Abstract
It has been common in contemporary logic and philosophy of logic to identify the validity of an inference with its conclusion being a (logical) consequence of its premisses.
Chapter PDF
Similar content being viewed by others
References
Boghossian, P. (2014). What is inference? Philosophical Studies 169 (1), 1–18.
Cozzo, C. (2021). Fallibility and fruitfulness of deductions. Erkenntnis. doi: https://doi.org/10.1007/s10670-021-00487-6.
Dummett, M. (1975). The philosophical basis of intuitionistic logic. In: Logic Colloquium ’73. Ed. by H. E. Rose et al. Amsterdam: North Holland, 5–40.
Dummett, M. (1991). The Logical Basis of Metaphysics. London: Duckworth.
Gentzen, G. (1935). Untersuchungen über das logische Schließen, I. Mathematische Zeitschrift 39 (1), 176–210.
Heyting, A. (1934). Mathematische Grundlagenforschung, Intuitionismus, Beweistheorie. Berlin: Springer.
Heyting, A. (1958). Intuitionism in mathematics. In: Philosophy in the Mid-Century. Ed. By R. Klibansky. Florence: La Nuova Italia, 101–115.
Jaśkowski, S. (1934). On the rules of suppositions in formal logic. Studia Logica 1, 5–32.
Martin-Löf, P. (1971). Hauptsatz for the intuitionistic theory of iterated inductive definitions. In: Proceedings of the Second Scandinavian Logic Symposium. Ed. By J. E. Fenstad. Amsterdam: North-Holland, 179–216.
Martin-Löf, P. (1984). Intuitionistic type theory. Napoli: Bibliopolis.
Martin-Löf, P. (1985). On the meanings of the logical constants and the justifications of the logical laws. In: Atti degli Incontri di Logica Matematica, Vol. 2. Ed. by C. Bernardi and P. Pagli. Siena: Scuola di Specializzazione in Logica Matematica, Dipartimento di Matematica, Università degli Studi di Siena, 203–281. Republished in Nordic Journal of Philosophical Logic 1, 11–60 (1996).
Prawitz, D. (1965). Natural Deduction: A Proof-Theoretical Study. Stockholm: Almqvist & Wiksell. Reprinted Mineola NY: Dover Publications (2006).
Prawitz, D. (1973). Towards a foundation of general proof theory. In: Logic, Methodology and Philosophy of Science IV. Ed. by P. Suppes et al. Amsterdam: North-Holland, 225–250.
Prawitz, D. (1974). On the idea of a general proof theory. Synthese 27, 63–77.
Prawitz, D. (2015a). Classical versus intuitionistic logic. In: Why is this a Proof? Festschrift for Luiz Carlos Pereira. Ed. by E. H. Haeusler et al. London, 15–32.
Prawitz, D. (2015b). Explaining deductive inference. In: Dag Prawitz on Proofs and Meaning. Ed. by H. Wansing. Cham: Springer, 65–100.
Prawitz, D. (2019a). The fundamental problem of general proof theory. Studia Logica 107. Special Issue: General Proof Theory. Ed. by T. Piecha and P. Schroeder-Heister. Cham: Springer, 11–29.
Prawitz, D. (2019b). The seeming interdependence between the concepts of valid inference and proof. Topoi 38, 493–503.
Ross, W. D. (1949). Aristotle’s Prior and Posterior Analytics. Oxford: Oxford University Press.
Schroeder-Heister, P. (1983). The completeness of intuitionistic logic with respect to a validity concept based on an inversion principle. Journal of Philosophical Logic 12, 359–377.
Ross, W. D. (2006). Validity concepts in proof-theoretic semantics. Synthese 148, 525–571.
Ross, W. D. (2014). Frege’s sequent calculus. In: Trends in Logic XIII: Gentzen’s and Jaśkowski’s Heritage – 80 Years of Natural Deduction and Sequent Calculi. Ed. By A. Indrzejczak, J. Kaczmarek, and M. Zawidzki. Łódż University Press, 233–245. doi: https://doi.org/10.15496/publikation-72324.
Sundholm, G. (1983). Constructions, proofs and the meaning of logical constants. Journal of Philosophical Logic 12 (2), 151–172.
Sundholm, G. (1998). Inferences versus consequence. In: The LOGICA Yearbook 1998. Prague: Czech Academy of Sciences, 26–36.
Sundholm, G. (2004). Anti-realism and the notion of truth. In: Handbook of Epistemology. Ed. by I. Niiniluoto et al. Kluwer Academic Publishers, 437–466.
Sundholm, G. (2006). Semantic values for natural deduction derivations. Synthese 146, 623–638.
Tichý, P. (1988). The Foundations of Frege’s Logic. Berlin: De Gruyter.
Troelstra, A. S. (1977). Aspects of Constructive Mathematics. In: Handbook of Mathematical Logic. Ed. by J. Barwise. Amsterdam: North-Holland, 973–1052.
Troelstra, A. S. and D. van Dalen (1988). Constructivism in Mathematics, 2 vol. Amsterdam: North-Holland.
von Kutchera, F. (1996). Frege and Natural Deduction. In: Frege: Importance and Language. Ed. by M. Schirn. Berlin: De Gruyter, 301–304.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International License (http://creativecommons.org/licenses/by-sa/4.0/), which permits use, sharing, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. If you remix, transform, or build upon this chapter or a part thereof, you must distribute your contributions under the same license as the original.
The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Copyright information
© 2024 The Author(s)
About this chapter
Cite this chapter
Prawitz, D. (2024). The Validity of Inference and Argument. In: Piecha, T., Wehmeier, K.F. (eds) Peter Schroeder-Heister on Proof-Theoretic Semantics. Outstanding Contributions to Logic, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-031-50981-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-031-50981-0_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-50980-3
Online ISBN: 978-3-031-50981-0
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)