Rodolfo Cunha Carnier

In this paper, we introduce the basics of what we shall call "partial model theory", which is an extension of traditional model theory to partial structures. These are a specific kind of structure developed within the partial structures approach, which is a view constituting the semantic approach of theories. And together with other related semantical concepts, like the concept of quasi-truth, partial structures have been used in contemporary philosophy of science for several purposes. Nonetheless, those uses presuppose certain technical results, or could be improved by resorting to certain technical notions and results, that have not been put forward so far. Thus, in the present work, we intend to introduce part of this particular technical apparatus that is still lacking especially in logic, throughout the development of partial model theory. We begin by extending traditional notions of model theory for partial structures, like the notions of substructure and homomorphism, and by proving some results concerning the notion of quasi-truth. Posteriorly, we show how the content introduced can be used to improve a particular application of partial structures and quasi-truth in the philosophy of science.

In the present paper, we return to one of the main theses we already defended concerning the role of the tarskian truth notion within the semantic approach (CARNIER, 2022). As it was argued, this truth notion proves to be insufficient to be applied to scientific theories as they are conceived by this approach, i.e., as extralinguistic entities, because it is a property of sentences and because the tarskian truth of a sentence doesn't necessarily mean the world is as it describes, which results in the fact that other truth conceptions more appropriate need to be articulated within the several members of the semanticist family, in order to characterize the relationship between theory and phenomenon. Our argument in this regard was based in a case study applied to constructive empiricism and quasi-realism, but in this paper we extend our analysis to structuralism, assuming and endorsing the position according to which this proposal may be considered a member of the semantic approach.

Mediante uma análise da utilização da noção de verdade tarskiana no contexto da abordagem semântica, argumentaremos que ela é desnecessária assim como insuficiente. Ela se mostra desnecessária porque no interior desta abordagem seu papel é meramente operacional, de tal modo que pode ser cumprido por noções de verdade alternativas também de teor operacional. Por outro lado, sua insuficiência se deve ao fato de que outras concepções de verdade de um tipo mais apropriado devem ser articuladas, para satisfazer os propósitos das diversas integrantes da família semanticista, como o empirismo construtivo e o quase-realismo. Tradicionalmente, estas concepções são definidas fazendo recurso à noção de verdade tarskiana, porém elas também podem ser definidas por meio de noções de verdade alternativas.