Strong and Weak Hypotheses

Daniele Chiffi; Ciro De Florio

doi:10.12775/LLP.2025.002

Authors

Daniele Chiffi DAStU, Politecnico di Milano, Milan https://orcid.org/0000-0002-5487-8244
Ciro De Florio Faculty of Economics, Università Cattolica del Sacro Cuore, Milan, Italy https://orcid.org/0000-0002-5503-7463

DOI:

https://doi.org/10.12775/LLP.2025.002

Keywords

hypothesis, evidence, denial, scientific reasoning, semantics, illocutionary acts

Abstract

I

In this paper, we investigate the nature of empirical hypotheses used in scientific reasoning and the act of formulating hypotheses. This is achieved through a novel logical framework in which we provide specific semantics for two types of hypotheses: a strong and a weak sense of hypothesis, each characterized by different logical structures. This framework enables us to better characterize certain aspects of hypothetical reasoning in scientific practice, especially when we attempt to rationally deny the content of an empirical hypothesis.

References

Adams, E. W., “Four probability-preserving properties of inferences”, Journal of Philosophical Logic, 25(1), 1996: 1–24. DOI: https://doi.org/10.1007/BF00357840

Bellin, G., M. Carrara, M., D. Chiffi and A. Menti, “Pragmatic and dialogic interpretations of bi-intuitionism. Part I”, Logic and Logical Philosophy, 23(4), (2014): 449–480. DOI: https://doi.org/10.12775/LLP.2014.011

Bellucci, F., and A.-V. Pietarinen, “Assertion and denial: A contribution from logical notation”, Journal of Applied Logic, 24, 2017: 1–22. DOI: https://doi.org/10.1016/j.jal.2017.01.001

Carnielli, W., and A. Rodrigues, “An epistemic approach to paraconsistency: A logic of evidence and truth”, Synthese, 196(9), 2019: 3789–3813. DOI: https://doi.org/10.1007/s11229-017-1621-7

Carrara, M., D. Chiffi and C. De Florio, “Assertions and hypotheses: A logical framework for their opposition relations”, Logic Journal of the IGPL, 25(2), 2017: 131–144. DOI: https://doi.org/10.1093/jigpal/jzw036

Carrara, M., D. Chiffi and C. De Florio, “Pragmatic logics for hypotheses and evidence”, Logic Journal of the IGPL, 29(4), 2021: 585–600. DOI: https://doi.org/10.1093/jigpal/jzz042

Carrara, M., D. Chiffi, C. De Florio and A.-V. Pietarinen, “We don’t know we don’t know: asserting ignorance”, Synthese, 198, 2021: 3565–3580. DOI: https://doi.org/10.1007/s11229-019-02300-y

Carrara, M., D. Chiffi and C. De Florio, “Towards a polarized semantics for assertion and denial”, Logic Journal of the IGPL, 2024. DOI: https://doi.org/10.1093/jigpal/jzae090

Chiffi, D., and F. Schang, “The logical burdens of proof. Assertion and hypothesis”, Logic and Logical Philosophy, 26(2), 2017: 509–530. DOI: https://doi.org/10.12775/LLP.2017.006

Dalla Pozza, C., “Un’interpretazione pragmatica della logica proposizionale intuizionistica”, in G. Usberti (ed.), Problemi fondazionali nella teoria del significato, Firenze: Leo S. Olschki, 1991.

Dalla Pozza, C., and C. Garola, “A pragmatic interpretation of intuitionistic propositional logic”, Erkenntnis, 43, 1995: 81–109. DOI: https://doi.org/10.1007/BF01131841

Douglas, H., “Inductive risk and values in science”, Philosophy of Science, 67(4), 2000: 559–579. DOI: https://doi.org/10.1086/392855

Hempel, C. G., “Science and human values”, pages 81–96 in C. G. Hempel (ed.), Aspects of Scientific Explanation and Other Essays in the Philosophy of Science, New York: The Free Press, 1965.

López-Astorga, M., M. Ragni and P. N. Johnson-Laird, “The probability of conditionals: A review”, Psychonomic Bulletin & Review, 29(1), 2022, 1–20. DOI: https://doi.org/10.3758/s13423-021-01938-5

Łukasiewicz, J., “Logika dwuwartosciowa” (Two-valued logic), Przegląd Filozoficzny, 23, 1921: 189–205. English version: pages in 89–109 Selected Works, edited by L. Borkowski, trans. by O. Wojtasiewicz, Amsterdam: North-Holland, 1970.

Magnani, L., Abductive Cognition. The Epistemological and Eco-cognitive Dimensions of Hypothetical Reasoning, Berlin: Springer-Verlag, 2009. DOI: https://doi.org/10.1007/978-3-642-03631-6

Peirce, C. S., Collected Papers of Charles S. Peirce, edited by P. Weiss and A. Burks, Cambridge, MA: Harvard University Press, 1931–1958. (References are to CP by volume and paragraph number.)

Rescher, N., “A theory of evidence”, Philosophy of Science, 25(1), 1958: 83–94. DOI: https://doi.org/10.1086/287579

Rescher, N., “Peirce and the economy of research”, Philosophy of Science, 43(1), 1976: 71–98. DOI: https://doi.org/10.1086/288670

Shramko, Y., “Dual intuitionistic logic and a variety of negations: The logic of scientific research”, Studia Logica, 80, 2005: 347–367. DOI: https://doi.org/10.1007/s11225-005-8474-7

Wei, Z., A. Yang, L. Rocha, L., M. F. Miranda and F. S. Nathoo, “A review of Bayesian hypothesis testing and its practical implementations”, Entropy, 24(2), 2022: 161. DOI: https://doi.org/10.3390/e24020161

Woods, J., “Cognitive economics and the logic of abduction”, The Review of Symbolic Logic, 5(1), 2012: 148–161. DOI: https://doi.org/10.1017/S175502031100027X

Yalcin, S., “Probability operators”, Philosophy Compass, 5(11), 2010: 916–937. DOI: https://doi.org/10.1111/j.1747-9991.2010.00360.x