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An affirmation is the statement of a fact with regard to a
subject, and this subject is either a noun or that which has no
name; |
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There can be no affirmation or denial without a verb; |
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When the verb 'is' is used as a third element in the
sentence, there
can be positive and negative propositions of two sorts. |
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I mean that the verb 'is' is added either to the term 'just' or to
the term 'not-just', and two negative propositions are formed in the
same way. |
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Here 'is' and 'is not' are added either to 'just' or to 'not-just'. |
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Yet here it is not possible, in the same way as in the former case,
that the propositions joined in the table by a diagonal line should
both be true; |
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We have thus set out two pairs of opposite propositions; |
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This is an exhaustive enumeration of all the pairs of opposite
propositions that can possibly be framed. |
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When the verb 'is' does not fit the structure of the sentence (for
instance, when the verbs 'walks', 'enjoys health' are used), that
scheme applies, which applied when the word 'is' was added. |
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Thus we have the propositions: |
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Since the contrary of the proposition 'every animal is just' is
'no animal is just', it is plain that these two propositions will
never both be true at the same time or with reference to the same
subject. |
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Further, the proposition 'no man is just' follows from the
proposition 'every man is not just' and the proposition
'not every man is not just', which is the opposite of 'every man is not-just',
follows from the proposition 'some men are just'; |
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It is evident, also, that when the subject is individual, if a
question is asked and the negative answer is the true one, a certain
positive proposition is also true. |
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The propositions 'everything that is not man is just', and the
contradictory of this, are not equivalent to any of the other
propositions; |
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The conversion of the position of subject and predicate in a
sentence involves no difference in its meaning. |
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It is evident, therefore, that the inversion of the relative
position of subject and predicate does not affect the sense of
affirmations and denials. |