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It is possible for the premisses of the syllogism to be true, or
to be false, or to be the one true, the other false. |
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First then that it is not possible to draw a false conclusion from
true premisses, is made clear by this consideration. |
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But from what is false a true conclusion may be drawn, whether
both the premisses are false or only one, provided that this is not
either of the premisses indifferently, if it is taken as
wholly false: |
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(1) Let A belong to the whole of C, but
to none of the Bs, neither let B belong to C. |
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(2) A similar proof
may be given if each premiss is partially false. |
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(3) But if one only of the premisses is false, when the first
premiss is wholly false, e.g. AB, the conclusion will not be
true, but
if the premiss BC is wholly false, a true conclusion will be
possible. |
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(4) But if the premiss is not wholly false, a true conclusion is
possible. |
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(5) But if the premiss AB, which is assumed, is wholly
true, and the
premiss BC is wholly false, a true syllogism will be possible: |
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(6) And if the premiss BC is not wholly false but in part
only, even
so the conclusion may be true. |
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In particular syllogisms it is possible when the first premiss is
wholly false, and the other true, that the conclusion should be
true; |
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(7) For nothing prevents A belonging to
no B, but
to some C, and B to some C, e.g. animal belongs to no snow, but to
some white thing, and snow to some white thing. |
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(9) Again if the premiss AB is true, and the premiss BC is false,
the conclusion may be true. |
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(10) Also if the premiss AB is partially false, and the premiss BC
is false too, the conclusion may be true. |
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(11) Also though both premisses are false the conclusion may be
true. |
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created 1996/11/25 modified 2009/04/26