Advancements in formal logic in the 21st century?

Question

I've recently learned a lot about the history of formal logic, from Frege and Pierce in the late 19th century, to Russell, Hilbert, and Quine (et al)'s development of 1st-order logic, to advances with modal/non-classical logics (by Kripke, Hintikka, and Boolos), in the 70s, 80s, and 90s.

However, it seems that the last 20 to 30 years have been the quietest chapter yet. As far as I know, there have been no major kinds of logic thought up recently, no new figures rising to prominence, and no new innovations towards solving existing issues and controversies that continue to plague various modal logics.

Is formal logic a static discipline today, or am I missing something significant?

Answer 1

Paraconsistent logic has progressed fairly well. A couple of articles in which this logic is applied:

1. Zach Weber, "Transfinite Cardinals in Paraconsistent Set Theory." Goes over a classically themed set theory with a paraconsistent background logic. Includes funny objects like ℵ_On, the cardinality of the set of all ordinal numbers in Weber's theory. Because for better or worse, he's got universal sets, since contradictions arising from them are not so objectionable (or, he does not object so much to those contradictions...), or he has unusual inferential resources for evading some of the contradictions besides.

2. Agudelo and Carnielli, "Quantum Computation Via Paraconsistent Computation." References to dialethic Turing machines.

See also J. Béziau's report on how he became engaged with the question of paraconsistent logic. Béziau is linked to Alessio Moretti, whose "geometrical logic" (not a logic for geometry, but an analysis of geometrical structures that graph-theoretically express parts of logic) has intersected developments in deontic logic.

Depending on how one interprets computer science, that could be a domain that has featured many salient examples of what you're asking for (except the thing about "famous" essayists, maybe). There are then the intersections with AI research to consider. I can't think of any recent specific papers or reports from those quarters, though; I mean, I'm not well-versed in that field. I've also heard about categorical logic and how category theory involves new ways of trying to describe, and argue about, the nature of logic; not sure how recent that all is, though.

Overall, I don't know that the historical conditions, including cultural ones, that lead to "prominent-figure" accounts in an overview of logic's development as an academic subdiscipline, have been quite so in place for a while now. I mean that hero-worship/main-character-syndrome/valiant-entrepreneur motifs in various societies have decreased in popularity, so maybe there's no modern Frege or Russell or whoever, so to say; or maybe those past examples actually weren't directly established as "legends" in their own time, but were faced with detractors, paradoxes in their systems, and so on enough to where they and others doubted them more at those times. More, that is, than many people have been given to doubt the "authority" of those past essayists; the whole theme of a "written canon" has burned to ashes in the air, in a lot of places.