Lakatos’s Methodology and its Application to Logic Research Programs: A Comparative Study
DOI:
https://doi.org/10.12775/LLP.2026.008Keywords
philosophy of logic, research programs, Imre Lakatos, logical disputesAbstract
Lakatos’s (1978) methodology of research programs is renowned for describing the evolution of scientific theories through a combination of heuristic mechanisms that guide their development. Various attempts to apply Lakatos’s framework to research programs in logic and mathematics are found in (Priest, 1989; Aberdein and Read, 2009; Hallett, 1979a). The paper draws on Lakatosian assessments of progressive and degenerating mathematical theories found in (Hallett, 1979a) to advance a heuristic proposal for studying the progress and development of logical theories. The upshot is a characterization of Lakatos’s framework as applied to logical theories, along with a defense of a holistic approach that acknowledges the iterative relationship between empirical input and logical refinement during the process of development of progressive logical theories.
References
Aberdein, A. and S. Read. (2009). The philosophy of alternative logics. In L. Haaparanta (ed.), The Development of Modern Logic. Oxford Scholarship Online, chapter 14, pages 613–723. Oxford University Press. DOI: CrossRef
Arenhart, J. R. and S. Molick. (2025). Anti-exceptionalism about logic and the a priori/a posteriori divide. Revista Perspectiva Filosófica, 52: 22–52. DOI: CrossRef
Backhouse, R. E. (2006). Explorations in Economic Methodology: From Lakatos to Empirical Philosophy of Science. Routledge. DOI: CrossRef
Bell, J. L. and H. Korté. (2025). Hermann Weyl. In E. N. Zalta, and U. Nodelman (eds.), The Stanford Encyclopedia of Philosophy. Stanford University, Fall 2025 edition. Link
Blackburn, P., M. De Rijke, and Y. Venema, (2001). Modal logic, volume 53. Cambridge University Press. DOI: CrossRef
Brouwer, L. E. J. (1907). On the foundations of mathematics. Collected works, 1: 11–101. DOI: CrossRef
Brouwer, L. E. J. (1952). Historical background, principles and methods of intuitionism. South African Journal of Science, 49(3–4): 139.
Chalmers, A. (2013). What is this thing called science? Hackett Publishing.
da Costa, N. C., D. Krause, and O. Bueno. (2007). Paraconsistent logics and paraconsistency. In Philosophy of Logic, pages 791–911. Elsevier. DOI: CrossRef
Gomes, E. L., and I. M. L. D’Ottaviano, (2017). Para além das Colunas de Hércules, uma história da paraconsistência: de Heráclito a Newton da Costa. Editora da Unicamp.
Haack, S. (1978). Philosophy of Logics. Cambridge University Press. DOI: CrossRef
Hallett, M. (1979a). Towards a theory of mathematical research programmes (i). The British Journal for the Philosophy of Science, 30(1): 1–25. DOI: CrossRef
Hallett, M. (1979b). Towards a theory of mathematical research programmes (ii). The British Journal for the Philosophy of Science, 30(2): 135–159. DOI: CrossRef
Hettema, H. (1995). Bohr’s theory of the atom 1913–1923: A case study in the progress of scientific research programmes. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 26(3): 307–323. DOI: CrossRef
Heyting, A. (1966). Intuitionism: an introduction, volume 41. Elsevier. DOI: CrossRef
Hilbert, D. (1926). On the infinite. Mathematische Annalen, 95: 161–190. DOI: CrossRef
Hjortland, O. T. (2017). Anti-exceptionalism about logic. Philosophical Studies, 174: 631–658. DOI: CrossRef
Kalmár, L. (1967). Foundations of mathematics—whither now? In Studies in Logic and the Foundations of Mathematics, volume 47, pages 187–207. Elsevier.
Kalmár, L. (2011). The Development of Mathematical Rigor from Intuition to Axiomatic Method. Springer. DOI: CrossRef
Kuhn, T. S. (1962). The structure of scientific revolutions. The University of Chicago Press, 2: 90.
Lakatos, I. (1964). Proofs and refutations. The British Journal for the Philosophy of Science, 14(56): 296–342. DOI: CrossRef
Lakatos, I. (1970). History of science and its rational reconstructions. In PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, volume 1970, pages 91–136. Cambridge University Press. DOI: CrossRef
Lakatos, I. (1976). A renaissance of empiricism in the recent philosophy of mathematics. The British Journal for the Philosophy of Science, 27(3): 201–223. DOI: CrossRef
Lakatos, I. (1978). The Methodology of Scientific Research Programmes: Ed by John Worrall and Regory Currie. Cambridge University Press. DOI: CrossRef
Lakatos, I. (2014). Falsification and the methodology of scientific research programmes. In Philosophy, Science, and History, pages 89–94. Routledge.
Laudan, L. (1977). Progress and its Problems: Towards a Theory of Scientific Growth, volume 282. University of California Press.
Martin, B. (2023). The philosophy of logical practice. Examining Philosophy Itself, pages 151–174. DOI: CrossRef
Oliveri, G. (2006). Mathematics as a quasi-empirical science. Foundations of Science, 11: 41–79. DOI: CrossRef
Popper, K. (2005). The Logic of Scientific Discovery. Routledge.
Priest, G. (1989). Classical logic aufgehoben. Paraconsistent Logic: Essays on the Inconsistent. Munich: Philosophia Verlag, pages 131–150. DOI: CrossRef
Priest, G. (2007). Paraconsistency and dialetheism. In Handbook of the History of Logic, volume 8, pages 129–204. Elsevier. DOI: CrossRef
Priest, G., K. Tanaka, and Z. Weber. (2022). Paraconsistent Logic. In E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. Stanford University, Spring 2022 edition. Link
Sundholm, G. (1983). Constructions, proofs and the meaning of logical constants. Journal of Philosophical Logic, 12: 151–172. DOI: CrossRef
Tahko, T. E. (2017). Empirically-informed modal rationalism. In F. Bob, and F. Leon (eds.), Modal Epistemology after Rationalism, Studies in Epistemology, Logic, Methodology, and Philosophy of Science, chapter 3, pages 29–45. Springer. DOI: CrossRef
Troelstra, A. S. (1990). On the early history of intuitionistic logic. In Mathematical Logic, pages 3–17. Springer. DOI: CrossRef
Troelstra, A. S., and D. van Dalen. (2014). Constructivism in Mathematics, Vol. 2. Elsevier.
van Atten, M. (2023). The Development of Intuitionistic Logic. In E. N. Zalta and U. Nodelman (eds.), The Stanford Encyclopedia of Philosophy. Stanford University, Fall 2023 edition. Link
van Benthem, J. (2010). Modal Logic for Open Minds. No. 199 of series CSLI Lecture Notes Number 199. Stanford.
von Neumann, J. (1984). The mathematician. Heywood [Hey47].
Williamson, T. (2018). Alternative logics and applied mathematics. Philosophical Issues, 28(1): 399–424. DOI: CrossRef
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Sanderson Molick
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
Stats
Number of views and downloads: 183
Number of citations: 0
