I^tTNCnONS AND VALtTE OF THE SYLLOGISM. ii^ 



in the form of the syllogisms, the 

 axioms on which the syllogistic process 

 is founded must undergo a correspond- 

 ing transformation. In this altered 

 phraseology, both these axioms may 

 be brought under one general expres- 

 sion, namely, that whatever has any 

 mark, has that which it is a mark of. 

 Or, when the minor premise as well as 

 the major is universal, we may state 

 it thus : Whatever is a mark of any 

 mark, is a mark of that which this 

 last is a mark of. To trace the 

 identity of these axioms with those 

 previously laid down may be left to 

 the intelligent reader. We shall find, 

 as we proceed, the great convenience 

 of the phraseology into which we have 

 last thrown them, and which is better 

 adapted than any I am ac(|uainted 

 with to express with precision and 

 force what is aimed at, and actually 

 accomplished, in every case of the 

 ascertainment of a truth by ratiocina- 

 tion.* 



♦Professor Bikin (Logic, i. 157) considers 

 the axiom (or rather axioms) here proposed 

 as a sub>titure for the dictum de omni to 

 possess certain advaiitages, but to be " un- 

 ■workable as a basis of tiie sylloijisin. The 

 fatal defect consists in this, that it is ill- 

 adapted to brinu' out the difference between 

 total and partial coincidence of terms, the 

 observation of which is tlie essential pre- 

 caution in 63'llogisiiig correctly. If all the 

 termo wero co-extensive, the axiom would 

 flow on admirably; A carries B. all Band 

 none but B ; T. carries C in the Fame man- 

 ner; at once A carries C^ without limitation 

 or reserve. But in point of fact, we know 

 that while A carries B, otuer things carry 

 B also ; whence a process of limitation I's 

 required, in transfeiring A lO C through B. 

 A (in common with other things) carries 

 B ; B (in common witli other thinjifs) carries 

 C; whence A(in common with other things) 

 carries C. Tlie axiom provides no means 

 of making this limitation ; if we were to 

 fo low A lierally, we should be led to sup- 

 pose A and (J co-extensive : for such is the 

 only obvious meaning of ' the attribute A 

 coincides with the attribute C" 



It is certainly possible th;it a careless 

 learner here and there may suppose that if 

 A c-.rries B, it follows that B carries A. 

 But if anyone isso incautious as to commit 

 this mistake, the very earliest lesson in the 

 logic of infer nee, tlie Conversion of Pro- 

 positions, will coiTectit. The first of the 

 two formsin which I have stated the axiom 

 is in some de^jree open to Mr. Bain's criti- 



CHAPTER IIL 



OF THE FUNCTIONS AND LOGICAL 

 VALUE OF THE SYLLOGISM. 



§ I. We have shown what is the 

 real nature of the truths with which 

 the Syllogism is conversant, in contra- 

 distinction to the more superficial 

 manner in which their import is con- 



cism : when B is said to co-exist with A, 

 (it must be by h lapsus calami that Mr. 

 Bain uses the word coincide,) it is possible, 

 in tlie absence of warning, to suppose the 

 meaning to bo that tiie two things are only 

 found totrei her. But tins misinterpretation 

 is excluded by the other, orpiactcal, form 

 of the maxim ; Nota notce est nota rei 

 ipxius. No one would be in any danger of 

 inferring that because a is a mark or 6, 6 

 can never exist without a; that because 

 being in a confirmed consumption is a mark 

 of being about to die, 1,0 one ciieswho is 

 not in a consumption ; that because being 

 coal is a mark of having come out of the 

 earth, nothing can come out of the earth 

 except coal. Ordinary knowledge of Eng- 

 lish seems a sufficient p otection against 

 these mistakes, since inspeaking of a mark 

 of anything we are never understood as 

 implying reciprocity. 



A more fundamental objection isptated 

 j by Mr. Bain in a subsequent passage (p. 

 j 158). "The axiom does not accommodate 

 j itself to the tvpeof Deductive Reasoning as 

 ! contrasted with Induction — the application ^ 

 ' of a general principle to a special case. 

 Anything that fads to make prouiinent 

 this circumstance is not adapted as a 

 foundation for the syllogism. " But though 

 it may be proper to limit tlie term Deduc- 

 tion to the application of a general prin- 

 ciple to a special case, it has never been 

 held that Ratiocination or Svllogism is 

 subject to the same limitation ; and tlie 

 adoption of it would excludea^^r atamouut 

 of valid and conclusive syllogistic reason- 

 ing. Moreover, if the dictum deomni makes 

 prominent the fact of tlie application of a 

 general principle to a particular case, the 

 axiom I propose makes prominenttiie con- 

 dition which alone makes that apphcaiiou 

 a real inference. 



I conclude, therefore, that both forms 

 have their value, and their place in Logic. 

 The dictum de omni should be retained as 

 the fundamental axiom of the logic of mere 

 consistency, often ca led Formal Logic ; nor 

 have I ever quarrelled with the use of it in 

 that character, nor proposed to banish it 

 from treatises on Formal Losric. But tti« 

 other is the proper axiom for the logic of 

 the pursuit of truth by w;ty of Deduction ; 

 and the recoL'nition of it can alone show 

 how It is possib e that deductive reasoniuc 

 can be a road to truth. 



