亚里士多德解释编—-可能与或然命题的困难

As  these  distinctions  have  been  made,  we  must  consider  the  mutual

relation of those affirmations and  denials  which  assert  or deny pos sibility or

contingency, impossibility or necessity: for the subject is not without difficulty.

We  admit  that  of  composite  expressions  those  are  contradictory  each  to

each which  have the verb ’to be’  its positive  and  negative form  respec tively.

Thus the contradic tory of the proposition ’man is’ is ’man is not’, not ’not-man

is’,  and the  contradictory of  ’man  is  white’  is  ’man is  not  white’, not  ’man  is

not-white’. For otherwise, sinc e either the positive or the negative proposition

is true of any subject, it will turn out true to say that a piece of wood is a man

that is not white.

Now if this is the case, in those propos itions which do not c ontain the verb

’to be’ the verb which takes its  place will exercise the same function. Thus the

contradictory of ’man walks ’ is ’man does not walk’, not ’not-man walks’; for to

say ’man walks’ merely equivalent to saying ’man is walking’.

If then this rule is  universal,  the contradictory of ’it may  be’ is  may  not be’,

not ’it cannot be’.

Now it appears that the same thing both may and may not be; for instance,

everything that may be  cut or may  walk may also  escape cutting  and refrain

from walking; and the reason is that those things that have potentiality in this

sense  are  not  always  actual.  In  such  cases,  both  the  positive  and  the

negative propositions  will  be  true; for  that  which is capable  of walking or  of

being seen has also a potentiality in the opposite direction.

But  since  it  is  impossible  that  contradictory  propositions  should  both  be

true of the same subject, it follows that’ it may not be’ is not the contradictory

of ’it may be’. For it is a logical consequence of what we have said, either that

the same  predicate can be  both  applicable  and  inapplicable to  one  and the

same subject at the same time, or that it is not by the addition of the verbs ’be’

and ’not be’, respectiv ely, that positive and negative propositions are formed.

If  the  former  of  these  alternatives  must  be  rejected,  we  must  choose  the

latter.