PERMISSIONS A ND DEONTICAL L Y PERFECT WORLDS
Kornél SOLT
Let us suppose that in our actual world Tr there is only a single
normative code C. L e t C b e consistent. W e suppose that C ' s
addressees are able t o perform every norm o f C. Thus, we can
imagine a series o f possible phantasy-worlds w, — W„ whose 'inhabitants' always perform every n o rm o f C. Th e worlds w, — w„ are
deontically perfect alternative worlds to the actual wo rld 14' ( C ' s
norms are sometimes violated at (v.) Thus, if a norm A i s valid, i.e.
the corresponding proposition OA is true at HY according to C
9 true
is
t h at
e every
n
world
A
vv, — w„. (
1 This conception of deontically perfect worlds was suggested at first
) J. HINTIKKA. ([2], [31) His deontic model proved enormously
by
successful. With its help, a lot of difficult problems got their solutions
in deontic logic.
There are not only norms in C (i.e. commands or prohibitions), but
also sentences o f the f o rm PA (' A is permitted'), and / A (' A is
indifferent'). The P- or /-sentences are either explicitly given in C or
are derivable from C.
Regarding the P-sentences there is a well-known standpoint in
deontic logic which we can formulate in this way :
(1) P A is true at w if f A is true at least at a w, among w, — w,,.
E.g. Jean-Louis GARDIES wrote recently : " a est permis dans le
monde originaire si e t seulement s' il existe de moins un monde
admissible dans lequel a est vra i:" ([1], p. 81. — This is, o f course,
only one example picked out from a lot of similar statements in the
contemporary literature.) As far as I know, (1) is generally accepted
by logicians, but, I think, it is false. (
2
) (') I tried to show in [51 that the generally accepted thesis:
(*) A ! is valid (OA is true) at w if f A is true at every deontic alternative world to w is
false. Only a weakened form of (*) is true. I f (*) were true, then (I). (2) were also
necessarily true.
(
circular.
2
)
E
.
g
.
G
.
K
A
L
I
N
O
178
K
.
SOL T
In standard deontic logic the biconditional IA & P — A) is
valid, therefore, if (1) holds, then the following statement automatically holds too:
(2) I A is true at w if f A is true at least at a w„ and false at least at
another w, among w, — w„.
I
here.
n
Imbelieve, (I) and (2) have two motivations. Firstly, they intend to
deontically
y
ground PA's and /A's respective truths at w. Secondly,
they
intend
to regulate how a deontically perfect world has to behave
v
facing
C's sentences o f the form P A
i
preserve
. eI A . its deontic perfectness. But both motivations are mistaken.
My
r ewarguments
s p e c against
t i v e (1)
l yand
, (2) are as follows.
u
s
suppose
that
the
PA-sentence: " I t is permitted t o d o
i Let
n
(
gymnastics
o 1 r
ddaily"eis derivable
r
from C. Th e n (l) excludes that nobody
does
daily at every deontically perfect world to Iv. Is this
t ) gymnastics
o
requirement
acceptable ? No , i t is not. P A 's truth a t w does n o t
a
depend
on
A
•s falsity at every w, —14'„ I t depends exclusively on the
n
ways
of
regulation
by C at 14', on what is given in w itself. If it is true at
d
w , (according to C. that it is permitted to do gymnastics daily, this
permission
also remains true if nobody does anywhere. at any w, — w„
2
gymnastics
daily.(') — Furthermore, would it diminish the supposed
)
deontic
perfectness
o f 14'
a
allowed
to
do'?
It
would,
certainly, not.
i —
w
„
i
f
r
Let
us
now
suppose
that
the following /A-sentence is derivable from
n eo b o d y
C:
to take a walk daily, and it is permitted not to take
d b" I t iis permitted
d
i walk
a
daily."
n
By
(2)
two variants are excluded : (i) that everybody
o
takes
at every w, — w„, and (ii) that nobody takes a walk
t t ahwalk daily
e
m h at every w, — w„. Do these exclusions hold '? I do not believe they
daily
do.
w e— The
h truth oa f the sentence in quotationsmarks at w does not
depend
on whether the 'inhabitants' o f a deontically perfect world
t r
take
h r a walk daily or do not, namely, whether they in fact exercise their
liberty
e o o r not. Further, neither (i) n o r (ii) would touch w, — w„'s
supposed
deontic
perfectness.
w n
a
s e
(o
which
3 u suffices to show that p is permitted...• • ([31. p. 69.)
)
s
H
I.
NT
Fh
Ii
Ks
K
i
A
ss
PERMISSIONS A ND DEONT1CALLY PERFECT WORLDS
1 7 9
Only norms, that is sentences o f the form V A ' , '0 — A' have a
model in deontically accessible worlds, but sentences of the form 'PA'
or VA' have none, because they are not norms.
Assumed: (1) and (2) are both false. They are erroneous 'transpositions' from alethic modal logic into the realm o f deontic logic. PA's
and IA • s truth-conditions respectively are n o t analogous t o the
truth-conditions of MA (" A is possible") and CA (" A is contingent
—
respectively.
Deontic logic is not a simple copy of alethic modal logic.
)
Kornél SOL
Budapest
IX. Kinizsi u. 22.
H - 1092
Hungary
REFERENCES
111 Jean-Louis Gardies, 'Logique de l'action (ou de changement) et logique deontique',
Logique et Analyse, 101 (1983), pp. 71-90.
[2] Jaakko Hintikka, 'Deontic Logic and its Philosophical Morals '. I n: Jaakko Hintikka: Models f o r Modalities . Selected Essays. Reidel, Dordrec ht, 1969,
pp. 184-214.
[3] Jaakko Hintikka, 'Some Main Problems of Deontic Logic '. I n: Deottric Logic :
Introductory and Systematic Readings, (ed. Risk) Hilpinen), Reidel, Dordrecht,
1971, pp. 59-104.
141 Georges Kalinowski, 'Sur les semantiques des mondes possible pour les systèmes de
logique deontique'. Logique et Analyse, 93 (1982), pp. 81-98.
[5] Kornél Solt, • Deontic Alternative Worlds and the Truth-Value of OA' , Logique et
Analyse, 107 (1984), pp. 349-351.