Skip to main content Skip to main navigation menu Skip to site footer
  • Register
  • Login
  • Language
    • English
    • Język Polski
  • Menu
  • Home
  • Current
  • Archives
  • Online First Articles
  • About
    • About the Journal
    • Submissions
    • Editorial Team
    • Advisory Board
    • Peer Review Process
    • Logic and Logical Philosophy Committee
    • Open Access Policy
    • Privacy Statement
    • Contact
  • Register
  • Login
  • Language:
  • English
  • Język Polski

Logic and Logical Philosophy

Can We Test Inconsistent Empirical Theories?
  • Home
  • /
  • Can We Test Inconsistent Empirical Theories?
  1. Home /
  2. Archives /
  3. Online First Articles /
  4. Articles

Can We Test Inconsistent Empirical Theories?

Authors

  • Luis Felipe Bartolo Alegre Facultad de Letras y Ciencias Humanas, Universidad Nacional Mayor de San Marcos (UNMSM) Lima, Peru; Munich Center for Mathematical Philosophy (MCMP) Ludwig-Maximilians-Universität München (LMU) Munich, Germany https://orcid.org/0000-0002-3312-6297

DOI:

https://doi.org/10.12775/LLP.2025.011

Keywords

paraconsistency, dialetheism, ; trivialism, proposal, rejection

Abstract

Despite the logical possibility and alleged existence of inconsistent empirical theories, the problem of their testability remains largely unexplored. I develop a testability criterion which makes some of these theories testable, including some observationally inconsistent ones. However, they are not rejectable qua inconsistent by this criterion. These results, while opening the domain of scientific theories to inconsistent ones, challenge the prospects of dialetheism in the philosophy of science.

References

Alves, E. H., ‘Paraconsistent logic and model theory’, Studia Logica 43 (1984): 17–32. DOI: https://doi.org/10.1007/10.1007/BF00935737

Arenhart, J. R. B., ‘The price of true contradictions about the world’, pafes 11–31 in [18]. DOI: https://doi.org/10.1007/978-3-319-98797-2_2

Bartelborth, T., ‘Kann es rational sein, eine inkonsistente Theorie zu akzeptieren?’, Philosophia Naturalis 26 (1989): 91–120.

Bartolo Alegre, L. F., ‘Über Poppers Forderung nach Widerspruchlosigkeit’, Felsefe Arkivi 51 (2019): 31–36. DOI: https://doi.org/10.26650/arcp2019-5103

Bartolo Alegre, L. F., ‘El falsacionismo revisado’, Analítica 11 (2021): 85–102.

Bartolo Alegre, L. F., ‘Peut-on tester si le mouvement est contradictoire?’, Revue de théologie et de philosophie (forthcoming).

Bartolo Alegre, L. F., and Cifuentes, J. C. (eds.), South American Journal of Logic 6, 2 (2020). The Heterodox in Logic and Reason: Special issue dedicated to F. Miró Quesada Cantuarias. https://www.sa-logic.org/sajl-62.html

Batens, D., ‘Meaning, acceptance and dialectics’, pages 333–360 in J. C. Pitt (ed.), Change and Progress in Modern Science, Dordrecht: D. Reidel, 1985. DOI: https://doi.org/10.1007/978-94-009-6525-6_12

Batens, D., ‘Pluralism in scientific problem solving: Why inconsistency is no big deal’, pages 149–177 in [49].

Bertossi, L., Hunter, A., Schaub, T. (eds.), Inconsistency-tolerance, Berlin: Springer, 2005. DOI: https://doi.org/10.1007/b104925

Bobenrieth Miserda, A., Inconsistencias, ¿Por qué no? Un Estudio Filosófico Sobre la Lógica Paraconsistente, Bogotá: Colcultura, 1996.

Bobenrieth Miserda, A., ‘Paraconsistency and the consistency or inconsistency of the world’, pages 493–512 in J.-Y. Béziau, W. A. Carnielli, and D. M. Gabbay (eds.), Handbook of Paraconsistency, London: College Publications, 2007.

Boccardi, E., and Macias-Bustos, M., ‘Contradictions in motion: Why they’re not needed and why they wouldn’t help’, pages 195–227 in [49].

