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Newton Carneiro Affonso da Costa

Newton Carneiro Affonso da Costa, Brazilian mathematical logic and science philosopher (Curitiba 16 September 1929 –

From Portuguese, French, German and Danish descent

Authored over 250 works between notes, papers and books

Regarded as one of founders of paraconsistent logic

His thesis Sistemas formais inconsistentes (1963) was abridged in English as On the theory of inconsistent formal systems in Notre Dame Journal of Formal Logic (1974)

Introduced the notion of Curry algebra (1967)

Defined the concepts of pragmatic truth and pragmatic probability (1986)

Conceived the critical pragmatism

Created Cn, hierarchies of logical calculus (1963)

Introduced CHUn, a new hierarchy in set theory (1986)

Introduced hyper real numbers ring and extended hyper-real numbers quasi-ring (2000)

Introduced the concepts of paraconsistent superstructure and monomorphism between paraconsistent superstructures (2000)

Enunciated the principle of tolerance or non-triviality in mathematics “from syntactical semantic standpoint, every mathematical theory is admissible unless it is trivial”

With Rolando B. Chuaqui & Irene Mikenberg developed quasi-truth theory

With R. Chuaqui established the concept of Suppes predicate (1988)

With W.A. Carnielli showed that a less rigid logic can give a new response to called deontological paradoxes

With J. Corcoran codiscovered the truth-set principle and the classical logic of variable-binding term operators

With F.A. Doria showed that in the axiomatized version of dynamical systems theory chaotic properties of those system are undecidable and Gödel-incomplete

With F.A. Doria solved the Hirsch and quadrature problems in chaos theory and classic mechanics

With F.A. Doria showed that there is no algorithm for deciding from the equations of a dynamical system, whether the system is chaotic or not, or for deciding, from a given Hamiltonian, whether it can be integrated by quadratures (1991)

With F.A. Doria introduced the exotic formalization

With M.S. Berman proved that the universe is global and locally stable

Introduced a general theory of valuations 

With J. Kotas. A new formulation of discussive logic. Studia Logica 38:429-45, 1979

Une nouvelle hierarchie de theories inconsistants. Publ. Depart. Math. Univ. Lyon 4:2-8, 1967

Un nouveau systeme formel suggéré par Dedecker. Comptes Rendus de l’Acad. Sciences Ser 1 Math. 256:85-8, 1967

CO-DESCRIBED DIPTERA GENERA & SPECIES (with Artigas & Papavero 1997)







Da Costa Cn calculus  

Da Costa algebra

Da Costa C logic

Von Weiszacker-da Costa principle of semantic consistency