Solving the paradoxes of naive validity and informal provability through non-deterministic and truth-maker semantics. (01P10618)
In this project I will study the notion of naive validity. Roughly speaking, an argument is naively valid if the truth of its premises implies or guarantees the truth of its intended conclusion, given what the sentences involved mean. The main problem with this notion is that, as soon as we employ formal methods in order to represent it in the object language, a paradox involving a selfreferential sentence arises. To solve the paradox I will look at naive validity as a generalization of the notion of informal provability. An informal proof is a commonly accepted mathematical justification of a mathematical claim. The ultimate goal of my research is to overcome the paradox by constructing a formal theory based on a philosophically interesting framework of informal provability.