Nancy Hernandez

Accounting for the epistemic contribution of deduction has been a pervasive problem for logicians interested in deduction, such as, among others, Jakko Hintikka. The problem arises because the conclusion validly deduced from a set of premises is said to be “contained” in that set; because of this containment relation, the conclusion would be known from the moment the premises are known. Assuming this, it is problematic to explain how we can gain knowledge by deducing a logical consequence implied by a set of known premises. To address this problem, we offer an alternative account of the epistemic contribution of deduction as the process required to deduce a conclusion or a theorem, understanding such a process not only in terms of the number of steps in the derivation but also, more importantly, in terms of the reason for or justification for every step. That is, we do not know a proposition unless we have a justification or proof of that proposition. With this goal in mind, we develop a justification logic system which exhibits the epistemic contribution of a deductive derivation as the resulting justified formula.

In deduction the truth of the premises guarantees the truth of the conclusion because the conclusion is contained in the premises; because of that many philosophers have denied the possibility of gaining knowledge through deduction or through deductive reasoning, which leads to a problem known as the paradox of inference. To address this problem, I propose a distinction between deductive reasoning as a cognitive process capable of generating new knowledge, and implication as a logical relation between propositions, which accounts for deduction’s validity, and I present scientific evidence to underpin this proposal. En la deducción la verdad de las premisas garantiza la verdad de la conclusión porque la conclusión está contenida en las premisas; por ello varios filósofos han negado la posibilidad de obtener conocimientos a través de la deducción o del razonamiento deductivo, dando lugar a un problema que se conoce como paradoja de la inferencia. Pare enfrentar este problema propongo distinguir entre el razonamiento deductivo como proceso cognitivo capaz de generar conocimientos nuevos y la implicación deductiva como una relación lógica entre proposiciones que da cuenta de la validez de la deducción, y presento evidencia científica que apoya esta propuesta.