Pravdivost mezi syntaxí a sémantikou

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...Institute of Philosophy and Religious StudiesÚstav filosofie a religionistikyFilozofická fakultaFaculty of Art

Ins and outs of Russell's theory of types

The thesis examines A.N. Whitehead and B. Russell’s Ramified Theory of Types (RTT). It consists of three parts. The first part is devoted to understanding the source of impredicativity implicit in the induction principle. The question I raise here is whether second-order explicit definitions are responsible for cases when impredicativity turns pathological. The second part considers the interplay between the vicious-circle principle and the no-class theory. The main goal is to give an explanation for the predicative restrictions entailed by the vicious-circle principle. The explanation is that set-existence is parasitic upon prior predicative specifications. The justification for this claim is given by employing the method of hierarchy of languages. Supposing the natural number structure and the language of Peano Arithmetic (PA) as given, I describe the construction of a set-theoretic language equipped with substitutionally interpreted quantifiers ranging over arithmetically definable sets. The third part considers the proposition-theoretic version of Russell’s antinomy. A solution to this paradox is offered on the basis of the ramified hierarchy propositions

Predicativity and parametric polymorphism of Brouwerian implication

A common objection to the definition of intuitionistic implication in the Proof Interpretation is that it is impredicative. I discuss the history of that objection, argue that in Brouwer's writings predicativity of implication is ensured through parametric polymorphism of functions on species, and compare this construal with the alternative approaches to predicative implication of Goodman, Dummett, Prawitz, and Martin-L\"of.Comment: Added further references (Pistone, Poincar\'e, Tabatabai, Van Atten

The Logic of Principia Mathematica

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1995.Includes bibliographical references (p. 181-184).by Darryl Jung.Ph.D

The typing approach to Church-Fitch’s knowability paradox and its revenge form

Williamson, Linsky, Paseau and others proposed a solution to Church- Fitch’s knowability paradox that is based on typing knowledge; however, it received some criticism. Carrara and Fassio objected that the approach has no paradox-independent motivation, it is thus ad hoc. In the first part of the paper, I dismiss such criticism by carefully stating typing approach principles that are based on non-circular formation of propositions and intensional operators operating on them. In the second part of the paper, I demonstrate that the firm foundation of the approach prevents the variants of the paradox by Florio, Murzi and Jago that were developed as allegedly unresolvable by typing knowledge. The revenge form of Church-Fitch’s knowability paradox, which had been proposed by Williamson, Hart, Carrara and Fassio, fares badly as well, since it is likewise based on violation of reasonable typing rules

Impredicativity and turn of the century foundations of mathematics : presupposition in Poincare and Russell

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1993.Includes bibliographical references (leaves 145-158).by Joseph Romeo William Michael PicardPh.D