Prior Analytics - Book I   

necessary and what is potential is possible), affirmative statements

will all convert in a manner similar to those described. For if it

is possible that all or some B is A, it will be possible that some A

is B. For if that were not possible, then no B could possibly be A.

This has been already proved. But in negative statements the case is

different. Whatever is said to be possible, either because B

necessarily is A, or because B is not necessarily A, admits of

conversion like other negative statements, e.g. if one should say,

it is possible that man is not horse, or that no garment is white. For

in the former case the one term necessarily does not belong to the

other; in the latter there is no necessity that it should: and the

premiss converts like other negative statements. For if it is possible

for no man to be a horse, it is also admissible for no horse to be a

man; and if it is admissible for no garment to be white, it is also

admissible for nothing white to be a garment. For if any white thing

must be a garment, then some garment will necessarily be white. This

has been already proved. The particular negative also must be

treated like those dealt with above. But if anything is said to be

possible because it is the general rule and natural (and it is in this

way we define the possible), the negative premisses can no longer be

converted like the simple negatives; the universal negative premiss

does not convert, and the particular does. This will be plain when

we speak about the possible. At present we may take this much as clear

in addition to what has been said: the statement that it is possible

that no B is A or some B is not A is affirmative in form: for the

expression 'is possible' ranks along with 'is', and 'is' makes an

affirmation always and in every case, whatever the terms to which it

is added, in predication, e.g. 'it is not-good' or 'it is not-white'

or in a word 'it is not-this'. But this also will be proved in the

sequel. In conversion these premisses will behave like the other

affirmative propositions.