Informal Reasoning and Logical Formalization

According to a prominent view among philosophers, formal logic is the philosopher's main tool for evaluating the validity of arguments, i.e., the philosopher's Ars Iudicandi. In this presentation, I challenge the Ars Iudicandi conception by highlighting a fundamental justificatory circle in the process of logical formalization. Drawing on modern criteria for adequate formalization, I argue that the adequacy of a logical formalization presupposes a prior understanding of the truth conditions of the formalized statements. In the case of arguments, this clarity regarding truth conditions is functionally equivalent to a prior assessment of their informal validity. Consequently, every dispute about an argument's validity inevitably turns into a dispute about that argument's adequate formalization; and such disputes obviously are not resolvable by formal logic. I illustrate this impasse by means of the famous debate between Russell and Strawson on the validity of arguments featuring definite descriptions. No matter how vigorously Russell and Strawson try to resolve their disagreement by means of formal logic, they end up turning in circles, trading non-equivalent formalizations back and forth. Rather than settling the question whether the contentious arguments are valid or not, they merely contrast opposing informal validity assessments rendered explicit by non-equivalent logical formalizations.