_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. [Footnote 20: _Logic_, Book I. § 3.] [Footnote 21: _Logic_, Book II. c. 3. § 2.] [Footnote 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!] [Footnote 23: _Laws of Thought_, p. 35.] [Footnote 24: _Ibid._ p. 47.] STUDIES IN DIALECTIC XXXIX The theorems given for practice in logic books are useful dialectic material, but they do not fully illustrate all the categories. Logicians have no definite categories, and in selecting examples they are unconsciously biassed in favour of those that can be most easily interpreted to signify classification. The really generalistic examples are rare; the most are judgments of inherence, admitted in virtue of the assumption that inherent properties can--when it is needful to preserve the traditional notion of predication--be considered class-ideas. Theorems in perspection and concretion we do not expect to find in logic books, for these, in so far as they are distinct from association, are categories peculiar to the Berkeleyan philosophy.