PREFACE TO THE SECOND EDITION xxiii 



remarkable scholium : " Equidein in uumeris 4 + 4 facit 

 8, seu bini nummi binis additi i'uciunt quatuor nummos, 

 sed tune bini additi sunt alii a prioribus ; si iidem essent 

 nihil novi prodiret eb perinde esset ac si joco ex tribus 

 ovis facere vellemus sex numerando, primuni 3 ova, deinde 

 uno sublato residua 2, ac denique uno rursus sublato 

 residuum." 



Translated this would read as follows : 



"Axiom I. If the same thing is taken together with 

 itself, nothing new arises, or A + A == A. 



" Scholium. In numbers, indeed, 4+4 makes 8, or two 

 coins added to two coins make four coins, but then the 

 two added are different from the former ones ; if they were 

 the same nothing new would be produced, and it would 

 be just as if we tried in joke to make six eggs out of three, 

 by counting firstly the three eggs, then, one being removed, 

 counting the remaining two, and lastly, one being again 

 removed, counting the remaining egg." 



Compare the above with pp. 156 to 162 of the present 

 work. 



M. Littre has quite recently pointed out 1 what he thinks 

 is an analogy between the system of formal logic, stated 

 in the following pages, and the logical devices of the 

 celebrated Kaymond Lully. Lully's method of invention 

 was described in a great number of mediaeval books, but 

 is best stated in his^rs Compendiosa Inveniendi Veritatem, 

 seu Ars Magna et Major. This method consisted in placing 

 various names of things in the sectors of concentric 

 circles, so that when the circles were turned, every possible 

 combination of the things was easily produced by mechani- 

 cal means. It might, perhaps, be possible to discover in 

 this method a vague and rude anticipation of combinational 

 logic; but it is well known that the results of Lully's 

 method were usually of a fanciful, if not absurd character. 



A much closer analogue of the Logical Alphabet is 

 probably to be found in the Logical Square, invented by 



1 La Philosophic, Positive Mai-Juiu, 1877, torn, xviii. p. 456. 



