亚里士多德解释编—-命题的格式关系

Logical  sequences  follow  in  due  course  when  we  have  arranged  the

propositions  thus.  From  the  proposition  ’it  may  be’  it  follows  that  it  is

contingent,  and  the  relation  is  reciprocal.  It  follows  also  that  it  is  not

impossible and not necess ary.

From the proposition ’it may not be’ or ’it is contingent that it should not be’

it  follows  that  it  is  not  necessary  that  it  should  not  be  and  that  it  is  not

impossible that it should not be. From the proposition ’it cannot be’ or ’it is not

contingent’  it  follows  that  it  is  necessary  that  it  should  not  be  and  that  it  is

impossible that it should be. From the proposition ’it cannot not be’ or ’it is not

contingent that it should not be’ it follows that it is necessary that it should be

and that it is  impossible that it should not be.

Let us consider these statements by the help of a table:

A.                        B.

It may be.                  It cannot be.

It is  contingent.             It is not contingent.

It is  not impossible         It is imposs ible that it

that it should be.            should be.

It is  not necessary          It is necessary that it

that it should be.            should not be.

C.                        D.

It may not be.            It cannot not be.

It is  contingent that it      It is not contingent that

should not be.              it should not be.

It is  not impossible       It is impossible thatit

that it should not be.        should not be.

It is  not necessary that     It is necessary that it

it should not be.             should be.

Now  the  propositions  ’it  is  impossible  that  it  should  be’  and  ’it  is  not

impossible that it should be’ are consequent upon the propositions ’it may be’,

’it is contingent’, and ’it cannot be’,

’it is not contingent’, the contradictories upon the contradictories. But there

is  inversion. The  negative  of the  proposition  ’it  is  impossible’  is  consequent

upon  the  proposition  ’it  may  be’  and  the  corresponding  pos itive  in  the  first

cas e  upon  the  negative  in  the  second.  For  ’it  is  impossible’  is  a  positive

proposition and ’it is not impossible’ is negative.

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We  must  investigate  the  relation  subsisting  between  these  propositions

and  those  which  predicate  necessity.  That  there  is  a  distinction  is  clear.  In

this  case,  contrary  propositions  follow  respectively  from  contradic tory

propositions,   and   the   contradictory   propositions   belong   to   separate

sequences. For the proposition ’it is not necessary that it should be’ is not the

negative of  ’it is necessary that it should not  be’, for both these  propositions

may be true of the same subject; for when it is necessary that a thing should

not be, it is not necessary that it should be. The reason why the propositions

predicating necessity do not follow in the same kind of sequence as the rest,

lies in the fact that the proposition  ’it is  imposs ible’  is equivalent,  when used

with  a  contrary  subject,  to  the  proposition  ’it  is  necess ary’.  For  when  it  is

impossible  that a  thing  should  be,  it  is  necessary,  not that  it s hould  be, but

that it should not be, and when it is impossible that a thing should not be, it is

necessary that it should be. Thus, if the propositions  predicating impossibility

or  non-impossibility  follow  without  change  of  subject  from  those predicating

possibility or non-possibility,  those predicating necessity must follow  with the

contrary subject; for the propositions ’it is  impossible’ and ’it is necessary’ are

not equivalent, but, as has been said, inversely connected.

Yet perhaps  it  is impossible  that the  contradictory propositions predicating

necessity  should  be  thus  arranged.  For  when  it  is  necess ary  that  a  thing

should  be,  it  is  possible  that  it  should  be.  (For  if  not,  the  opposite  follows,

since one or the other must follow; so, if it is not possible, it is impossible, and

it is thus impos sible that a thing should be, which must necessarily be; which

is absurd.)

Yet from the proposition  ’it may  be’ it  follows  that it  is not  impossible, and

from that it  follows that  it  is  not  necessary; it  comes  about therefore that the

thing which must necessarily be need not be; which is absurd. But again, the

proposition  ’it  is  necessary  that  it  should  be’  does  not  follow  from  the

proposition ’it may be’, nor does  the proposition ’it is necessary that it should

not be’. For  the  proposition ’it may  be’  implies  a twofold  possibility,  while,  if

either of the two former propositions is  true, the twofold possibility vanishes.

