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Newton da Costa and why paraconsistency has a Brazilian accent

Ana Clara Ferreira Fellow
· 5 replies · 246 views
Modal & non-classical logicAnalyticLatin AmericanNewton da Costa#brazilian-logic#history-of-logic#paraconsistent-logic
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Newton da Costa died in 2024, and I've wanted to write something about him for the forum since. For anyone outside Brazil: he built the first systematic paraconsistent logics, logics in which a theory can contain a contradiction without every statement becoming provable. His early work was done in Curitiba in the late 1950s and 1960s, which is not where most people imagine a new branch of logic starting.

The core idea of his C-systems is clever. Classical negation behaves normally for formulas that are "well behaved", meaning not involved in contradiction. For the badly behaved ones, the logic simply stops some classical inferences, so the contradiction stays local. He built a whole hierarchy of these systems, each slightly weaker than the last.

Two things I always tell my undergraduates:

  • Paraconsistency is not dialetheism. Da Costa did not claim that contradictions are true. He claimed that inconsistent theories can be worth reasoning with: naive set theory, for example, or a body of data with conflicting entries. That's a much more modest claim than Priest's, and many people conflate them.
  • It wasn't only Brazil. Stanisław Jaśkowski in Poland had a "discussive" logic in 1948, and the field grew across Latin America, Australia and Europe.

But it's still true that, when I say I work on logic in São Paulo, logicians abroad say "ah, paraconsistency". I'd like to hear whether others think that national accent is real, or a story we tell ourselves.

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5 replies

  1. Mateo Quispe

    Fellow

    A Peruvian claim on the accent: the word "paraconsistent" itself is usually credited to Francisco Miró Quesada, the Peruvian philosopher, who suggested it to da Costa in the 1970s. So the name is ours even if the logic is yours. I grew up hearing Miró Quesada's name in Lima, but never in connection with logic until much later.

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  2. Tomasz Wójcik

    Fellow

    From the Polish side, a toast to Jaśkowski, who came out of the Lwów–Warsaw world. His discussive logic models a debate where several participants each assert things, and the "theory" is everything anyone has said. That collection can be inconsistent without any one participant being incoherent. It's a beautiful motivation, and very different from da Costa's, which was more about mathematics.

  3. Derek Hollis

    Fellow

    The engineering uses are underrated. Any system that merges data from several sources ends up with conflicting entries. Classical logic says that database now proves everything. Nobody's query engine actually does that, of course, which means in practice we're all running ad hoc paraconsistent reasoning. It would be better to run a principled version.

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  4. Valentina Ríos

    Fellow

    There's a Latin American philosophy angle too. In the late 1960s Salazar Bondy and Zea argued over whether there is an authentic Latin American philosophy at all, or only imitation of Europe. Logic usually gets left out of that debate. But da Costa's work is an obvious counterexample to the "only imitation" view: a genuinely new branch of a central discipline, built here.

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  5. Ana Clara Ferreira

    Fellow

    Valentina, I'd never connected those two debates and I think you're right that logic is the forgotten counterexample. Mateo, I'll correct my slides: the name is Peruvian. Maybe the accent is Latin American rather than Brazilian.

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