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deontic modes. 127
Modal term Alethic Epistemic Deontic (mode of right)
Possible is what can be true can be clearly and distinctly understood can be done.
Impossible is what cannot be true cannot be clearly and distinctly understood cannot be done.
Necessary is what cannot not be true cannot not be clearly and distinctly understood cannot not be done.
Contingent is what can be not true can be not clearly and distinctly understood can be not done.
This shows how the different modal terms are to be interpreted. Each mode has different
requirements and truth conditions relative to its kind (alethic, epistemic, or deontic). In
the deontic mode “can” means “morally able,” or “morally speaking, X can be done,” etc.
But these actions are not logically necessary truths in the alethic sense.
The logical relationships between the alethic and deontic modes can be more
clearly compared in the following diagram of the Aristotelian square of opposition. 128
The diagram also efficiently summarizes all of the logical permutations through which
Leibniz takes the definition of vir bonus in Draft 6. 129
A Necessary (All S is P) contraries E Impossible (No S is P)
Cannot not be true (Cannot both be true; Cannot be true
Equitable, owing both may be false) Unjust, forbidden
Cannot not be done Cannot be done
implies contradictories implies
I Possible (Some S is P) subcontraries O Possible not (Some S is not P)
Can be true (Cannot both be false; Can be not true
Just, permitted both may be true) Omissible
Can be done Can be not done
The Aristotelian square of inference shows the relations of immediate inference among
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I have translated, arranged, and added headings to this diagram to make the relationships Leibniz
displays easier to grasp. The Latin of the first line of the diagram would be: “Possibile est qvicqvid (potest)
fieri seu qvod verum est (qvodam) casu” (A.6.1.466).
128
The idea for this diagram came from Poser (1969). I have dropped the epistemic mode since it has no
consequence here.
129
It is not crucial to go into depth of detail on Aristotle’s analysis of the syllogism and the development of
the square of opposition. However it is interesting to have some idea of where the notions of necessity and
possibility came from in Aristotle. In the Hermeneutics, Aristotle analyzes the propositional types of the
syllogism, and classifies them generally into two kinds, determinate and indeterminate. In other words,
there are only two types of propositions, necessary and contingent, the former are those that cannot be false
and the later those that can be false. Aristotle then derives the logical implications of these types, and these
results have been organized into this square.
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