DEMONSTRATION AND SELF-EVIDENCE 11 



true of both triangle and isosceles triangle. But it is true of 

 isosceles triangle only insofar as isosceles triangle is triangle. 

 Thus we might well say that this property belongs immediately 

 to triangle and mediately (through triangle) to isosceles triangle. 

 However, the proposition Every triangle has three angles equal 

 to two right angles can be demonstrated as the conclusion of a 

 syllogism employing the essential definition of triangle as its 

 middle term. Insofar as it is able to be proven through a middle, 

 it is clearly not immediate in the sense in which self-evident 

 propositions are immediate. " Immediate " here means, rather, 

 commensurately universal or convertible {primo or possessed 

 of the intention spoken of as did ut universale) . As a matter 

 of fact, not every proposition which is commensurately uni- 

 versal is self-evident and not every self-evident proposition is 

 commensurately universal.^^ Secondly, even though we under- 

 stand the self-evident proposition to be immediate in such wise 

 as to lack a demonstrative middle, it is not the case that every 

 proposition which is immediate in this sense is self-evident. 

 A self-evident proposition is a proposition with a subject and 

 a predicate in necessary matter, and with a subject and predi- 

 cate so proximately connected with one another that the 

 necessary truth of the proposition can escape no one who 

 understands this subject and predicate. Hence, propositions are 

 said to be self-evident precisely insofar as they can be seen 

 necessarily to be true once their terms are known. ^* These 



'^^For St. Thomas' position on the did ut universale, cf., In I Post. Anal., lect. 11. 

 We shall see that the prime instance of the self-evident proposition has a predicate 

 which is of the definition of the subject. If the predicate is the whole of the 

 definition of the subject it is, of course, convertible with the subject, and we have 

 a commensurately universal proposition. Every man is capable of speech is com- 

 mensurately universal without being self-evident, and Every man is animal is self- 

 evident without being commensurately universal. 



^* Only this type of proposition is so necessarily true, while being at the same 

 time immediate, that it can ground the necessity of a scientific conclusion. In IV 

 Met., lect. 5, n. 595: "Ad huius autem evidentiam sciendum, quod propositiones 

 per se notae sunt, quae statim notis terminis cognoscuntur. . . ." De Mala, q. 3, 

 a. 3, c: " Unde intellectus ex necessitate assentit principiis primis naturaliter 

 notis. . . . Unde in intellectu contingit quod ea quae necessariam cohaerentiam 

 habent cum primis principiis naturaliter cognitis, ex necessitate moveant intellectum, 



