ON VARIOUS POINTS OP THE ONYMATIC SYSTEM. 



453 



In syllogisms of undecided assertion, in which assertion and non-assertion give non-asser- 

 tion, tlie law of validity is as follows. When one proposition only is particular, that parti- 

 cular must be the undecided assertion. Every form is valid in which a universal and a par- 

 ticular occur : but when both are universal, or both particular, the middle term must be 

 balanced, that is, of the same quantity in both. The symbol of the conclusion is derived as 

 in the ordinary syllogism, with this exception, that the spicula which we are to obtain from 

 the decided proposition must be inverted. Thus, denoting want of power to assert by ^ 

 affixed, we may shew that ))()'^ gives (y, )))*)^ gives (-y, O^ ({ gives ()\ (O^'C-) 

 gives ((", )('')•) gives )•(", &c. But ))))'' and )))•) give no conclusion. 



For example : — " We can hardly undertake to say that all men are responsible for the 

 effects of their actions, independently of motive : for there are men who are really incapable of 

 any consecutive tracing of consequences, a thing we must hesitate to affirm of beings whose 

 responsibility is for consequences". This form is (•()•)> giving )y ; as follows: 



(•( Some men are not capable of tracing consequences. 



)'y We will not affirm that there are beings responsible for consequences who are inca- 

 pable of tracing consequences. 

 ) y Therefore we will not affirm that all men are responsible for consequences. 



For will not, we may read^ must not, cannot, ought not, need not, &c., provided only that 

 we make the conclusion follow the premise ; all that is wanted is wora-affirmation, be the 

 restraining cause what it may. The forms of indecision are precisely those in which affirm- 

 ation and denial give denial : but the mere presentation of indecision would have been a 

 valuable addition to the logic of the middle ages. Here there was nothing but sharp asser- 

 tion and denial : and theology, the science in which the word dogmatism got its evil sense, 

 was made to look even more positive than she really was. Forbearance is not categorical ; 

 and the syllogism of charity is the syllogism of indecision. 



The portion of all possible thought within which our concepts are and are* to be 



' The terms of relation can be applied: and it will be good 

 exercise to learn to see the combinations. If we call 'that which 

 we cannot affirm to be a species' an unaffirmed species, we 

 may read as follows. In XjjVCCZ, or X((^Z, we see that a 

 species of an unaffirmed genus of Z is itself an unaffirmed 

 genus of Z. In ))^{{, giving ))^, we see that an unaffirmed 

 species of a genus is an unaffirmed species. In (( )•)% giving 

 )•)", we see that the genus of an unaffirmed deficient is itself 

 an unaffirmed deficient. In )(")•(, giving )-)'^> W8 s^e that 

 the unaffirmed coinadequate of an external is an unaffirmed 

 deficient. 



' Falling asleep while I was considering how to answer 

 this objection — that a definite universe is material — in the most 

 elementary form, I found Ijogicus, Mathematicus, and Neuter, 

 in the middle of an argument upon the very point. L. In 

 " All X is Y " we have a pure form of thought, divested of 

 matter: we see how we think, independently of what. N. It's 

 not true, though. M. He does not mean that whenever he says 

 X he says Y. L. By no means : X and Y are names ; and 

 my proposition asserts that whatever I may name X, I may 

 Dame Y. N. Why, so may I, or so may any man; but — 



L. Nay ! I meant with truth, according to received meanings : 

 X and Y are representations of concepts, and the concept X is 

 asserted as what ought never to be in thought without the con- 

 cept Y. M. But concepts are matter of thought, are they not ? 

 li. Yes : but X and Y are but concepts as concepts, recognised 

 as different concepts by diflerence of symbol, stated to be 

 thought as included and including by the proposition. M. But 

 if your form contain concepts as concepts, and if concept be 

 matter, surely your form contains matter as matter. N. You 

 wont get out of that, I see, let concept be which it will, Greek 

 or Hebrew ; it may be one or the other for me. L. You con- 

 firm me entirely in what I was going to say, that the goodness 

 of formal inference may be perceived independently of the 

 meaning of the terms ; concept is to you as would be X or Y. 

 M. Then my remark is admitted to be just? L. Certainly: 

 matter as matter is present in every enunciation ; but the per- 

 ception of the formal force of a proposition is independent of 

 the material differences between the different matters which it 

 contains or might contain. M. That is to say, you treat con- 

 cept as algebra treats number ? L. Precisely : logic preceded 

 algebra in the use of general terms. M. But algebra never 