Brown, B., ‘How to be realistic about inconsistency in science’, Studies in History and Philosophy of Science, Part A 21, 2 (1990): 281–294. DOI: https://doi.org/10.1016/0039-3681(90)90027-6

Brown, B., and Priest, G., ‘Chunk and permeate, a paraconsistent inference strategy. Part I: The infinitesimal calculus’, Journal of Philosophical Logic 33, 4 (1990): 379–388. DOI: https://doi.org/10.1023/B:LOGI.0000036831.48866.12

Bueno, O., ‘Empirical adequacy: A partial structures approach’, Studies in History and Philosophy of Science, Part A 28, 4 (1997): 585–610. DOI: https://doi.org/10.1016/S0039-3681(97)00012-5

Bueno, O., ‘Scientific pluralism, consistency preservation, and inconsistency toleration’, pages 229–245 in [49].

Carnielli, W., and Malinowski, J. (eds.), Contradictions, from Consistency to Inconsistency, Cham: Springer, 2018. DOI: https://doi.org/10.1007/978-3-319-98797-2

Churchland, P. M., ‘To transform the phenomena: Feyerabend, proliferation, and recurrent neural networks’, pages 148–158 in J. Preston, G. Munévar, and D. Lamb (eds.), The Worst Enemy if Science? Essays in Memory of Paul Feyerabend, Oxford: Oxford University Press, 2000. DOI: https://doi.org/10.1093/oso/9780195128741.003.0011

da Costa, N. C. A., ‘On the theory of inconsistent formal systems’, Notre Dame Journal of Formal Logic 15, 4 (1974): 497–510. https://projecteuclid.org/euclid.ndjfl/1093891487

da Costa, N. C. A., Sistemas formais inconsistentes, 2nd ed., Curitiba: UFPR, 1963/1993.

da Costa, N. C. A., Ensaio sobre os Fundamentos da Lógica, 2nd ed., São Paulo: Hucitec, 1980/1994.

da Costa, N. C. A., and French, S., ‘Inconsistency in science: A partial perspective’, pages 105–118 in [50]. DOI: https://doi.org/10.1007/978-94-017-0085-6_6

da Costa, N. C. A., and French, S., Science and Partial Truth: A Unitary Approach to Models and Scientific Reasoning, Oxford: Oxford University Press, 2003. DOI: https://doi.org/10.1093/019515651X.001.0001

Davey, K., ‘Can good science be logically inconsistent?’, Synthese 191 (2014): 3009–3026. DOI: https://doi.org/10.1007/s11229-014-0470-x

de Souza, E. G., ‘Multideductive logic and the theoretic-formal unification of physical theories’, Synthese 125, 1 (2000): 253–262. DOI: https://doi.org/10.1023/A: 1005254826656

D’Ottaviano, I. M. L., and Gomes, E. L., ‘Baptizing paraconsistent logics: The unique touch of Miró Quesada’,pages 249–269 in [7]. https://www.sa-logic.org/sajl-v6-i2/07-D’Ottaviano.pdf

Drago, A., ‘Classical, intuitionistic and paraconsistent logic in scientific theories’, CLE e-Prints 2, 7 (2002): 187–195. https://www.cle.unicamp.br/eprints/index.php/CLE_e-Prints/article/view/816

Elpidorou, A., ‘Seeing the impossible’, The Journal of Aesthetics and Art Criticism 191, 1 (2016): 11–21. DOI: https://doi.org/10.1111/jaac.12241

Estrada-González, L., ‘Prospects for triviality’, pages 81–89 in A. Holger and P. Verdée (eds.), Logical Studies of Paraconsistent Reasoning in Science and Mathematics, Cham: Springer, 2016. DOI: https://doi.org/10.1007/978-3-319-40220-8_5

Feyerabend, P. K., Against Method, London: Verso, 1993.

