100 The Debate over the Consequence Argument
we elaborate on a point alluded to in note 6 above.) That is, the following proposition
does not follow:
N[□((Po&L) → P)]
This stronger proposition would follow from a stronger inference rule. Call it
α-strong:
α-strong: □p ˫ □Np
And this stronger rule would state that from the fact that a proposition is necessary, it
follows that no one has, or ever had, a choice about whether that proposition is neces-
sary. Now, this stronger inference rule might be just as plausible as is Rule α. Never-
theless, it is not the one used in the argument we are currently examining. As for the
one that is, Rule α, all it allows us to infer from □((Po&L) → P) is that the following
material conditional, (Po&L) → P, is power necessary. That is:
N((Po&L) → P)
Of course, this material conditional is a logical consequence of the modalized condi-
tional, □((Po&L) → P). And the modalized conditional expresses a metaphysical or
broadly logical necessity. But readers should be cautioned against misunderstanding
what, strictly speaking, the argument asserts. It is not assumed in the argument that,
for instance, it is power necessary for a person that the metaphysical thesis of deter-
minism is true—that is, it is not assumed that it is power necessary that necessarily
the past and the laws imply one unique future. Nor is it claimed in the argument that it
is power necessary for any person, with respect to some particular fact, such as that
Nixon is pardoned, that it is metaphysically necessary that the fact is implied by the
laws and the past. All it claims that is power necessary for any person with respect to
any particular fact is that the fact (e.g., P, that Nixon is pardoned for all his crimes
while in office) is materially implied by the facts of the past and the laws (Po&L).
17 This is a point we explained in Section 1.5.
18 For those unfamiliar with the logic used here, the easiest way to see that
□((Po&L) → P) and □(Po → (L → P)) are logically equivalent is just to consider what
conditions would be required to render the unmodalized propositions ((Po&L) → P)
and (Po → (L → P)) true, and what conditions would be required to render them false.
Doing so, one will see that they are the exact same conditions, and so are logically
equivalent. Now just assume that the modal necessity operator preserves that relation.
19 See note 5 above for worries about inferring from NPo and NL that N(Po&L), which
have to do with the idea that power necessity (“N”) is agglomerative.
20 This indictment seems especially problematic since, as we have noted above, van
Inwagen was at pains to avoid the assumption of agglomerativity by taking care to
introduce NPo and NL as distinct steps rather than simply work with the premise
N(Po&L).
21 Here we assume some basic knowledge of first- order propositional logic, as we have
elsewhere in the text. But as a simple clue to aid one thinking through this the first
time, keep in mind that on any interpretation in which p is false, the entire sentence
must come out as true, since as a (complex) material conditional, if the antecedent of
it is false, then the entire sentence is true. So focus instead on only those interpreta-
tions in which p is true, which leaves only two, one in which q is false, and one in
which q is true. On each of these remaining interpretations, the complex proposition
comes out true.