ftl# 



Mb DE morgan, ON THE SYLLOGISM, No. Ill, 



out the species of impossibility which it belongs to. Again, X )) Y and X (•) Y, incompatible 

 when X is part of the universe, become compatible when X and Y are coextensive with the 

 universe. Again, ( ), )(, (•(, )•), may all coexist. Any other junctions give only parts of 

 the propositions we already have. The three junctions noted answer to the universal pre- 

 dicates in the fourth table, which are introduced to give completeness of language : the 

 correspondents of the second table are hardly worth setting down. For the explanation of 

 the terms of the fourth table see ^ xvii. 4. 



XXXIII. Affirmative and negative propositions. With me these are technical terms, 

 not wholly corresponding to assertion and denial. A proposition is affirmative which is always 

 true of identicals and false of contraries : a proposition is negative which is always false of 

 identicals and true of contraries. Thus )), ((, ( ), )(, are affirmatives ; )•), (•(, )•(, (•), 

 are negatives : the inserted dot indicates a negative ; if an express symbol be required for an 

 affirmative, it may be two dots, or )) may be )••). We see that X (•) Y is negative, though 

 in common* language, it is an assertion, ' Every thing is either X or Y.' But it has the 

 properties of the other negatives. 



XXXIV. Previously to entering upon the subject of quantity the following considerations 

 are conveniently inserted here. 



Proof of a proposition is the acquisition of necessary assent : and it must consist in 

 ascertaining, first, that the names are rightly applied, secondly, that the relation between 

 them is truly stated. 



Inductive proof, or induction, or proof a posteriori, is the aggregation of separate verifica- 

 tions, whether upon individual qualities or objects, or species or component attributes, in 

 number enough to make assent to the proposition an unavoidable necessity of thought. 



Deductive proof, or deduction, or proof a priori, is the composition of separate previous 

 propositions, from which the same unavoidable necessity follows. 



The name depends upon the immediate character. Thus a deductive proof may have 

 its components, or some of them, furnished by separate inductions, or may be a compound 

 of inductions ; and an inductive proof may be an aggregate of deductions. For instance, as 

 often occurs in mathematics, an inductive proof may have every aggregant a compound of 

 deduction from all those which precede. 



Probable or physical induction is where the number of cases verified is so large, without 

 any failure, that the mind feels the sort of necessity called moral certainty that no failure 

 ever can occur within any limited experience. Where or why this proof is wanted, we are 

 not to inquire : it is enough that this kind of proof is one of the forms of thought. All these 

 cases come under the word proof in logic, because, under all these cases, the mind works with 

 and from the proposition in one and the same way : be it with more of certainty, or less ; with 

 one ground of certainty, or another. 



• The disjunctive form in which the proposition (■) is 

 most clearly enunciated, that is, ' Everything is either X or Y,' 

 instead of ' No not-X is not-Y ' — has been made the occasion 

 of an assertion that I, in ignorance, introduce disjunctive 

 syllogisms among categorical ones. This I do, beyond doubt : 

 for, in adopting categorical syllogisms, I cannot avoid adopting 



disjunctive ones. Contraries once allowed, every categorical 

 syllogism is also disjunctive. Tims the old instance, ' Every 

 man is animal; Sortes (so Socrates was at last written) is 

 man; therefore Sortes is animal,' can be identified with the 

 following : ' Every thing is either animal, or not-mau ; Sortes 

 is not not-man ; therefore Sortes is animal. 



