16 EDWARD D. SIMMONS 



equals.'^ These propositions are called dignitates or axioms 

 because they are the absolutely ultimate and common prin- 

 ciples which guarantee the integrity of all discourse and into 

 which all discourse is resolved. Discourse would be impossible 

 for anyone ignorant of these axioms. Propositions per se nota 

 quoad sapientes are related to the axioms as the proper is 

 related to the common. They can be known only by the 

 learned because the terms involved are more deteiTuinate than 

 the common notions which alone are able to be understood by 

 the academically unskilled. St. Thomas illustrates this by 

 suggesting the proposition All right angles are equal. This is a 

 proposition which is immediately evident only to one who 

 knows that equality enters into the definition of right angle; 

 and this is a definition, of course, which escapes the knowledge 

 of many. Another example which is traditionally offered is the 

 proposition Incorporeal substances are not situated in place. 

 We can add to these any proposition in which the essential 

 definition or some part of it is predicated of a specific subject, 

 such as Every man is a rational animal. A proposition of this 

 type is known as a positio or thesis."^ The axioms are necessary 

 if we are to demonstrate in any scientific area, but the theses 

 proper to a given area are necessary only for demonstrations 

 properly within this area. Axioms may or may not be used 

 explicitly as premises in demonstration, but theses are principles 

 of demonstration only if they appear explicity as premises. 

 Axioms can be distinguished generally into those which are 

 ontological in character (e. g., the principle of identity) and 

 those which are logical in character (e. g., the principle of 

 contradiction) . Those which are ontological in character are 



^^/ra 1 Post. Anal., lect. 5, n. 7; In IV Met., lect. 5, n. 595. 



"^ St. Thomas considers the division of the immediate principles of demonstration 

 especially in lessons 5, 18, and 19 in the first book of his Commentary on the 

 Posterior Analytics. We have already noted the inclusion of definition as a principle 

 (although incomplex) of demonstration. St. Thomas also speaks of a proposition 

 taken as though it were immediate in one science, but proved in another (lect. 5, 

 n. 7) . This proposition is called a suppositio or hypothesis. We are not concerned 

 properly with this proposition in this paper. 



