An Analysis of Necessity and Possibility in Formal Logic from a Constructivist Perspective

Context • Formal logic is a field that has largely resisted constructivist explanations. Only a few people have studied it empirically/socially. Formal logic has even been presented as a realist case against constructivism. >Problem • My claim is that formal logic, like other non-formal knowledge, lends itself to constructivist explanations. I will show how para-logical factors, and then controversies over the ontological presuppositions, are embedded in concepts and claims about logical necessity and possibility. Method • I apply a primary constructivist argument to formal logic. To do so, I list a number of contingent factors that constructivists typically use to analyze and explain phenomena that realists describe as “true,” “objective,” “rigid,” “necessary,” or “universal.” I will then show that these factors are similarly embedded in logical necessity and possibility. Results • The appeal of logical realists to “the nature of things,” necessary inferences, and necessary logical truths is unsatisfactory, because not only are there diverse logical systems each of which constructs worlds in a particular way, but necessary inferences and necessary logical truths are explainable constructively. Implications • Based on the conclusions drawn in this article, constructivism cannot be disproven by formal logic. Rather, the constructivist perspective paves the way to a more fruitful approach toward philosophical logic and more cooperation between constructivist literature and avant-garde currents in philosophical logic. >Constructivist content • This article revolves around the core constructive argument that can be derived from constructivist literature. After reviewing several strands of constructivism, I point out a number of contingent factors that constructivists use to justify the constructability of forms of knowledge. Then I show that logical necessity and possibility can or should be explained based on these factors. This line of reasoning is simple enough that the results of this article will be compatible with, and derivable from, many branches of constructivism.