§2 The Relation b etw een Holism and th e J u stifica tio n of D eduction §3 The Form of Dummett’s Programm e and th e Im portance of th e Notion o f T ruth
§4 The P o ssib ility of an A n ti-R ealist J u stifica tio n of D eduction §5 A nti-R ealism and S o u n d n ess
§6 The O b jectiv ity of M eaning §7 Summary
The Need for a J u stifica tio n of D edu ction
The sco p e of th is ch a p ter is lim ited. I attem pt to reb u t certa in argu m en ts for th e co n clu sio n th a t th e a n ti-r e a list can and, p erh a p s, sh ou ld esch ew a ju stific a tio n of d ed u ction . T h ese argu m en ts (glean ed m ainly from th e w r itin g s of C rispin W right) h ave two main fo c u sse s. F irst, it is claim ed th at a sem antic ju stific a tio n is not m andatory g iv en o n ly th e a n ti-r e a lis t’s c o n str a in t o f m olecularity. S econ d ly (and more p ow erfu lly) it is a rg u ed th a t su c h ju stific a tio n s p resu p p o se a con cep tion o f m eaning w h ich is u n availab le to th e a n ti-r e a list sin ce in th e p r o c e ss o f ju stifica tio n one assu m es th a t th e re are determ inate and tra n scen d en t co n d itio n s o f c o r re c t u se. My c o n tra r y claim is th at a re fu sa l to con cern o n e se lf w ith a sem antic ju stific a tio n of d ed u ction in v o lv e s a d ep artu re from a m olecular co n cep tio n o f m eaning and th at we h ave been g iv en no rea so n for su p p o sin g th at th e ju stific a to r y p ro ject n e c e ssita te s an a n ti-r e a listica lly rep u g n a n t notion of m eaning. T hus th e (m olecular) a n ti-r e a list p osition is , at lea st, p o ten tia lly re v isio n a r y sin ce it req u ires a sig n ific a n t ju stific a tio n of th e p ra ctice. The v a lid ity of c la ssica l logic w ill th u s d ep en d on an a p p rop riate sem an tics being forth com in g. I do not claim th at no a n ti-r e a listic a lly accep ta b le valid ation of cla ssica l logic is p o ssib le. I do, h ow ever, a c c ep t th at th e cla ssica l two valu ed tru th -fu n c tio n a l a ccou n t of c la ssica l logic in v o lv e s an inadm issable c o n cessio n to realism (or, p erh a p s, sh ou ld rath er be id en tified w ith w hat it is to assum e a re a list p o sitio n w ith r e sp e c t to a g iv en d isco u rse ). So e v e n if we can be b ro u g h t to a c c ep t cla ssica l logic as va lid , we are, as a n ti-r e a lists, n e c e ssa r ily in v o lv ed in rev isio n of, at lea st, th e sem antic th eo ry u n d erp in n in g cla ssica l logic.
I do not a rg u e (in th is ch a p ter or an yw h ere else) th at an a n ti-r e a list p osition m u st coin cid e w ith a v e r sio n of intu ition ism . I lea v e op en the q u estio n of w h eth er an a n ti-r e a listic a lly accep tab le sem antics w hich su c c ee d s in ju s tify in g c la ssica l logic is p o ssib le. That is a large
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q u estion . (It w ould, for a sta r t, in v o lv e a su r v e y of v a rio u s su p er-v a lu a tio n a l sem an tics and o th er r e d u c tiv e sem antic a cco u n ts.) The su p p ort I o ffer fo r in tu ition ism c o n sists, fir s t, in exp lain in g th e in tu itio n istic sem an tics as a p la u sib le (but by no m eans an in ev ita b le) outcom e o f a n ti-r e a list sem antic co n sid era tio n s and, seco n d ly , in d efen d in g th at p o sitio n from c erta in a ccu sa tio n s of in co h eren ce. (This, I u n d ertak e m ainly in c h a p te rs 4 and 6.) So th e str e n g th of my argum ent fo r in tu ition ism a s a p h ilo so p h y o f m athem atics is lim ited to sh ow in g th at it is a n ti-r e a listic a lly a ccep ta b le, not th at it is m andatory to an a n ti-r e a list.
The c o u rse o f my argu m en t has been d ictated by a se t of co n sid era tio n s rallied by W right. The str u c u r e of th e ch ap ter is th u s som ewhat co n v o lu ted . I hope th at by a n ticip a tin g my argum en t h ere I can make th a t str u c tu r e clea rer. I b egin (§1) by o u tlin in g th e relev a n t notion s of holism and m olecularism . In §2 I o ffer a d irect reb u tta l of th e c o n siste n c y o f h old in g both W right’s im plicit d efin ition al view of logic, and a m olecular view o f la n g u a g e.
§3 in v e stig a te s a som ew hat d iffe r en t and, p erh a p s, d eep er ch a llen g e to r e v isio n a r y a n ti-rea lism . The broad ch a llen g e (w hich d ep en d s on a com plex se t of co n sid era tio n s to do w ith th e p r o c e ss of v a lid a tin g a logic) is for th e a n ti-r e a list to g iv e co n ten t to th e sp ecifica lly sem an tic
n otion s he r e g a r d s him self a s en title d to. The p oint of th e ch a llen g e is th at u n le ss th e a n ti-r e a list can make good an accu sa tio n a g a in st a sem antic th eo ry o f u sin g a n ti-r e a listic a lly rep u g n a n t n otion s th e ch aracteriza tio n of th e m etap h ysical iss u e of realism in sem antic term s th rea ten s to co lla p se. My d efen ce of a n ti-realism h in g es on, i) r e se r v a tio n s about th e d etail of th e argum ent and, ii) a reco g n itio n th at alth ou gh th e p o ssib ility of ra isin g the m etaphysical iss u e of realism r eq u ires th at th ere be some m easure of agreem en t b etw een p a rties to th e d isp u te, th is n eed not be a so u rce o f co n cern p rovid ed no m etap h ysical q u estio n is b eg g ed .
