relative truth properties and other concepts. For expository purposes, let’s restrict our
selves to {o, 1, 2) as the set o f truth values and { i, 2) as the set o f designated values. We
say th a t i represents s u p e ra s s e rtib ility a n d 2 represents c o rre s p o n d e n c e . T h e rules using
m in a n d m a x w ill give us a sem antics fo r “ A ” a n d “ V ” th a t can be re jjre s e n te d by the fa m ilia r th re e-va lu ed tr u th tables:
0 2 0 0 0 0 1 0 1 2 0 1 2 0 2 0 0 2 1 1 1 2 2 2 2 2
L e t m e give o n e s tra ig h tfo rw a rd m a n ife s ta tio n o f th e hostage s itu a tio n . / \ n in ip o r t in t m o tiv a tio n fo r in tr o d u c in g s u p e ra s s e rtib itiliy is th a t we w a n t to some d o m a in relative
tr u th p ro p e rty fo r d o m a in s th a t c a n n o t o u ts trip o u r e p is te m ic grasp. 1 th in k aesthetics is a v e iy g o o d ca n d id a te . I d o n ’t th in k it makes n u ic h sense to say th a t s o m e th in g c o u ld be p re tty, o r h an dso m e , o r ugly, o r h o t, w ith o u t a nyone ever b e in g in a p o s itio n to recognize
this. T h e c la im th a t “ N o one c o u ld ever co m e k n o w w h e th e r T om C ruise is pretty, but it m ig h t tru e ” is f lir t in g w ith nonsen.se. W lie th e r you accept m y view here is n ’t c ru c ia l. Just assiune fo r sake o f a rg u m e n t th a t s u p e ra s s e rtib ility is th e a p p ro p ria te [iro p e rty to e xplain tn it h fo r sentences th a t c o n c e rn the aesthetic dc:>main. I le re are two c o m m o n ly accep'.ed p rin c ip le s a b o u t k n o w a b ility ;
(1 ) I f is su pe ra ssertible th e n (f) is kn ow ab le.
(2 ) I f '” (?!) A ■
0
"' is k n o w a b le th e n (j) is k n o w a b le a n d "ip is know able.Now, im a g in e th a t S is som e u nd is c o v e re d tr u th in physics, and th a t being corresponding is
th e re le v a n t tr u th p ro p e rty fo r th a t d o m a in . I also take i t fo r g ra n te d th a t we a ll agree T o m C ruise is p retty. Suppose I w ere to say
(3 ) S A T o m C ruise is p retty.
W e’ re a ssiu nin g th a t v (S ) = 2 and v ( “ T o m C ru is e ” is jjre tty ) = 1. So given the semantics fo r c o n jiu ic tio n above, u ( “ S A T o m C m is e is p re tty ” ) = 1. T h a t is to say, i t fo llo w s fro m
it b e in g superassertible th a t T o m C ruise is p re tty th a t it is superassertible th a t (3 ). This im p lie s to g e th e r w ith (1 ) th a t (3 ) is kn ow ab le. T h a t’s o d d e n o u g h as it stands, b u t given
(2 ) it im p lie s th a t S is k n o w a b le . A n d th a t c a n ’t be rig h t. Sentences c o n c e rn in g physics, o n th e a ssu m p tio n th a t c o rre s p o n d e n c e is th e a p p ro p ria te d o m a in relative tr u th p ro pe rty, s h o u ld p o te n tia lly be b e y o n d w h a t we can know . T h e m any-valued sem antics ig n o re s such
im p ortan t c o n c e p tu a l d istin ction s b etw een d o m ain relative truth p rop erties b ecau se it treats th em sim ply as iion -d istin ct vahies.
4.2
S equences
A m ore in terestin g take o n the tn u h value strategy co m es from A aron C otn oir (2 0 1 3). H is su g g estio n is that we sh o u ld con stru e the set o f truth values as a set o f seq u en ces, T = { ( c ii, • • ■, Cin) '■ ea c h ttj € { 1 , 0 } } . Each Qj represents a p oten tial d om ain relative truth property. If d i = 1 this m eans that the d o m ain relative property for the d o m ain di
is in stan tiated , an d if q , = 0 it m ean s that it is not. Like the previous su g g estio n , d o m a in relative truth p rop erties are here assigned directly to sen ten ces.
C o tn o ir gives the fo llo w in g sem antics for the logical coim ectives:
w here 1 + 1 = 1. A dditionally, we are given a d efin itio n o f logical c o n se q u e n c e . T his is d o n e via the re la tio n ‘< ’, w hich is reflexive, antisym m etric and transitive - a partial
ord erin g. (It is d e fin e d as: v{<f)) < iff V tp~') =
A se n te n c e 0 is a logical c o n se q u e n c e o f a set o f se n te n c es F iff for every valuation
V,
A
<v{(t>).iper
Intuitively: ^ is a logical c o n se q u e n c e o f F ju st in case the value o f the co n ju n ctio n o f the prem ises in F is less or eq u al to the value o f (f) in all cases. A gain we are able to h a n d le preservation o f so m e truth property or o th e r from prem ises to co n c lu sio n w ithout a p p e a lin g to so m e d o m a in invariant n o tio n . At a first gla n ce this is a p rom isin g lin e for the pluralist to follow . But only at first glance.
T h e sem an tics p rovid ed com m its the pluralist to radically m iscon stru e the m ea n in g o f the c o n n ectiv es. L e t’s focus o n co n ju n ctio n , and only co n sid er two dom ain s. L et’s say that
uC"~ <?:>■') = ( 1 - Q i , . . . , 1 - a n ) , if v{4>) = ( a i , . . . ,a „ >
v{(p) = ( qi , . . . , Q„)
v{(j)) = (1 ,0 ) i f f is siipe ra ssertible ,
v{(f)) — (0, 1) i f f (f) is c o rre s p o n d in g .