Friend, M., and Martínez-Ordaz, M. del R., ‘Keeping globally inconsistent scientific theories locally consistent’, pages 53–88 in [18]. DOI: https://doi.org/10.1007/978-3-319-98797-2_4

Frisch, M., ‘Inconsistency in classical electrodynamics’, Philosophy of Science 71, 4 (2004): 525–549. DOI: https://doi.org/10.1086/423627

Gotesky, R., ‘The uses of inconsistency’, Philosophy and Phenomenological Research 28, 4 (1968): 471–500. DOI: https://doi.org/10.2307/2105687

Hempel, C. G., ‘The irrelevance of the concept of truth for the critical appraisal of scientific theories’, pages 75–84 in Selected Philosophical Essays (ed. by R. Jeffrey), Cambridge: Cambridge University Press, 2000. DOI: https://doi.org/10.1017/CBO9780511815157.009

Hjortland, O. T., ‘Anti-exceptionalism about logic’, Philosophical Studies 174, 3 (2017): 631–658. DOI: https://doi.org/10.1007/s11098-016-0701-8

Jaśkowski, S., ‘A propositional calculus for inconsistent deductive systems’, Logic and Logical Philosophy 7 (1999): 35–56. English translation of a paper in Polish published in 1948. DOI: https://doi.org/10.12775/LLP.1999.003

Kabay, P. D., A Defense of Trivialism, PhD thesis, Melbourne, Australia: University of Melbourne, 2008. http://hdl.handle.net/11343/35203

Krause, D., and Arenhart, J. R. B., The Logical Foundations of Scientific Theories: Languages, Structures, and Models, New York: Routledge, 2017.

Kuhn, T. S., The Structure of Scientific Revolutions, 3rd ed., Chicago: University of Chicago Press, 1996.

L’Huilier, S. A. J., Exposition élémentaire des principes des calculs supérieurs, Berlin: Decker, 1786.

Lakatos, I., Philosophical Papers, Vol. 1: The Methodology of Scientific Research Programmes (ed. by J. Worrall and G. Currie), Cambridge, UK: Cambridge University Press, 1978. DOI: https://doi.org/10.1017/CBO9780511621123

Leitgeb, H., ‘Logic and philosophy: A reconstruction’, in F. Ferrari, E. Brendel, M. Carrara, O. Hjortland, G. Sagi, G. Sher, and F. Steinberger (eds.), Oxford Handbook of Philosophy of Logic, Oxford: Oxford University Press, forthcoming.

Lipton, P., ‘Accepting contradictions’, pages 117–133 in Br. Monton (ed.), Images of Empiricism. Essays on Science and Stances, Oxford: Oxford University Press, 2007. DOI: https://doi.org/10.1093/acprof:oso/9780199218844.003.0007

Łukasiewicz, J. L., ‘Über den Satz des Widerspruchs bei Aristoteles’, Bulletin International de l’Acadèmie des Sciences de Cracovie 1 (1910): 15–38.

Mares, E., ‘Semantic dialetheism’, pages 264–275 in G. Priest, Jc Beall, and B. Armour-Garb (eds.), The Law of Non-Contradiction: New Philosophical Essays, Oxford: Oxford University Press, 2004.

Martínez-Ordaz, M. del R., ‘Holism, inconsistency toleration and inconsistencies between theory and observation’, pages 117–147 in [49].

Martínez-Ordaz, M. del R., ‘The ignorance behind inconsistency toleration’, Synthese 198, 9 (2021): 8665–8686. DOI: https://doi.org/10.1007/s11229-020-02593-4

Martínez-Ordaz, M. del R., and Estrada-González, L. (eds.), Humana.Mente. Journal of Philosophical Studies 10, 32 (2017). Special issue Beyond Toleration? Inconsistency and Pluralism in the Empirical Sciences. https://www.humanamente.eu/index.php/HM/issue/view/22

Meheus, J. (ed.), Inconsistency in Science, Origins 2, Dordrecht: Springer, 2002. DOI: https://doi.org/10.1007/978-94-017-0085-6

Meheus, J., ‘How to reason sensibly yet naturally from inconsistencies’, pages 151–164 in [50]. DOI: https://doi.org/10.1007/978-94-017-0085-6_9

Miller, D., ‘Errando al blanco. La historia desdichada de las críticas al falsacionismo’, pages 89–124 in R. López Orellana, C. Verdugo Serna, and B. Bevensee Beltrami (eds.), El legado de Karl Popper (1902–1994): Reflexiones a 20 años de su muerte, Valparaíso: UV, 2015.

Miró Quesada Cantuarias, F., ‘In the name of paraconsistency’, pages 163–171 in [7]. Annotated English translation by L. F. Bartolo Alegre of a letter originally written in Spanish, dated 29 September 1975. https://www.sa-logic.org/sajl-v6-i2/01-MiroQuesada.pdf

Mosterín, J., Epistemología y racionalidad, Lima: UIGV, 1999.

