Handbook of the History of Logic: - Fordham University Faculty

320 Henrik Lagerlund
would make the proposition non-modal. He has, however, made it clear that it is
the Abelardian reading he adheres to (without mentioning Abelard, of course).
Having presented the form of a modal proposition, Peter states some initial
rules of equipollence.
ME-Rule 1: ‘If an affirmative proposition is possible or contingent and
not impossible, then its contradictory is not necessary’.
Example: ‘A is possible B’ contradicts ‘A is necessarily not B’.
ME-Rule 2: ‘If a negative proposition is possible and contingent and
not impossible, then its contradictory is not necessary’.
Example: ‘A is not possibly B’ contradicts
ME-Rule 3: ‘If an affirmative proposition is not possible, not contingent,
and impossible, then its contradictory is necessary’.
Example:
ME-Rule 4: ‘If a negative proposition is not possible, not contingent,
and impossible, then its contradictory is necessary’.
Example:
Given the modalities and negation it is possible to state some equivalences between
the modalities. It was common to present four groups and say that within each
group the modalities are all equivalent.
I.
Possibly
Contingently
Not-impossibly
Not-necessary not
II.
Possibly not
Contingently not
Not-impossibly not
Not-necessary
III.
Not-possibly
Not-contingently
Impossibly
Necessarily not
IV.
Not-possibly not
Not-contingently not