For if a thing may be, it may also not be, but if it is necessary that it should be

or that it should not be, one of the two alternatives will be excluded. It remains ,

therefore, that the proposition ’it is not neces sary that it should not be’ follows

from  the  proposition  ’it  may  be’.  For  this  is  true  also  of  that  which  must

necessarily be.

Moreover  the  proposition  ’it  is  not  necessary  that  it  should  not  be’  is  the

contradictory  of that  which  follows  from  the  proposition  ’it  cannot  be’;  for  ’it

cannot  be’  is  followed  by  ’it  is  impossible  that  it  should  be’  and  by  ’it  is

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

proposition ’it is not  necessary  that  it should not  be’.  Thus  in this  case  also

contradictory  propositions  follow  contradictory  in  the  way  indicated,  and  no

logical impossibilities occur when they are thus arranged.

It may  be questioned  whether the  proposition ’it may  be’  follows  from  the

proposition  ’it  is   necessary  that  it  should  be’.  If  not,  the  contradictory  must

follow,  namely that  it  cannot be,  or,  if a man should maintain that  this  is not

the c ontradictory, then the proposition ’it may not be’.

Now both of these are false of that which  necessarily  is. At the same time,

it is thought that if a thing may be cut it may also not be cut, if a thing may be

it  may  also  not  be,  and  thus  it  would  follow  that  a  thing  which  must

necessarily be may possibly not be; which is false. It is  evident, then, that it is

not  always  the  case that  that which  may be or  may  walk poss esses also a

potentiality in the  other  direction.  There are exceptions. In the first place we

must except those things which possess a potentiality not in ac cordance with

a rational principle, as fire possesses the potentiality of giving out heat, that is,

an  irrational  capacity.  Those  potentialities  which  involve  a  rational  principle

are  potentialities  of  more  than  one  result,  that  is,  of  contrary  results;  those

that  are irrational are not always thus constituted. As I have said, fire cannot

both heat and not heat, neither has anything that is always actual any twofold

potentiality. Yet some even of those potentialities which are irrational admit of

opposite results .  However, thus  much  has been  said to emphasize  the truth

that  it  is  not  every  potentiality  which  admits  of  opposite  results,  even  where

the word is used always in the same sense.

But in some cases  the word is used equivocally. For  the  term ’possible’  is

ambiguous, being used in the one case with reference to facts, to that which

is  actualized,  as  when a man  is said to find  walking  possible  because he  is

actually  walking,  and  generally  when a  capacity is  predicated  because  it  is

actually  realized;  in  the  other  case,  with  reference  to  a  state  in  which

realization is conditionally practicable, as when  a man is said to find walking

possible  because  under  certain  c onditions  he  would  walk.  This  last  sort  of

potentiality belongs only  to that which  can be in motion, the former c an exist

also in the case of that which has not this power. Both of that which is walking

and  is  actual,  and  of  that  which  has  the  capacity  though  not  necessarily

realized, it is true to say that it is not impossible that it should  walk  (or, in the

other c ase, that it should be), but while we cannot predicate this latter kind of

potentiality of that which is necessary in the unqualified sense of the word, we

can predicate the former.

Our conc lusion,  then,  is  this:  that since the  universal  is  consequent  upon

the  particular, that  which  is  necessary  is  also  possible,  though not  in  every

sense in which the word may be used.

We  may  perhaps  s tate  that  necessity  and  its  absence  are  the  initial

princ iples of existence and non-exis tenc e, and that all else must be regarded

as posterior to these.

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It is plain from what has been said that that  which is of necessity is actual.

Thus,  if  that  which  is  eternal  is  prior,  actuality  also  is  prior  to  potentiality.

Some  things  are  actualities  without  potentiality,  namely,  the  primary

substances; a second class consists of those things which are actual but also

potential,  whose  actuality  is  in  nature  prior  to  their  potentiality,  though

posterior  in  time;  a  third  class  comprises  those  things  which  are  never

actualized, but are pure potentialities.