T-schema

Abstract: T-biconditionals have often been regarded as insufficient as axioms for truth. This verdict is based on Tarski’s (1935) observation that the typed T-sentences suffer from deductive weakness. As indicated by McGee (1992), the situation might change radically if we consider type-free disquotational theories of truth. However, finding a well-motivated set of untyped T-biconditionals that is consistent and recursively enumerable has proven to be very difficult. Moreover, some authors (e.g. Glanzberg (2005)) have argued that any solution to the semantic paradoxes necessarily involves ‘inflationary’ means, thus spelling doom to deflationist and minimalist truth theories in particular. The situation is indeed worrisome as formal theories of minimalist truth are (almost) missing so far. This makes it very hard to properly evaluate the tenets of minimalism. In the present article, we will show how to find safe instances of the T-schema just by relying on syntactic features of the sentences of our language—in particular, we will explore Quine’s (1937) idea of stratification. Based on that, we will introduce some disquotational truth theories that are deductively very strong.

Abstract: Bolzano's Theory of Science presents the first explicit and methodical espousal of internal logical realism It also contains a formidable number of theoretical innovations They include: the first account of the distinction between sense and reference; definitions of analyticity and consequence, ie deducibility based on a new substitutional procedure that anticipates Quine's and Tarski's, respectively; and an account of mathematical knowledge that excludes, contra Kant In Bolzano's case, one of the main purposes in introducing propositions in themselves is to achieve precise and satisfactory definitions By way of consequence, on Bolzano's own account the success of the endeavour depends on whether his commitment to propositions allows him to deliver a good theory of logic, or at least one that is preferable to its rivals Bolzano did have views on epistemic modality, though unfortunately, there is no place for a discussion of the latter here

Abstract: We discuss two desirable properties of deflationary truth theories: conservativeness and maximality. Joining them together, we obtain a notion of a maximal conservative truth theory – a theory which is conservative over its base, but can’t be enlarged any further without losing its conservative character. There are indeed such theories; we show however that none of them is axiomatizable, and moreover, that there will be in fact continuum many theories of this sort. It turns out in effect that the deflationist still needs some additional principles, which would permit him to construct his preferred theory of truth.