Ferio in the same manner is reduced to Celarent. The dotted part of C is cut away, and the part really significant in the syllogism is called E. Then 'No B is A, all E is B, no E is A.'
Finally Celarent can be reduced to Barbara. B cannot indeed be enclosed in A, but we assume the existence of a whole having all the characters which A has not, or having none of the characters which A has. This is the whole F = Not-A. Then Celarent becomes Barbara thus: 'All B is F, all C is B, therefore all C is F.'
This demonstrates that there is only one fundamental operation where syllogists suppose there are at least four. The difference is wholly a matter of language, and disappears on changing the names of the terms and ignoring irrelevant suggestions. But the syllogism, I repeat, does not represent the act of reasoning, and its moods and figures are fit only to be a game for children.
[20:] Logic, Book I. § 3.
[21:] Logic, Book II. c. 3. § 2.
[22:] Lectures, iii. pp. 287 and 356. The impossibility of reconciling their definitions and rules to real thinking and argument is the despair of logicians. Most of them take to symbols, which are more accommodating than real experience, having just such properties as their makers choose to put in them. Sir William Hamilton had the courage to declare that a logician might use arguments of a concrete or real form, but that it is not necessary they should agree with real fact. 'The logician has a right to suppose any material impossibility, any material falsity; he takes no account of what is objectively impossible or false, he has a right to assume what premises he please, provided that they do not involve a contradiction in terms.'—Id. 322. That means in plain English that a logician may misrepresent matters of fact, if he cannot otherwise establish his theory!
[23:] Laws of Thought, p. 35.
[24:] Ibid. p. 47.