Stony Brook University

the four types of statements of the syllogism: A: Universal affirmative; E: Universal
negative; I: Particular affirmative; O: Particular negative (shown within parentheses).
Corresponding to these are the four alethic modal predicates (underlined): necessary,
impossible, possible, possible not. The corresponding deontic modes are set in italics.
Also important is that the modes can be classified more generally into two types: (A)
necessary and (I) possible. The other two, (E) and (O), are immediately derived from (A)
and (I). This classification into two basic types corresponds with Leibniz’s division of the
modes of right into necessary and possible (and corresponds with the moral qualities of
obligation and possibility/permissibility. The other two modes, (E) forbidden and (O)
omissible, are derivable from (A) and (I)). In sum, all logical relations among the modes
of right are inferable in the same way that the logical relations among alethic modes are
inferable. To see this, consider (A) in the alethic mode. Let us say that □p (i.e., p is
necessary). From this we can infer that ◊p (p is possible). But starting with ◊p we cannot
of course infer that □p. Also, starting from □p we can infer that ~□p is false, since the
contrary of a necessary proposition is false. The same logical relations hold for deontic
operators. Consider (A) in the deontic mode. We then say that Op (it is obligatory that p).
From this we can infer that Pp (p is permitted). But from Pp we cannot infer that Op.
Similarly, starting from Op we can infer that ~Op is false, since the contrary of a
necessary proposition is false, and so on.
However, the truth conditions of the deontic mode as a whole are essentially
different from the truth conditions of the alethic mode. In the alethic mode, truth is a
function of a relation between propositions and states of affairs. In the deontic mode,
truth is a function of the relation between the deontic propositions and normative states of
affairs i.e., states of affairs that ought (or ought not) obtain. This means that the deontic
mode is “ontologically precarious.” 130 The difference can be well-illustrated using logical
operators. In the alethic mode, ‘□p -> p’ says that ‘if p is necessary, then p is true.’
However, if we were to treat deontic operators as alethic operators, we would get
obviously false results. For example, ‘Op -> p’ would say that ‘if p is obligatory, then p is
true.’ Not only does this not follow, but it is hard to make sense of. Certainly, it does not
mean, for example, that if I am obligated to tell the truth, then I do tell the truth.
Obligations can be forever demanded, but may never obtain. What the deontic
proposition really expresses is, ‘if p is obligatory (i.e., morally necessary) then p ought to
be a state of affairs.’ Deontic truth is determined by whether the action in the consequent
fulfills the obligation specified by the antecedent. Whether p is obligatory depends on
what makes p an obligation. Below, I will address the question of what makes p an
obligation, for Leibniz.
We have seen what Leibniz means when he says that Aristotelian logic may be
“not uselessly transferred” onto his juris modalia. The modes of right, derived from the
moral qualities, have a distinctly normative logic. Yet one may be tempted to ask at this
point, to what use may the good person put this logic? Is this nothing but an exercise in
formalism? After the demonstration he carries out (in the next section), Leibniz shows
how the definitions contained in “the good person” can be applied to the modes of right.
130 Patrice Bailhache (1991) puts the matter nicely. “The fact that states of affairs are not deducible from
obligations (Op-> p is not a thesis...) expressess an essential property of the norm, which can be called its
precariousness: that something is obligatory does not prove that it is realized. In fact, that a norm can be
transgressed is one of its essential features” (p. 11).
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