亚里士多德解释编—-可能与或然命题的困难

The  contradictory,  then,  of  ’it  may  be’  is  ’it  cannot  be’.  The  same  rule

applies  to the  proposition  ’it is  contingent that it should be’; the  contradictory

of this is ’it is not contingent  that it should be’. The similar propos itions, such

as  ’it  is  necessary’  and  ’it  is   impossible’,  may  be  dealt  with  in  the  same

manner. For it comes about that just as in the former instances the  verbs ’is’

and ’is not’ were added to the subject-matter of the sentence ’white’ and ’man’,

so here ’that it should be’ and ’that it should not be’ are the subject-matter and

’is  possible’,  ’is  contingent’, are added. These  indicate  that  a  certain thing is

or is not possible, just as in the former instances ’is’ and ’is not’ indic ated that

certain things were or were not the case.

The contradictory, then, of ’it may not be’ is not ’it cannot be’,  but ’it cannot

not be’,  and  the contradictory  of  ’it may  be’ is not ’it may not  be’, but c annot

be’. Thus the propositions ’it may be’ and ’it may not be’ appear each to imply

the  other:  for, since these  two  propositions  are not  contradictory,  the  same

thing both may and may not be. But the propositions ’it may be’ and ’it cannot

be’  c an  never  be  true  of  the  same  subject  at  the  same  time,  for  they  are

contradictory. Nor can the propositions ’it may not be’ and ’it cannot not be’ be

at once true of the same subject.

The  propositions  which  have  to  do  with  necessity  are  governed  by  the

same principle. The contradictory of ’it is necessary that it should be’, is not ’it

is  necessary  that  it should not  be,’ but  ’it is  not necessary that  it should be’,

and  the  contradictory  of  ’it  is  necessary  that  it  should  not  be’  is   ’it  is  not

necessary that it should not be’.

Again,  the  contradictory  of  ’it  is  impossible  that  it  should  be’  is   not  ’it  is

impossible that it should not be’ but ’it is not impossible that it should be’, and

the contradictory of ’it is impos sible that it s hould not be’ is ’it is not impossible

that it should not be’.

To  generalize,  we  must,  as  has  been  stated,  define  the  clauses  ’that  it

should be’ and ’that it should not be’ as the subject-matter of the propositions ,

and  in  mak ing  these  terms  into  affirmations  and  denials  we  mus t  combine

them with ’that it should be’ and ’that it should not be’ respectively.

We must consider the following pairs as contradictory propositions:

It may be.            It cannot be.

It is  contingent.       It is not contingent.

It is  impossible.       It is not impossible.

It is  necessary.       It is not nec essary.

It is  true.             It is not true.