84 THE SCIENCE OF LOGIC. 



tion of its specific class name. It must therefore be something which can be 

 inferred from the connotation by the absolutely necessary laws that govern 

 our thought processes ; something whose absence would in the first instance 

 involve a contradiction in thought, a violation of &quot; some law which we regard 

 as a part of the constitution . . . of our minds &quot;. But, since the laws of thought 

 are not purely subjective (15) ; since, too, the truth of knowledge (10) de 

 pends on whether or not we fix the connotation of our concepts and terms in 

 conformity with things, in other words, on whether or not there are things 

 corresponding to our concepts, on whether things are what we assert them to 

 be when we predicate such concepts of them in judgment : it follows that the 

 absence of a proprium, by violating some subjective or mental law, would, by 

 that very fact, be also violating some objective or real law, &quot; some law which 

 we regard as part of the constitution ... of the universe,&quot; as well as &quot; of 

 our minds,&quot; that is to say, some law which is a law &quot; of both &quot;. 



The knowledge, therefore, that a certain attribute constitutes a property 

 of a given class of objects is much more than a knowledge of the subjective 

 implications of certain arbitrarily fixed notions and names. It is knowledge 

 about the nature of real things. The essences revealed to the human mind 

 in the intension of the concepts and names by which it thinks and expresses its 

 knowledge, are not merely &quot; nominal essences &quot; but also &quot; real essences &quot; ; so 

 too are the properties discerned in these essences real, and not merely nominal. 



A further inference is that real knowledge of things, objectively valid 

 information about the nature of reality, is conveyed to our minds not 

 merely in and through that class of judgments called synthetic or accidental, 

 in which the predicate is an accidens of the subject (85), but also in that other 

 class of judgments called analytic or essential, whose predicates reveal some 

 essential attribute or necessary property of their subjects. 



The distinction bet ween ^r^^r/y on the one hand, and specific essence (as 

 constituted by genus and differentia] on the other, is easily intelligible in 

 deductive sciences like geometry and mathematics. For these sciences deal 

 with magnitude and multitude, i.e. with the spatial and numerical aspects of 

 material reality ; and since the universal laws or conditions of space and 

 number are ever the same, constant and unchanging, we can take as defini 

 tions such concepts as will bring these quantitative aspects of reality before 

 our minds (e.g. the definition of a triangle), and proceed to deduce or draw 

 out and demonstrate from these, other more complex aspects which we will 

 regard as properties of those objects e.g. that the three angles of a triangle 

 are equal to two rig ht angles. It is in these sciences, then, that we have copious 

 examples of properties in the strictest sense of this term. 



But the concrete objects, organic and inorganic, with which the natural 

 and physical sciences deal, do not lend themselves so easily to definition, to 

 the detection of what is fundamental in their natures. Nor do the constant 

 changes to which they are subject, the endless diversity and variety of condi 

 tions in which they manifest themselves, permit us to demonstrate their 

 properties with the same rigour as in the case of the purely abstract sciences 

 of mathematics and geometry. &quot; Hence for definition, such as we have it in 

 geometry, we must substitute classification ; and for the demonstration of pro 

 perties, the discovery of laws.&quot; 1 Those classes are formed, as we shall see 



JOSEPH, op. cit. t p. 89 ; infra, 66, 



