THE SCIENCE OF LOGIC 



&quot; All inference is from particulars to particulars : General propositions 

 are merely registers of such inferences already made, and short formulae for 

 making more : The major premise of a syllogism, consequently, is a formula 

 of this description : and the conclusion is not an inference drawn from the 

 formula, but an inference drawn according to the formula : the real logical 

 antecedent, or premise, being the particular facts from which the general 

 proposition was collected by induction. Those facts . . . may have been 

 forgotten : but a record remains. . . . According to the indications of this 

 record we draw our conclusion. . . . For this it is essential that we should 

 read the record correctly : and the rules of the syllogism are a set of precau 

 tions to ensure our doing so.&quot; 



The view here expressed that the universal premiss of a 

 syllogism is a mere register of an enumeration or collection of 

 instances, and that the conclusion is inferred, not from the uni 

 versal, but from the particulars from which the latter was &quot; collected 

 by induction&quot; (199) raises the question as to where exactly, in 

 the whole mental movement from the sense perception of particu 

 lar facts to the proved universal conclusions of science, the special 

 step from known to unknown, which we call &quot; logical inference,&quot; 

 comes in. And an analysis of this inferential step from the 

 known to the unknown reveals, in turn, a peculiar difficulty which 

 has been styled the Paradox of Inference. Finally, the considera 

 tion of this paradox will bring us face to face with the time-worn 

 objection to the syllogism : that the latter is not a valid process 

 of inference at all, but always and necessarily involves the fallacy 

 of assuming what it purports to prove : the fallacy known as 

 Begging the Question (Petitio Principii). 



We will deal first with the paradox of inference. 



Logical inference must be a conscious passage from one or 

 more judgments to some new judgment which was implied in the 

 former (79, 82, 1 16, 147). The passage of thought, too, must be 

 recognized to be valid : to have in the antecedent a sufficient ground 

 for the consequent. Having distinguished between the meaning 

 and the implications of a given prepositional form (82), we saw that, 

 owing to the difficulty of determining where mere verbal change 

 ended and change of meaning commenced, it might be doubted 

 whether certain processes of immediate inference really deserved 

 the name of inference at all (109, 1 1 6). Hence arises the general 

 question, applicable to all forms of logical inference, mediate and 

 immediate : What sort or what degree of difference must there be 

 between premisses and conclusion, in order to constitute the pas 

 sage from the former to the latter a logical inference ? The signi- 



