AND ON LOGIC IN GENERAL. 



207 



Language would be more perfect if these distinctions were made by inflexion in all cases : 

 logic would do well to think of introducing such* words as X-ic and X-ity. 



The class is an aggregate of individuals ; the individual is a compound of qualities ; the 

 attribute is a compound of attributes. 



Objective names, representing objects and qualities, were once called names of first in- 

 tention or first notions, as being used according to the mind's first bent towards names. Sub- 

 jective names, representing classes and attributes, were names of second intention, or second 

 notions. Thus, ' every crow is black ' considered merely as a collation of cases, is of first in- 

 tention : but 'the class crow has the attribute black' is of second intention. Nevertheless, 

 the first sentence, spoken or written, may be thought under the second form. (| XII.) 



Logic is the science and art, the theory and practice, of the form of thought, the law of its 

 action, the working of its machinery ; independently of the matter thought on. It considers 

 different kinds of matter only when, if ever, and so far as, they necessitate different forms 

 of thought. It must deal with names, and therefore should deal with all the forms of 

 thought demanded in the four uses of names. It has no right to reject any use of a name : 

 for every such use appertains to a form of thought. (§§ II, III.) 



Logic considers both first and second intentions, because both are forms of thought ; but 

 the first chiefly as leading to the second : and in both it considers quce non debentur rebus 

 secundum se, sed secundum esse quod habent in anima. That is, logic belongs to psychology, 

 not to metaphysics. 



It is not to be assumed that the practice of the logic of first intentions is the common 

 property of mankind, and that second intentions form a science to which the student is to be 

 led. The actual form of thought is an unanalysed mixture of first and second intention, with 

 the latter in decided predominance. 



A name may be formed from other names as follows. First, by extension, symbolised in 

 X = (A, B, C) where the aggregate X includes as much as can be spoken of under each and 

 all of the aggregants A, B, C. Secondly, by intension, symbolised in X = A-B-C, or ABC, 

 where the compound X includes no more than can be spoken of under all the component names 

 A, B, C. Thirdly, by combinations of the two. 



Increase of extension is generally diminution of intension, never increase: and diminution 

 of extension is generally increase of intension, never diminution. And vice versa. 



The disjunctive particle, (yr, expresses aggregation : 'either A or B ' means 'in the class 

 (A, B).' 



Class is most connected with extension, and attribute with intension. Extended attribute 

 is merely class of qualities, and there is some effective use in the distinction between class and 

 its subdivisions on the one hand, and the whole class-mark and its subdivision into qualities on 

 the other hand. These two forms of thought, though closely related, must not be confounded 

 with the relations arising out of comparison of extension and intension. (§ VIII.) 



• The boldest symbolic word ever made was proposed — I 

 think in print, but I cannot find the reference and I am not 

 sure by one of the young analysts ( I speak of 1813, or there- 

 abouts) who first cultivated the continental analysis in England. 



It was such as 'iso-a?-ical,' to signify that in which x has always 

 one value. Thus every circle which has its centre at the origin 

 is \io-{3i^ ^y'yieaX. When the crude form is not too com- 

 plicated, the word might be useful. 



