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On Sophistical Refutations   

is white in respect of his teeth; and then, if he be white in that

respect, were to suppose at the conclusion of his questions that

therefore he had proved dialectically that he was both white and not

white. But in some cases it often passes undetected, viz. in all cases

where, whenever a statement is made of something in a certain respect,

it would be generally thought that the absolute statement follows as

well; and also in all cases where it is not easy to see which of the

attributes ought to be rendered strictly. A situation of this kind

arises, where both the opposite attributes belong alike: for then

there is general support for the view that one must agree absolutely

to the assertion of both, or of neither: e.g. if a thing is half white

and half black, is it white or black?

Other fallacies occur because the terms 'proof' or 'refutation' have

not been defined, and because something is left out in their

definition. For to refute is to contradict one and the same

attribute-not merely the name, but the reality-and a name that is

not merely synonymous but the same name-and to confute it from the

propositions granted, necessarily, without including in the

reckoning the original point to be proved, in the same respect and

relation and manner and time in which it was asserted. A 'false

assertion' about anything has to be defined in the same way. Some

people, however, omit some one of the said conditions and give a

merely apparent refutation, showing (e.g.) that the same thing is both

double and not double: for two is double of one, but not double of

three. Or, it may be, they show that it is both double and not

double of the same thing, but not that it is so in the same respect:

for it is double in length but not double in breadth. Or, it may be,

they show it to be both double and not double of the same thing and in

the same respect and manner, but not that it is so at the same time:

and therefore their refutation is merely apparent. One might, with

some violence, bring this fallacy into the group of fallacies

dependent on language as well.

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