亚里士多德解释编—-相反命题

Some things are universal, others individual. By the term ’univers al’ I mean

that  which  is  of  such  a  nature  as  to  be  predicated  of  many  subjects,  by

’individual’  that  which  is  not  thus  predicated.  Thus   ’man’  is  a  universal,

’Callias’ an individual.

Our  propositions  necessarily  sometimes  concern  a  universal  subject,

sometimes  an individual.

If,  then,  a  man  states  a  positive  and  a  negative  proposition  of  universal

character with regard to a universal, thes e two propositions are ’contrary’. By

the expression ’a proposition of universal character with regard to a universal’,

suc h propositions as ’every man is white’, ’no man is white’ are meant. When,

on the  other  hand, the  positive and negative propositions, though they  have

regard  to  a  universal,  are  yet  not  of  universal  character,  they  will  not  be

contrary, albeit the meaning intended is sometimes contrary. As instances of

propositions made  with  regard to  a  universal, but not  of univers al  character,

we  may  take  the  ’propositions  ’man  is  white’,  ’man  is  not  white’.  ’Man’  is  a

universal, but  the  propos ition  is  not  made  as  of  universal  character;  for the

word  ’every’  does  not  make  the  subject  a  universal,  but  rather  gives  the

proposition a universal character. If, however, both predicate and subject are

distributed, the proposition thus constituted is contrary to truth; no affirmation

will,  under  such circumstances, be true. The proposition ’every man  is every

animal’ is  an example of this type.

An affirmation  is  opposed  to  a denial  in the  sense  which  I denote  by  the

term  ’contradictory’,  when,  while  the  subject  remains  the  same,  the

affirmation  is  of  universal  character  and  the  denial  is  not.  The  affirmation

’every man is white’ is the contradictory of the denial ’not every man is white’,

or  again,  the  proposition  ’no  man  is  white’  is  the  c ontradictory  of  the

proposition ’some men are white’. But propos itions are opposed as contraries

when both  the  affirmation  and  the denial  are  universal, as  in  the s entences

’every man is white’, ’no man is white’, ’every man is just’, ’no man is just’.

We see  that  in  a  pair of this sort both  propositions cannot be  true, but the

contradictories  of  a  pair  of  contraries  can  sometimes  both  be  true  with

reference to the same subject; for instance ’not every man is white’ and s ome

men  are  white’  are  both  true.  Of  such  corresponding  positive  and  negative

propositions as  refer  to universals and have a universal character,  one  must

be  true  and  the  other false.  This  is  the  case  also  when the  reference  is  to

individuals, as in the propositions ’Socrates is white’, ’Socrates is not white’.

When,  on  the  other  hand,  the  reference  is  to  universals,  but  the

propositions are not  universal,  it is not  always  the case  that  one  is  true and

the other false, for it is possible to state truly that man is white and that man is

not white and that man is  beautiful and that man is not beautiful; for if a man

is  deformed  he is  the  reverse  of  beautiful,  also  if  he is progressing  towards

beauty he is not yet beautiful.

This  statement  might  seem  at  first  s ight  to  carry  with  it  a  contradiction,

owing  to  the  fac t  that  the  proposition  ’man  is  not  white’  appears  to  be

equivalent to the proposition ’no man is white’. This, however, is not the case,

nor are they necessarily at the same time true or false.

It  is  evident  also  that  the  denial  corresponding  to  a  single  affirmation  is

itself  single;  for  the  denial  must  deny  just  that  which  the  affirmation  affirms

concerning the same subject,  and mus t  correspond with  the affirmation both

in the universal or particular character of the subject and in the distributed or

undistributed sense in which it is  understood.

For instance, the affirmation ’Socrates is white’ has its proper denial in the

proposition ’Socrates is not white’. If anything else be negatively predic ated of

the subjec t or if anything else be the subject though the predicate remain the

same, the denial will not be the denial proper to that affirmation, but on that is

distinct.

The denial proper to the affirmation ’every man is white’ is ’not every man is

white’; that proper to the affirmation ’some men are white’ is ’no man is white’,

while that proper to the affirmation ’man is white’ is ’man is not white’.

We have shown further  that  a  single denial is  contradictorily  opposite to  a

single  affirmation  and  we  have  explained  which  these  are;  we  have  als o

stated that contrary are distinct from contradictory propositions and which the

contrary are; also  that with regard  to  a  pair  of  opposite  propositions it  is not

always  the  case  that one  is  true  and the  other  false.  We  have  pointed  out,

moreover, what the reason of this is and under what circumstances the truth

of the one involves the falsity of the other.