Mosterín, J., ‘The role of consistency in empirical science’, Manuscrito 34, 1 (2021): 293–305. DOI: https://doi.org/10.1590/S0100-60452011000100013

Neurath, O., ‘Pseudorationalismus der Falsifikation’, Erkenntnis 5, 1 (1935): 353–365. DOI: https://doi.org/10.1007/BF00172326

Newton, I., ‘Four letters from Sir Isaac Newton to Doctor Bentley: Containing some arguments in proof of a deity’, pages 201–215 in The Works of Richard Bentley: Vol. III (ed. by A. Dyce), London: MacPherson, 1838.

Nickles, T., ‘From Copernicus to Ptolemy: Inconsistency and method’, pages 1–33 in [50]. DOI: https://doi.org/10.1007/978-94-017-0085-6_1

Norton, J. D., ‘The logical inconsistency of the old quantum theory of black body radiation’, Philosophy of Science 54, 3 (1983): 327–350. DOI: https://doi.org/10.1086/289387

Norton, J. D., ‘A paradox in Newtonian gravitation theory II’, pages 185–195 in [50]. DOI: https://doi.org/10.1007/978-94-017-0085-6_11

Parmenides, The Fragments of Parmenides: A Critical Text with Introduction and Translation, the Ancient Testimonia and a Commentary (ed. by A. H. Coxon), Las Vegas: Parmenides Publishings, 2009.

Perzanowski, J., ‘Parainconsistency, or inconsistency tamed, investigated and exploited’, Logic and Logical Philosophy 9 (2001): 5–24. DOI: https://doi.org/10.12775/LLP.2001.001

Piscoya, L. A., Investigación científica y educacional. Un enfoque epistemológico, 2nd ed., Lima: Amaru, 1995.

Popper, K. R., ‘Ein Kriterium des empirischen Charakters theoretischer Systeme’, Erkenntnis 3 (1943): 426–427. DOI: https://doi.org/10.2307/20011690

Popper, K. R., Logik der Forschung. Zur Erkenntnistheorie der modernen Naturwissenschaft, Wien: Springer, 1935. Actually published in 1934.

Popper, K. R., Objective Knowledge: A Realist View of Logic, Physics, and History, Oxford: Oxford University Press, 1972.

Popper, K. R., ‘Falsifizierbarkeit, zwei Bedeutungen von’, pages 82–85 in H. Seiffert and G. Radnitzky (eds.), Handlexikon zur Wissenschaftstheorie, München: Ehrenwirth, 1989.

Popper, K. R., The Logic of Scientific Discovery, Oxford: Oxford University Press, 2002.

Priest, G., ‘Perceiving contradictions’, Australasian Journal of Philosophy 77, 4 (1999): 439–446. DOI: https://doi.org/10.1080/00048409912349211

Priest, G., ‘Inconsistency and the empirical sciences’, pages 119–128 in [50]. DOI: https://doi.org/10.1007/978-94-017-0085-6_7

Priest, G., In Contradiction: A Study of the Transconsistent, 2nd ed., Oxford: Clarendon, 1987/2006. DOI: https://doi.org/acprof:oso/9780199263301.001.0001

Priest, G., Doubt Truth to be a Liar, Oxford: Clarendon, 2006. DOI: https://doi.org/10.1093/0199263280.001.0001

Quine, W. V. O., Methods of Logic, Revised Edition, New York: Holt, Rinehart and Winston, 1950/1959.

Reichenbach, H., ‘Bemerkung zu “Ein Kriterium des empirischen Charakters theoretischer Systeme”’, Erkenntnis 3 (1932): 427. DOI: https://doi.org/10.1007/BF01886435

Sandgren, A., and Tanaka, K., ‘Two kinds of logical impossibility’, Noûs 54 (2020): 795–806. DOI: https://doi.org/10.1111/nous.12281

Šešelja, D., ‘Scientific pluralism and inconsistency toleration’, pages 1–29 [49].

