THE DOCTRINE OF REDUCTION 349 



with 5 and with P, our conclusion depends ; and if our conclusion, that &quot; Some 

 S is [or is not] P &quot; or, which is the same, &quot; S may be [or need not be] P &quot; 

 if this conclusion be challenged, the direct and natural way of showing it 

 to be justified is by appealing to the instances of M s that are both S and P 

 [or, that are 5 and are not P}. 



This direct appeal to an instance was called by Aristotle eK0e&amp;lt;nr, or Ex 

 position : &quot; if all S is both P and R, we may take some particular 5, say N ; 

 this will be both P and /?, so that there will be some R which is P &quot;- 1 This 

 is the real line of thought followed in the third figure : we accept the con 

 clusion because we can cite instances of its truth. The instances need not be 

 individuals ; they may be kinds or species. And, of course, they need not be 

 produced physically, but only in our thought. They must, however, be pro 

 duced in thought ; and it is upon them, as embodying the truth of our con 

 clusion, that the latter is based. Hence, too, the middle term, as in the 

 second figure, gives us only a ratio cognoscendi for our conclusion, not a 

 ratio essendi. When we cite instances of M as we do in the third figure, for 

 the purpose of drawing a conclusion about the relation of 5 to P, the instances 

 are to us the means of knowing that such a relation exists, but they do not 

 furnish us with the reason why it exists. When we argue that a cloven-footed 

 animal may ruminate because we see horned animals that have both these at 

 tributes, we do not regard the possession of horns as causing the conjunction 

 of the other two attributes in the horned animal. No doubt, if we know that 

 &quot; all horned animals ruminate,&quot; we may regard horns as a sign of rumination 

 in animals possessed of horns ; we may then proceed to reflect that &quot; some 

 cloven-footed animals have horns &quot; ; and because they have this sign of 

 rumination we may conclude by a syllogism in the first figure (Darii] that 

 &quot; Some cloven-footed animals ruminate &quot;. We may thus transpose our reason 

 ing from the third to the first figure ; but it will be noticed that in doing so 

 we really change our mode of reasoning ; we now no longer base our con 

 clusion (about S and P) on instances (M) in which the asserted connexion 

 between 5 and P is exemplified, but, rather, we argue that P is related to 5 

 because we find in S some characteristic, M, which we know to be a sign of 

 the presence of P. 



In the minor premiss of the third figure, S is predicate and is primarily 

 regarded not as a class but as an attribute : indeed, it retains this aspect funda 

 mentally even in the conclusion. Those, however, who regard it as a class in 

 both positions have formulated the following axiom for the third figure ; 



&quot; If anything [M] which is stated to belong to a certain class [S] is 

 affirmed to possess, or to be devoid of, certain attributes \P\ then those attri 

 butes may be predicated in like manner of some members of that class&quot; 



The third figure may be regarded as inferring merely the denial of a 

 necessary connexion (negative or affirmative) between S and P. From this 

 point of view all its moods might be summed up in the following scheme : 

 &quot; Denial of Result . . . Some (or all] M is not P (or is P\ 



Case All (or some] M is S, 



Denial of Rule .... therefore, Some S is not P (or is P).&quot; 



JOSEPH, op. cit., p. 296 (from the Anal. Pri., a. vi., 28&quot;, 24-26). C/. KEYNES, 

 Formal Logic, p. 323, n. i. 



2 C/. KEYNES, op. cit., p. 337. 



