42 Mr Venn, On the various notations adopted for [Dec. 6, 



only want to deal with pairs of contradictories, whether terms or 

 propositions, and only want, as above remarked, to posit and sub- 

 late them, the signs + and — are convenient. But then we lose 

 the use of these signs for far more appropriate purposes, viz. for 

 logical aggregation and exception. Moreover the antithesis thus 

 suggested of a contradictory, rather than a supplementary relation 

 between S and not-S, soon leads to difficulties. How are we to 

 represent not-S . not-P ? By (- 8 - P) or by (- S) x (- P) ? There 

 is no convenient opening here for compounding terms or premises. 



The only brief and convenient rule for working this notation 

 seems to apply to the process of conversion. From ' Posit S and 

 sublate P,' we deduce of course ' Posit P and sublate S.' Genera- 

 lizing this to cover the four possible cases we see that it may be 

 summed up in the words 'change the order of the terms and 

 both the signs :' i.e. from (+S + P) we infer (— P — S), and so on. 



Though therefore the scheme of employing + and — in logic, 

 for this purpose, repeatedly presents itself, it does not seem to me 

 to merit any more detailed investigation. 



12 — 14. These are, to my thinking, precisely equivalent to 

 one another. It is true that Mr Maccoll insists upon it that his 

 interpretation of his class symbols as standing for statements, marks 

 a ' cardinal point ' of distinction ; but I regard this as an arbi- 

 trary restriction of the full generality of our symbolic language. 

 Phrase it how we will, — the presence of S implies that of P, the 

 existence of S implies that of P, the truth of S implies that of P ; 

 — the antithesis at bottom is always the same, or rather it comes 

 under one generalized signification. 



It may be added, in explanation of the differences of detail, 

 that the line over a letter, and the accent, respectively mark con- 

 tradiction ; and the three copula-symbols may in each case alike 

 be read 'implies.' We may read them therefore, 'S marks, or 

 implies, the absence of P.' The converse of course does not hold ; 

 that is, not-P does not imply S. If this additional information 

 were given to us we should in each case employ the copula (=), 

 and write them S=P',8=P. The sign of equality marks in 

 fact the double implication, just as 'All S is all P' contains the 

 two propositions, 'All S is P,' and 'All P is S.' 



Of course, in saying this, it must not for a moment be supposed 

 that the various systems which make use of these notations are 

 themselves coincident. On the contrary, there are various dif- 

 ferences, both in the detailed treatment and in the rest of the 

 notation, even between (12) and (13); whilst Mr Peirce has made 

 his symbols a means of attacking various problems (such as the 

 Logic of Relatives) which have not seemed to me to lie across the 

 path we have had to take. 