Smith, J. M., ‘Inconsistency and scientific reasoning’, Studies in History and Philosophy of Science: Part A 19, 4 (1988): 429–445. DOI: https://doi.org/10.1016/0039-3681(88)90010-6

Smith, J. M., ‘Scientific reasoning or damage control: Alternative proposals for reasoning with inconsistent representations of the world’, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1 (1988): 241–248. DOI: https://doi.org/10.1086/psaprocbienmeetp.1988.1.192991

Tennant, N., ‘Minimal logic is adequate for Popperian science’, British Journal for the Philosophy of Science 36, 3 (1985): 325–329. DOI: https://doi.org/10.1093/bjps/36.3.325

Vasil’ev, N., ‘Imaginary (non-Aristotelian) logic’, Logique & Analyse 182 (2003): 127–163. English translation by R. Vergauwen and K. Mercierplein of a paper in Russian published in 1912. https://logiqueetanalyse.be/archive/issues87-220/LA182/vasilev.pdf

Vickers, P., Understanding Inconsistent Science, Oxford: Oxford University Press, 2013. DOI: https://doi.org/10.1093/acprof:oso/9780199692026.001.0001

Weber, E., and De Clerq, K., ‘Why the logic of explanation is inconsistency-adaptive’, pages 165–184 in [50]. DOI: https://doi.org/10.1007/978-94-017-0085-6_10

Downloads

  • PDF

Published

2025-05-25

How to Cite

1.
BARTOLO ALEGRE, Luis Felipe. Can We Test Inconsistent Empirical Theories?. Logic and Logical Philosophy. Online. 25 May 2025. pp. 1-45. [Accessed 8 July 2025]. DOI 10.12775/LLP.2025.011.
  • ISO 690
  • ACM
  • ACS
  • APA
  • ABNT
  • Chicago
  • Harvard
  • IEEE
  • MLA
  • Turabian
  • Vancouver
Download Citation
  • Endnote/Zotero/Mendeley (RIS)
  • BibTeX

Issue

Online First Articles

Section

Articles

License

Copyright (c) 2025 Luis Felipe Bartolo Alegre

Creative Commons License

This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

Stats

Number of views and downloads: 142
Number of citations: 0

Crossref
Scopus
Google Scholar
Europe PMC

Search

Search

Browse

  • Browse Author Index
  • Issue archive

User

User

Current Issue

  • Atom logo
  • RSS2 logo
  • RSS1 logo

Information

  • For Readers
  • For Authors
  • For Librarians

Newsletter

Subscribe Unsubscribe

Language

  • English
  • Język Polski

Tags

Search using one of provided tags:

paraconsistency, dialetheism, ; trivialism, proposal, rejection
Up

Akademicka Platforma Czasopism

Najlepsze czasopisma naukowe i akademickie w jednym miejscu

apcz.umk.pl

Partners

  • Akademia Ignatianum w Krakowie
  • Akademickie Towarzystwo Andragogiczne
  • Fundacja Copernicus na rzecz Rozwoju Badań Naukowych
  • Instytut Historii im. Tadeusza Manteuffla Polskiej Akademii Nauk
  • Instytut Kultur Śródziemnomorskich i Orientalnych PAN
  • Instytut Tomistyczny
  • Karmelitański Instytut Duchowości w Krakowie
  • Ministerstwo Kultury i Dziedzictwa Narodowego
  • Państwowa Akademia Nauk Stosowanych w Krośnie
  • Państwowa Akademia Nauk Stosowanych we Włocławku
  • Państwowa Wyższa Szkoła Zawodowa im. Stanisława Pigonia w Krośnie
  • Polska Fundacja Przemysłu Kosmicznego
  • Polskie Towarzystwo Ekonomiczne
  • Polskie Towarzystwo Ludoznawcze
  • Towarzystwo Miłośników Torunia
  • Towarzystwo Naukowe w Toruniu
  • Uniwersytet im. Adama Mickiewicza w Poznaniu
  • Uniwersytet Komisji Edukacji Narodowej w Krakowie
  • Uniwersytet Mikołaja Kopernika
  • Uniwersytet w Białymstoku
  • Uniwersytet Warszawski
  • Wojewódzka Biblioteka Publiczna - Książnica Kopernikańska
  • Wyższe Seminarium Duchowne w Pelplinie / Wydawnictwo Diecezjalne „Bernardinum" w Pelplinie

© 2021- Nicolaus Copernicus University Accessibility statement Shop