you can make "corporations" (or engineers) give us more
fuel-efficient cars simply by increasing fuel efficiency standards. If
they passed a law tomorrow that said all cars sold by 2010 must get 45mpg,
could do that pretty easily. They just don't, because they don't have to.
making a law that P means that P is the case. Itís an interesting point
of view. Letís see if we can establish a modal logic for that view of
define the modal operators L
(the analogue to ) and P
Lp =: Itís a law that p
Pp =: ~L~p =: itís
legal that p
take the semantic approach by defining the rules of the semantic tableaux
for the appropriate logic.
where v is new to this path
accessibility relation A is a legal
accessibility relation, and the indexes on the right indicate legal
worlds.PR tells us that if X is not forbidden by law in w
then in some state v, accessible
by lawyers from w X occurs.
tells us that if X is mandated by law in w,
then in any state v accessible
by lawyers from w X occurs.
know that LA … A, which is a statement of
Legal Reflexivity, wonít be a valid formula in this logic (try the tree
and see,) but if we add the rule (following the Hintikka strategy:)
Or if we declare that the accessibility relation is
reflexive (according to the Orthodox strategy:)
any w on this branch
also know that there is an axiomatization that will give us just the same
valid formulas in LTS:
need a rule of inference of Legal Necessitation on the analogy of
curiously enough, indicates that anything that can be shown to be a thesis
in the logic must be a Law.
axioms required are
… (LA … LB)
(Distribution of L
over … )
LA … A
itself would give us KL (Lawyersí K,) and it has the at first
sight odd result of saying that if it is a law that A …
B then if itís a law that A, it is equally a law that B. But how odd is
that? We could reasonably understand this as a statement of proper legal
interpretation: if the law states that A and the law also states that
whenever A then B, then it is at least implicitly according to law that B.
(Roe vs. Wade seems to have
been decided in this way.)
axiom L2 gives us TL, Lawyersí
T. Itís an explicit statement of the claim that we started with.
is a fairly weak logic, even amongst
logics. Do we want to add any other conditions? Do we want to give the
legal accessibility relation symmetry or transitivity? What would these
the property of transitivity to the accessibility relation in LT
Lp … LLp
We find that it closes in L4 but not in LT.
this something we want? That if itís a law that X then itís a law that
itís a law that X? That actually seems quite reasonable, especially if
we interpret Ďbeing a lawí in the way that we did for the
distributivity axiom. Thus; if itís a law that X then itís at least
implicitly according to law that itís a law that X. Perhaps this is
referring to some sort of constitutional understanding of the law.
the property of symmetry to the accessibility relation in LT
p … LPp
We find that it closes in LB but not in LT.
this something we want? Itís a bit harder to understand. If something is
occurring then by law there is no law against it. I have to say, that
seems unlikely. So letís not go so far as LB.
(Nor, of course, can we accept L5,
which weíd get by making the relation an equivalence relation.) So the
accessibility relation canít be symmetric: if v is accessible to lawyers from w
it doesnít follow that w is
accessible to lawyers from v.
if we just stick to LT there
are plenty of interesting results for the lawyers to get busy on. The
following are all provable in LTS:
ļ B) … (LA
& B) ļ (LA & LB)
LTS4: L~A ļ ~PA
LTS5: ~P(A v B) ļ (~PA
LTS6: P(A v B) ļ (PA
LTS7: L(A … B)
… (PA … PB)
LTS8: (LA v LB) … L(A v B)
LTS9: P(A & B) … (PA
I started writing this as a bit of a joke, but I now wonder if there might
not be a non-silly way to apply modality to laws.