In the chapter “Information and Content” of their Impossible Worlds, Berto and Jago provide us with a semantic account of information in deductive reasoning such that we have an explanation for why some, but not all, logical deductions are informative. The framework Berto and Jago choose to make sense of the above-mentioned idea is a semantic interpretation of Sequent Calculus rules of inference for classical logic. I shall argue that although Berto and Jago’s idea and framework are hopeful, their definitions (...) do not capture what is intended. This is so because the definitions are solely based on the logical complexity of an argument and they fail to capture the richness of the non- logical content of that argument. Then I will suggest some amendments to address this problem. Finally, I will extend the application of the definitions to first-order logic. It shall be observed that in some classical deductions, applying contraction may lead to hiding some epistemic impossibilities. This happens when formulae which contribute different propositions to the proof get contracted at the quantified level. (shrink)

This is a contribution to the idea that some proofs in first-order logic are synthetic. Syntheticity is understood here in its classical geometrical sense. Starting from Jaakko Hintikka’s original idea and Allen Hazen’s insights, this paper develops a method to define the ‘graphical form’ of formulae in monadic and dyadic fraction of first-order logic. Then a synthetic inferential step in Natural Deduction is defined. A proof is defined as synthetic if it includes at least one synthetic inferential step. Finally, it (...) will be shown that the proposed definition is not sensitive to different ways of driving the same conclusion from the same assumptions. (shrink)

This thesis is about how deduction is analytic and, at the same time, informative. In the first two chapters I am after the question of the justification of deduction. This justification is circular in the sense that to explain how deduction works we use some basic deductive rules. However, this circularity is not trivial as not every rule can be justified circularly. Moreover, deductive rules may not need suasive justification because they are not ampliative. Deduction preserves meaning, that is, the (...) meaning of non-logical vocabulary of any theory which is developed by deductive reasoning remains unchanged. It means that deduction adds no information to what we already had in our premises. This is why deduction is analytic. -/- However, there are many ways deduction can be informative. In the next three chapters, I will pick a specific kind of deductive reasoning, namely arithmetical reasoning, and will attempt to understand the nature of information we obtain by this kind of reasoning. There is a difference between simple deductive moves such as inferring `Socrates is mortal' from `All human are mortal' and `Socrates is human', and inferring that a relation is reflexive given that it is directed, symmetric and transitive. The latter is more complicated and not as easy to prove as the former. Therefore it is informative and the proof we construct to prove it puts us in an epistemic position that we were not in before having the proof. To be more specific, I show that concepts we need to confirm the conclusion are made in the process of proving the conclusion. (shrink)