Durant le premier semestre de l'année 2010-2011, Per Martin-Löf organise deux fois par mois à l'IHPST le séminaire "Logic, epistemological or ontological" (Séminaire public)
What is logic ? Is it the study of the process of inference or reasoning, called demonstration in mathematics, by means of which we justify our judgements? Or is it the study of the logical and set-theoretical concepts, like proposition, truth and consequence on the one hand, and set, element and function on the other, that make their appearance in the contents of our judgements? This is the fundamental question whether logic is in essence, or by nature, epistemological or ontological. The answer is presumably that it is both, which is to say that, within logic, one can distinguish between two parts, or two layers, the one epistemological and the other ontological. But there remains the question of the order of priority between these two layers: Which comes first Is epistemology prior to ontology, or is it the other way round? Bolzano, whose logic in four volumes, called Wissenschaftslehre, has the most clear architectonic structure of all logics that have so far been written, treated of the ontological notions of proposition, truth and logical consequence (Ableitbarkeit) in the first two volumes of his Wissenschaftslehre, relegating the epistemology to the third volume. Thus he let ontology take priority over epistemology. Although the line of demarcation between the two was drawn in exactly the right place by Bolzano, my own work on constructive type theory has forced me to the conclusion that the order of priority between ontology and epistemology is nevertheless the reverse of the order in which they are treated in the Wissenschaftslehre. The epistemological notions of judgement and inference have to be in place already when you begin to deal with propositions, truth and consequence, as well as with other purely ontological notions, like the set-theoretical ones.
À noter : à l'Automne 2011, Per Martin-Löf donnera une seconde série de conférences au département d'informatique de l'Ecole Normale Supérieure sur le thème: Informal semantics of constructive type theory.