Late Medieval Views on Formal Consequence

The paper presents by means of examples various medieval classifications of consequences (consequentiae, or inferences) into formal and material or natural and accidental. Validity of a consequence was in the middle ages understood through the modal criterion that the antecedent cannot be true without the consequent. Medieval logicians employed two main intuitive ideas for separating a privileged class of valid consequences: (1) conceptual containment (the understanding of consequent is included in the understanding of the antecedent), and (2) logical form defined through the substitution principle (the consequence is valid for all terms). The concept “formal” (formalis, or de forma) became the standard term for the privileged class. Similarly “material” (materialis, or de materia) was adopted for the inferior class of non-formal inferences. The substitution principle carefully formulated and perhaps invented by John Buridan may seem particularly appealing to many modern logicians. In the fourteenth century it did not gain universal acceptance. When accepted, it was considered as secondary to the principle of conceptual containment, or in modern terms analytic validity.