two unknown are
always Contradictories.

Sec. 10. Secondary modes of Immediate Inference are obtained by applying
the process of Conversion or Obversion to the results already obtained
by the other process. The best known secondary form of Immediate
Inference is the Contrapositive, and this is the converse of the obverse
of a given proposition. Thus:

DATUM. OBVERSE. CONTRAPOSITIVE.

A. _All S is P_ .'. _No S is not-P_ .'. _No not-P is S_
I. _Some S is P_ .'. _Some S is not not-P_ .'. (none)
E. _No S is P_ .'. _All S is not-P_ .'. _Some not-P is S_
O. _Some S is not P_ .'. _Some S is not-P_ .'. _Some not-P is S_

There is no contrapositive of I., because the obverse of I. is in the
form of O., and we have seen that O. cannot be converted. O., however,
has a contrapositive (_Some not-P is S_); and this is sometimes given
instead of the converse, and called the 'converse by negation.'

Contraposition needs no justification by the Laws of Thought, as it is
nothing but a compounding of conversion with obversion, both of which
processes have already been justified. I give a table opposite of the
other ways of compounding these primary modes of Immediate Inference.

A I E O
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1 All A is B Some A is B No A is B Some A is not B

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Obverse 2 No A is b Some A is not b All A is b Some A is b

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Converse 3 Some B is A Some B is A No B is A

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Obverse
of 4 Some B is not a Some B is not a All B is a
Converse

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Contra-
positive 5 No b is A Some b is A Some b is A

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Obverse
of 6 All b is a Some b is not a Some b is not a
Contrapos

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Converse
of
Obverse 7