KINDS OF JUDGMENTS AND PROPOSITIONS. 173 



A second and less manifest, though scarcely less important, kind 

 of essential or analytic proposition, or &quot;modus dicendi per se&quot; is 

 the one in which analysis of the terms reveals the predicate to be 

 a property , necessarily involved in, and connected with, the sub 

 ject. For example, the predicate of the proposition : &quot; The 

 square on the hypotenuse of a right-angled triangle is equal to the 

 sum of the squares on the other two sides&quot; will be found on anal 

 ysis to give a necessary property of the subject. Similarly, the 

 proposition &quot;Every number is either odd or even&quot; and, finally, all 

 the more remote conclusions of mathematics, will be found to 

 belong to this second class of per se propositions. 1 



It may, therefore, require a long and elaborate analysis to 

 determine whether a given proposition is or is not in materia 

 necessaria. But it is important to note that this analysis is carried 

 on independently of any appeal to extrinsic sources of informa 

 tion. That is to say, if the proposition is in materia necessaria, 

 we can ascertain its truth independently of any additional ex 

 perience over and above the experience by which we acquired the 

 knowledge we already possess about the system of concepts with 

 which we are concerned: 2 in this sense, and in this sense only, 

 have such propositions a right to be called a priori, i.e. knowable 

 prior to, and independent of, sensible and intellectual experience ; 

 for they do and must presuppose some experience that, namely, 

 by which we acquired the concepts in question. 



In the case of accidental or synthetic judgments, on the other 

 hand as for example, &quot;Napoleon was defeated as Waterloo&quot; 

 our knowledge of their truth or falsity cannot be derived from 



44 A man s a man,&quot; 44 Boys will be boys,&quot; 4t War is war&quot;. The contradiction of a 

 purely formal proposition, might be called a formal contradiction, or a contradiction 

 in forms. The contradiction of an ordinary analytic proposition is usually called a 

 contradiction in terms. Both, of course, involve a contradiction in thought, an in 

 compatibility between the judgments opposed. 



* &quot;Per sc duplicitur dicitur,&quot; writes St. Thomas. t4 Uno enim modo dicitur 

 propositio per se, cujus praedicatum cadit in definitione subjecti, sicut ista : Homo 

 est animal ; animal enim cadit in definitione hominis. Et quia id quod est in de 

 finitione alicujus est aliquo modo causa ejus, in his quae sunt per se, dicuntur 

 praedicata esse causa subjecti. Alio modo dicitur propositio per se, cujus e con- 

 trario subjectum ponitur in definitione praedicati ; sicut si dicatur : Nasus est simus, 

 vel Numerus est par ; simum enim nihil aliud est quam nasus curvus, et par nihil 

 aliud est quam numerus medietatem habens, et in istis subjectum est causa praedi 

 cati.&quot; De Anima, lib. ii., 1. 14. &quot; Ut propositio dicatur per se, sufficit (writes 

 Cajetan) in subjecto includi id quod ponitur in definitione praedicati . . . sufficit 

 subjectum inesse definition! praedicati, per se vel per aliquid sibi intrinsecum.&quot; 

 CAJETAN, Comm. in Post Anal., chap. iv. 



3 Cf. JOSEPH, Logic, p. 174, n. 2. 



