies are really available as a test of the correctness of ratioc- 

 ination ; since propositions in the common form may always have their predicates quantified, 

 and so be made amenable to Sir W. Hamilton's rules. Considered, however, as a contribution 

 to the Science of Logic, that is, to the analysis of the mental processes concerned in reasoning, 

 the new doctrine appears to me, I confess, not merely superfluous, but erroneous ; since the 

 form in which it clothes propositions does not, like the ordinary fonn, express what is in the 

 mind of the speaker when he enunciates the proposition. I can not think Sir WiUiam Ham- 

 ilton right in maintaining that the quantity of the predicate is " always understood in thought." 

 It is implied, but is not present to the mind of the person who asserts the proposition. The 

 quantification of the predicate, instead of being a means of bringing out more clearly the mean- 

 ing of the proposition, actually leads the mind out of the proposition, into another order of 

 ideas. For when we say. All men are mortal, we simply mean to affirm the attribute mor- 

 tality of all men ; without thinking at all of the class mortal in the concrete, or troubling our- 

 selves about whether it contains any other beings or not. It is only for some artificial pur- 

 pose that we ever look at the proposition in the aspect in which the predicate also is thought 

 of as a class-name, either including the subject only, or the subject and something more. (See 

 above, p. 77, 78.) 



For a fuller discussion of this subject, see the twenty-second chapter of a work already i-o- 

 ferred to, "An Examination of Sir William Hamilton's Philosophy." 