§4 c o n sid e r s an argum en t of W right's w hich p u rp o rts to show th a t th e a n ti-r e a list is u n ab le to co n cern him self w ith q u estio n s of so u n d n e ss b ecau se an in sta n c e of erro r can o n ly be reco g n ized from w ith in an in feren tia l sy stem . T here is th u s no reco g n iza b le o b je c tiv e fa ct w hich d eterm in es w h eth er or not a g iv e n sy stem (sh o rt o f in c o n sisten cy ) is sound . I attem pt to in c re a se th e ten sio n by a rg u in g th at d esp ite th e r e la tiv ity W right claim s to h ave rev ea led in q u estio n s o f so u n d n e ss a n y
p ra ctitio n er o f in fe r e n c e can n ot a c c ep t th at more than one sy stem is sound .
§5 attem p ts to resp o n d to th is ten sio n . F irst, I claim th a t W right has on ly su cceed ed in d em on stratin g th e u n d ecid a b ility of q u estio n s of u n so u n d n ess. So from th e in tu itio n istic point of view it has been show n th at a n y sy stem is not u n sou n d (w hich is not, by in tu itio n istic lig h ts, to sa y th at it is so u n d ). S eco n d ly , I n o tice that th e a ccu sation made by th e in tu itio n istic a n ti-r e a list a g a in st c la ssic a l logic is not th at it is u n sou n d , it is th at it is n ot d em on strab ly sou n d . It is q u ite p o ssib le for an a n ti-r e a list a ccep tin g th e fir s t p o sitio n to ra ise q u estio n s about so u n d n ess (rath er th an u n so u n d n e ss) and th u s to make th e accu sation lev elled in th e seco n d p o sitio n .
In th is la st sectio n (§6) I a rg u e th at W right's r e se r v a tio n s about rev isio n a ry a n ti-rea lism stem w h olly from h is in terp reta tio n of W ittgen stein ’s Rule Follow ing C on sid eration s. I o ffer an a ltern a tiv e in terp reta tio n of th o se c o n sid era tio n s (draw n from th e w ritin g s of John McDowell) w hich I claim is c o n siste n t w ith a n ti-realism . So no in tern a l in co h eren cy in th a t p o sitio n has been rev ea led .
§1 Holism and M olecularism:
We are co n cern ed w ith th e e ffe c t o f holism on th e form of th e th eo ry of m eaning. T h us we can th in k of holism a s th e denial of th e p o ssib ility of a m olecular th e o ry of m eaning. A m olecular th eo ry holds th at u n d ersta n d in g an y e x p r e ssio n r e q u ire s com p etence in at m ost a fragm ent
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of lan g u a g e and th a t we can g iv e an accou n t for e v e r y ex p ressio n of w hat th at com p eten ce c o n s is ts in. T h ere are th ree w ays of d en y in g th is, so th ree form s o f holism .
Holism) some s e n te n c e s do not h ave a determ inate m eaning.
Holism^:- all s e n te n c e s h ave determ in ate m eanings but u n d ersta n d in g some se n te n c e s r e q u ire s com p eten ce in th e en tire la n gu age.
Holism^:- all se n te n c e s h ave determ in ate m ean ings n ot d ep en d en t on an u n d er sta n d in g of th e en tir e la n g u a g e but some e x p r e ssio n s are su ch th a t we can n ot g iv e an exp lan ation (in th e se n se of a sem antic ju stific a tio n a s g lo sse d in th e la st ch ap ter) of w hat an u n d ersta n d in g of them c o n s is ts in .
I sh ou ld h ere add a w ord to my u se o f th e notion o f determ in ate m eaning. The m anner in w h ich I w ould ch oose to elu cid ate th is notion would be th a t an e x p r e ssio n h as determ in ate m eaning if its m eaning is capable of bein g exp lain ed w ith in an ap p rop riate th eo ry of m eaning for th e la n gu age.
Holism y tr ie s to m eet m any of th e m olecular co n stra in ts th at em erge from c o n sid erin g th e n atu re of u n d ersta n d in g but is sh y of th e str e n g th o f th e m olecular m ethodological sta n ce (w hich in s is ts th at it be p o ssib le to g iv e a n o n -circu la r a cco u n t of th e m eaning o f each se n te n c e in term s w hich p r e su p p o se com p eten ce in at most a fragm en t of th e lan gu age) b ecau se of its a ccep ta n ce o f th e p o ssib ility of im posing a rev isio n in a fir s t ord er p ra ctice. It allow s th e p o ssib ility of a p ractice ev a d in g exp lan ation w ith in a th e o ry of m eaning w ith ou t se ein g th is, in m olecular fa sh io n , a s a condem nation of th e m ean in gfu ln ess of th e p ra ctice. We could th u s take it th a t it d iffe r s on ly term in ologically from