4 o SCIENTIFIC METHOD IN PHILOSOPHY 



technical development of logic has taken place : I mean 

 the direction of what is called logistic or mathematical 

 logic. This kind of logic is mathematical in two different 

 senses : it is itself a branch of mathematics, and it is the 

 logic which is specially applicable to other more traditional 

 branches of mathematics. Historically, it began as merely 

 a branch of mathematics : its special applicability to other 

 branches is a more recent development. In both respects, 

 it is the fulfilment of a hope which Leibniz cherished 

 throughout his life, and pursued with all the ardour of 

 his amazing intellectual energy. Much of his work on 

 this subject has been published recently, since his dis- 

 coveries have been remade by others ; but none was 

 published by him, because his results persisted in con- 

 tradicting certain points in the traditional doctrine of the 

 syllogism. We now know that on these points the 

 traditional doctrine is wrong, but respect for Aristotle 

 prevented Leibniz from realising that this was possible. 1 



The modern development of mathematical logic dates 

 from Boole's Laws of Thought (185 4). But in him and 

 his successors, before Peano and Frege, the only thing 

 really achieved, apart from certain details, was the in- 

 vention of a mathematical symbolism for deducing 

 consequences from the premisses which the newer 

 methods shared with those of Aristotle. This subject 

 has considerable interest as an independent branch of 

 mathematics, but it has very little to do with real logic. 

 The first serious advance in real logic since the time of 



be throughout expressive of identity. But to say " the particular is the 

 universal " is self- contradictory. Again Hegel does not suspect a mistake 

 but proceeds to synthesise particular and universal in the individual, or 

 concrete universal. This is an example of how, for want of care at the 

 start, vast and imposing systems of philosophy are built upon stupid and 

 trivial confusions, which, but for the almost incredible fact that they are 

 unintentional, one would be tempted to characterise as puns. 

 1 Cf. Couturat, La Logique de Leibniz, pp. 361, 386. 



