Truth between syntax and semantics

Abstract

Sir s m c lem t eto pr ace je vyjasnit vztah mezi syntax a s emantikou, zejm ena pokud jde o jazyky s p resn e speci kovanou strukturou. Hlavn ot azky, kter ymi se zab yv ame, jsou: Co cin s emantick y pojem s emantick ym? Co zp usobuje, ze je pouh a s emantick a anal yza takov eho pojmu nedostate cn a? Co je t m rozhoduj c m krokem, kter y mus me u cinit, abychom pronikli k v yznamov e str ance jazyka? T emito ot azkami se nezab yv ame p r mo, ale prost rednictv m anal yzy typick eho s emantick eho pojmu, a sice pravdivosti. Na s hlavn ot azkou tedy je: Jak e pojmov e prost redky jsou nezbytn e pro uspokojivou de nici pravdivosti? Ke zkoum an pojmu pravdivosti a jednotliv ych zp usob u, jak jej lze de- novat, jsme si vybrali t ri konkr etn syst emy: kumulativn verzi Russellovy rozv etven e teorie typ u, Zermelovu druho r adovou teorii mno zin a Carnapovu logickou syntax. Ka zd y syst em je podroben d ukladn emu studiu. P redkl adan a pr ace je tedy souborem t r v ce m en e samostatn ych studi , je z popisuj mo znosti explicitn de nice pravdivosti a nezbytn eho pojmov eho z azem . Poznamenejme, ze na s m c lem nen historicky v ern a prezentace uveden ych syst em u, n ybr z snaha o dal s rozvinut toho cenn eho, co nab zej , ve sv etle sou casn ych poznatk u. Obecn ym z av erem, k n emu z dosp ejeme na z...

The broad aim of this thesis is to clarify the relationship between syntax and semantics, mainly in connection with languages with exactly speci ed structure. The main questions we raise are: What is it that makes a semantic concept genuinely semantic? What exactly makes a merely semantic characterization of such a concept inadequate? What is the decisive step we have to make if we want to start speaking about the meaning-side of language? We approach these questions indirectly: via an analysis of a typically semantic concept, namely that of truth. Our principal question then becomes: What conceptual resources are required for a satisfactory de nition of truth? To investigate the concept of truth and di erent ways in which it can be de ned, we have chosen three individual systems: (a cumulative version of) Russell's rami ed theory of types, Zermelo's second-order set theory and Carnap's logical syntax. Each of the systems is studied in considerable detail. The presented thesis is, in e ect, a collection of three case-studies into the ways in which the concept of truth is explicitly de nable and into the requisite conceptual background, each study forming a more or less closed unity. It should be noted that we are not interested in a historically faithful representation of these systems; our goal is to get...