478. A kind of generality might indeed he imparted even to a singular
proposition by expressing it in the form 'A is always B.' Thus we may
say, 'This man is always idle'--a proposition which admits of being
contradicted under the form 'This man is sometimes not idle.'
CHAPTER IV.
_Of Conversion._
§ 479. Conversion is an immediate inference grounded On the
transposition of the subject and predicate of a proposition.
§ 480. In this form of inference the antecedent is technically known
as the Convertend, i.e. the proposition to be converted, and the
consequent as the Converse, i.e. the proposition which has been
converted.
§ 481. In a loose sense of the term we may be said to have converted a
proposition when we have merely transposed the subject and predicate,
when, for instance, we turn the proposition 'All A is B' into 'All B
is A' or 'Some A is not B' into 'Some B is not A.' But these
propositions plainly do not follow from the former ones, and it is
only with conversion as a form of inference--with Illative Conversion
as it is called--that Logic is concerned.
§ 482. For conversion as a form of inference two rules have been laid
down--
(1) No term must be distributed in the converse which was not
distributed in the convertend.
(2) The quality of the converse must be the same as that of the
convertend.
§ 483. The first of these rules is founded on the nature of things. A
violation of it involves the fallacy of arguing from part of a term to
the whole.
§ 484. The second rule is merely a conventional one. We may make a
valid inference in defiance of it: but such an inference will be seen
presently to involve something more than mere conversion.
§ 485. There are two kinds of conversion--
(1) Simple.
(2) Per Accidens or by Limitation.
§ 486. We are said to have simply converted a proposition when the
quantity remains the same as before.
§ 487. We are said to have converted a proposition per accidens, or by
limitation, when the rules for the distribution of terms necessitate a
reduction in the original quantity of the proposition.
§ 488.
A can only be converted per accidens.
E and I can be converted simply.
O cannot be converted at all.
§ 489. The reason why A can only be converted per accidens is that,
being affirmative, its predicate is undistributed (§ 293). Since 'All
A is B' does not mean more than 'All A is some B,' its proper converse
is 'Some B is A.' For, if we endeavoured to elicit the inference, 'All
B is A,' we should be distributing the term B in the converse, which
was not distributed in the convertend. Hence we should be involved in
the fallacy of arguing from the part to the whole. Because 'All
doctors are men' it by no means follows that 'All men are doctors.'
§ 499. E and I admit of simple conversion, because the quantity of the
subject and predicate is alike in each, both subject and predicate
being distributed in E and undistributed in I.
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