192 Mb DE morgan. ON THE SYLLOGISM, No. Ill, 



of referring thing to thing, and of inferring from classes, the majesty of ignorance having been 

 accustomed only, or chiefly, to the assignment of attributes. Common thought deals mostly 

 in double universals: the metaphysical whole applied to the mathematical whole. And so 

 the old logicians often phrased it : they said that in a universal affirmative the whole predicate 

 is applied to the whole subject. Some logicians deny the existence of this form, in logic at 

 least. Declaring that the word 'is'' shall be, ought to be, the only copula, in its meaning of 

 identifieation, they declare that attribute can only be predicated of attribute, or class of class. 

 With this I have nothing to do, except to appeal to the world at large whether by 'is' they do 

 not intend to convey predication of attribution and subjection of class, at least as often as any 

 other sense. To me the "elegant extracts" of the logicians are no answer: I deny their right 

 to exclude any form under which men do think; and I contend for the whole form of 

 thought. 



3. Metaphysical. This is an old and well-known use of the word, appropriate both to 

 its etymology and to its derived meaning. If chemistry had been known as it is now, that 

 which was called the metaphysical whole would have been called the chemical whole. The 

 manner in which the concept man is composed in our thoughts of animal and reason is a very 

 different thing from that in which animal is made up of man and brute. The logicians say 

 that a concept is the sum* of the attributes which it comprehends : the mathematician easily 

 corrects them. Animal is the sum of man and brute: withdraw brute, and the notion animal 

 is not destroyed ; man remains, and some animal is left. In fact, animal is made up of 

 human-awima^ and brute-owima^. But in comprehension, to use his own term, being the view 

 of which the logician was speaking, man is a compound, not a sum, of animal and reason : with- 

 draw reason, and the notion man ceases to exist. Man is not added up of animal-man and 

 reason-man. Again, in aggregating animal, we may conceive all man to be in Europe, and all 

 brute in Asia : but in compounding man we cannot conceive all the animal to be in Europe, 

 and all the rational in Asia, Put an impossible species into the genus, and the rest are not 

 affected : put an impossible component into the notion, and it ceases to be a notion. A black- 

 white horse is a subjective nonentity : nevertheless, if we divide horses into black, white, and 

 black-white, the genus is still usable; it is only a three-stall stable with one stall locked up 

 and the key lost, or never made. 



Extension and intension both exist in the metaphysical, but intension predominates. The 

 attribute human may be extensively subdivided into attributes, and also into individual 

 qualities. The misconception of the logicians which I have discussed at length consists in 

 seizing the extension of an attribute, and missing the intension. 



When the old logicians puzzled themselves with what they called the indefinite proposition, 



* The illustrations which follow are familiar to the mathe- 

 matician in the distinctive properties of a + 6 and ab. Such a 

 mistake as that made by the logicians would be, in mathe- 

 matics, equivalent to substitution of logarithms in place of 

 their primitives. This mistake was made by the old geome- 

 ters, when they styled composition of ratios addition of ratios : 



an undefined and uncomprehended form: and, when the time 

 arrived, the measure of the ratio was easily accepted as the 

 definition of the logarithm. Those who have affirmed that 

 Archimedes invented logarithms, were right so far as this, that 

 Archimedes or a predecessor invented the integer part of the 

 notion, if indeed it be not more correct to say that the integer 



it appears in Euclid's duplicate and triplicate ratio. But here part of the notion invented itself. Napier invented the frac- 

 it wag not all mistake. The logarithmic idea was present in j tional part of the notion, and applied all. 



