ADVANCEMENT OF LEARNING 243 



proof, judgment itself cannot be perfect. And as there are 

 four kinds of demonstration, viz., 1, by immediate consent 

 and common notions; 2, by induction; 3, by syllogism; and 

 4, by congruity, 17 which Aristotle justly calls demonstration 

 in circle, 18 each of these demonstrations has its peculiar sub 

 jects, and parts of the sciences, wherein they are of force, 

 and others again from which they are excluded; for insist 

 ing upon too strict proofs in some cases, and still more the 

 facility and remissness in resting upon slight proofs in 

 others, is what has greatly prejudiced and obstructed the 

 sciences. And so much for the art of judgment. 



17 Analogical demonstration, or proof a latere, to which Bacon seems to 

 refer, consists in showing that the disputed attribute may be affirmed of several 

 subjects analogical to the one proposed, and thence proceeds to draw the infer 

 ence that such attribute enters also into the subject in question. In addition to 

 these last three kinds of mediate positive proof, there are three others, which 

 may be called mediate negative; viz., 1, a posteriori, which in inferring conclu 

 sions erroneous from the contradictory of that which is sought to be maintained, 

 shows that the opposition is formed on false principles, and establishes the truth 

 of their contradictories. 2, a priori, which in showing that the contradictory 

 of the original proposition is a necessary consequence of some exploded princi 

 ple, and also contradictory to the principle of which the contested proposition 

 is also a consequence, infers the truth of such proposition with the principle of 

 which it is a corollary. 3, d latere, whose object is to show that the attribute 

 diametrically opposite to the one in question, agrees with a subject also dia 

 metrically opposite to the one proposed, that the last attribute may be inferred 

 to agree with the last subject. Ed. 



18 Bacon seems to imply that Aristotle not only admitted demonstration in 

 a circle, but even understood it in the sense of analogical proof or demonstration 

 d latere ; whereas the Stagyrite only introduced the term for the purpose of con 

 troverting it. Some of the ancient materialists, in order to rid themselves of the 

 illogical consequences of a series of proofs ad inflnitum, in which the denial of 

 first principles involved them, asserted the possibility of demonstrating all things 

 from each other, a line of argument in which the chain of proof would run into 



itself: aAAo. TrafTwv eZj/cu, airoSeigiv oufiev xcoAvcf ei/Se^erai yap KVK\U yeveffOai TTJV aTroSeifiv 



*cai e| iMijAwv. (Arist. Anal. Post. i. 3.) The Stagyrite, however, confronted 

 this assertion with the reason, that demonstration could only be effected by 

 evolving new truths out of things prior and more known, and pronounced the 

 formation of a body of scientific truths without admitting first principles more 

 palpable to the mind than any proof could make them, impossible. See, also, 

 Arist. Analyt. Pri. ii. 5, 1. Ed. 



