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Aristotle

"Posterior Analytics"

Therefore if, taken in this way, they are wholly
false, their contraries conversely should be wholly true. But this
is impossible. On the other hand, there is nothing to prevent both
premisses being partially false; e.g. if actually some A is C and some
B is C, then if it is premised that all A is C and no B is C, both
premisses are false, yet partially, not wholly, false. The same is
true if the major is made negative instead of the minor. Or one
premiss may be wholly false, and it may be either of them. Thus,
supposing that actually an attribute of all A must also be an
attribute of all B, then if C is yet taken to be a universal attribute
of all but universally non-attributable to B, C-A will be true but C-B
false. Again, actually that which is an attribute of no B will not
be an attribute of all A either; for if it be an attribute of all A,
it will also be an attribute of all B, which is contrary to
supposition; but if C be nevertheless assumed to be a universal
attribute of A, but an attribute of no B, then the premiss C-B is true
but the major is false. The case is similar if the major is made the
negative premiss. For in fact what is an attribute of no A will not be
an attribute of any B either; and if it be yet assumed that C is
universally non-attributable to A, but a universal attribute of B, the
premiss C-A is true but the minor wholly false.


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