L e t’s say i t is tru e th a t T o m C n iis e is a p re tty a n d th a t h e ’s h u m a n . So v ( “ T o m Cruise
is p re tty ” ) = (1,0) and u ( “ T o m C ruise is h u m a n ” ) = (0, 1). T h e n given tlie sem antics above; u ( “ T o m C ruise is p re tty A T o m C ruise is h u m a n ” ) = (0,0). In o th e r w ords, the c o n ju n c tio n is n o t tru e in any p a rtic u la r d o m a in , so i t ’s false s im p lic ite r. H ow ever, b o th
th e c o n ju n c ts are tru e , in th e sense o f b e in g superassertible and c o rre s p o n d in g , respec tively. T h e p o in t o f the o b je c tio n in §3.1 was th a t p lu ra lis m seem ed in c o m p a tib le w ith
h o w th e co nn ective s actually w o rk. D e fin in g some a lg eb raic c o n c e p t th a t c a n n o t be im p o rte d has zero value fo r th e p lu ra lis t p ro je c t. O r any o th e r p h ilo s o p h ic a l p ro je c t fo r th a t m a tte r T h e p lu ra lis t w o u ld have take th e ro u te o f a ttr ib u tin g a massive e r r o r to speakers, rh is tim e , we c a n ’t even p o in t to an e rr o r a b o u t w h a t tr u th consists in , because n o w i t ’s
a b o u t th e m e a n in g o f the c o n ju n c tio n . T h e c la im th a t speakers are c o n fu s e d a b o u t the m e a n in g o f ‘a n d ’ is n o t an a p p e a lin g c o m m itm e n t.
O n th a t n o te , C o tn o ir (2 0 1 3 , 7) states the re c ju ire m e n t th a t a sentence b elongs to
a d o m a in ju s t in case i t in sta n tia te s th e p a rtic u la r d o m a in relative tr u th p ro p e rty . As a consequence, th e sentence “ T o m C ruise is p re tty A T o m C itiis e is h u m a n ” d o e s n ’t be lo n g to any d o m a in , even th o u g h its c o n s titu e n ts do. H ow ever, given th e sem antics fo r d is ju n c tio n , “ T o m C ruise is p re tty V T o m C ruise is h u m a n ” belongs to b o th th e aesthetic a n d th e b io lo g ic a l d o m a in . It is c o m p le te ly ad h oc to a llo w o n e type o f lo g ic a lly c o m p le x
sentence to b e lo n g to two d o m a in s , b u t s im p ly refuse a n o th e r one, on th e g ro u n d s th a t i t messes u p th e sem antics. I f e ith e r b elongs to b o th d o m a in s th en b o th s h o u ld , as they b o th c o n ta in the same subsentences. I th in k C o tn o ir g o t it r ig h t w ith d is ju n c tio n , b u t
n o t c o n ju n c tio n . I f “T o m C ruise is p re tty ” ’ b elongs to th e d o m a in o f aesthetics and “ T om C ruise is h u m a n ” b elongs to th e d o m a in o f b io log y, th e n any c o m p le x sentence c o n ta in
in g b o th s h o u ld in h e r it a d u a l m e m b e rs h ip . Since the t n it h o f “T o m C ruise is p re tty ” d ep en ds the aesthetic d o m a in and th e tr u th o f “ T o m C ruise is h u m a n ” d ep en ds o n the b io lo g ic a l d o m a in , the tr u th value o f th e ir c o n ju n c tio n and d is ju n c tio n d e p e n d o n b o th .
I f I m ake a c la im to th e e ffe c t th a t som eone is a p re tty h u m a n , th e n I am m a k in g a c la im th a t has b o th aesthetics a n d b io lo g y as its su bject m a tte r
L e t’s m ove o n to th e p ra g m a tic level. H o w s h o u ld we u n d e rs ta n d the relevance o f this sem antics fo r assessing assertions? A firs t suggestion is th a t we can say th a t an a ssertion is
a c c u r a te if th e s e m a n tic s a ssig n s s o m e tru th p r o p e r ty o r o t h e r to th e a sse r te d s e n t e n c e
T h e a sse r tio n o f (p is a c c u r a te iff v ( 0 ) € {(o^ i, • • •, Q^n) ^ 3 a i ( a j = 1 ) }
B u t th a t w o n ’t d o . W e h a v e to h ave th e right tru th p rop erty. W e h a v e to m a k e su re th at o n ly th e d o m a in re la tiv e t n it h p r o p e r ty re le v a n t fo r th e s e n t e n c e is th e o n e th a t is in play. VV'e are fa c e d h e r e w ith a c o n c e p t u a l p r o b le m . T h e tru th v a lu es are r e q u ir e d to f u n c t io n b o th as in g r e d ie n t a n d a sse r to r ic v a lu es. H o w ev er, s in c e a to m ic a n d c o m p le x s e n t e n c e s are tr e a te d d iffe r e n tly , w e c a n n o t s tip u la te th a t th e r e m u st b e o n e p a rticu la r d o m a in . A b r id g e p r in c ip le th a t ca n a c c o m m o d a te th e a to m ic s e n t e n c e s w ill b e o n e that u n iq u e ly p ick s o u t s o m e th a t is i . T h a t ’s b e c a u s e it c a n o n ly b e a c c u r a te to a sse rt (piicj) in sta n tia te s th e p r o p e r ty r e le v a n t fo r its p a rticu la r d o m a in . B u t th e a cc u r a cy o f a sse r tin g