Note 417 — Chapter VII

In regard to this argument De Morgan writes, “This is not an instance of common syllogism: the premisses are ‘A is an equal of B ; B is an equal of C.’ So far as common syllogism is concerned, that ‘an equal of B’ is as good for the argument as ‘B’ is a material accident of the meaning of ‘equal.’ The logicians accordingly, to reduce this to a common syllogism, state the effect of composition of relation in a major premiss, and declare that the case before them is an example of that composition in a minor premiss. As in, A is an equal of an equal (of C); Every equal of an equal is an equal ; therefore, A is an equal of C. This I treat as a mere evasion. Among various sufficient answers this one is enough: men do not think as above. When A = B, B = C, is made to give A = C, the word equals is a copula in thought, and not a notion attached to a predicate. There are processes which are not those of common syllogism in the logician’s major premiss above: but waiving this, logic is an analysis of the form of thought, possible and actual, and the logician has no right to declare that other than the actual is actual” (Syllabus, pp. 31, 2).