Logical Constants and Arithmetical Forms
DOI:
https://doi.org/10.12775/LLP.2023.012Słowa kluczowe
logical constants, logical form, criterion of logicality, formalityAbstrakt
This paper reflects on the limits of logical form set by a novel criterion of logicality proposed in (Bonnay and Speitel, 2021). The interest stems from the fact that the delineation of logical terms according to the criterion exceeds the boundaries of standard first-order logic. Among ‘novel’ logical terms is the quantifier “there are infinitely many”. Since the structure of the natural numbers is categorically characterisable in a language including this quantifier we ask: does this imply that arithmetical forms have been reduced to logical forms? And, in general, what other conditions need to be satisfied for a form to qualify as “fully logical”? We survey answers to these questions.
Bibliografia
Bonnay, D., 2008, “Logicality and invariance”, Bulletin of Symbolic Logic 14 (1): 29–68. DOI: http://dx.doi.org/10.2178/bsl/1208358843
Bonnay, D., and F. Engström, 2018, “Invariance and definability, with and without equality”, Notre Dame Journal of Formal Logic 59 (1): 109–133. DOI: http://dx.doi.org/10.1215/00294527-2017-0020
Bonnay, D., and S. G. W. Speitel, 2021, “The Ways of Logicality: Invariance and Categoricity”, pages 55–80 in G. Sagi and J. Woods (eds.), The Semantic Conception of Logic: Essays on Consequence, Invariance, and Meaning, Cambridge: Cambridge University Press. DOI: http://dx.doi.org/10.1017/9781108524919.004
Bonnay, D., and D. Westerståhl, 2016, “Compositionality solves Carnap’s problem”, Erkenntnis 81: 721–739. DOI: http://dx.doi.org/10.1007/s10670-015-9764-8
Carnap, R., 1943, Formalization of Logic, Harvard University Press.
Ebbinghaus, H.-D., 2017, “Extended logics – the general framework”, pages 25–76 in J. Barwise and S. Feferman (eds.) Model-Theoretic Logics, Cambridge: Cambridge University Press. DOI: http://dx.doi.org/10.1017/9781316717158.005
Feferman, S., 1999, “Logic, logics, and logicism”, Notre Dame Journal of Formal Logic 40 (1): 31–54. DOI: http://dx.doi.org/10.1305/ndjfl/1039096304
Feferman, S., 2010, “Set-theoretical invariance criteria for logicality”, Notre Dame Journal of Formal Logic 51 (1): 3–20. DOI: http://dx.doi.org/10.1215/00294527-2010-002
Feferman, S., 2015, “Which quantifiers are logical? A combined semantical and inferential criterion”, pages 19–30 in A. Torza (ed.), Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language, Synthese Library (vol. 373), Springer. DOI: http://dx.doi.org/10.1007/978-3-319-18362-6_2
Gentzen, G., 1935, “Untersuchungen über das logische Schließen I”, Mathematische Zeitschrift 39: 176–210. DOI: http://dx.doi.org/10.1007/BF01201353
Griffiths, O., and A. Paseau, 2022, One True Logic. A Monist Manifesto, Oxford University Press. DOI: https://doi.org/10.1093/oso/9780198829713.002.0003
Kennedy, J., and J. Väänänen, 2021, “Logicality and model classes”, Bulletin of Symbolic Logic 27 (4): 385–414. DOI: http://dx.doi.org/10.1017/bsl.2021.42
Lindström, P., 1966, “First order predicate logic with generalized quantifiers”, Theoria 32 (3): 186–195. DOI: http://dx.doi.org/10.1111/j.1755-2567.1966.tb00600.x
MacFarlane, J., 2000, “What does it mean to say that logic is formal?”, PhD thesis, University of Pittsburgh.
MacFarlane, J., 2015, “Logical constants”, in E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/archives/win2017/entries/logical-constants/
McGee, V., 1997, “Logical operations”, Journal of Philosophical Logic 25 (6): 567–580. DOI: http://dx.doi.org/10.1007/BF00265253
Mostowski, A., 1957, “On a generalization of quantifiers”, Fundamenta Mathematicae 44 (1): 12–36. DOI: http://dx.doi.org/10.2307/2964414
Murzi, J., and F. Steinberger, 2017, “Inferentialism”, pages 197–224 in B. Hale, C. Wright and A. Miller (eds.), Blackwell Companion to Philosophy of Language, second edition, Wiley Blackwell. DOI: http://dx.doi.org/10.1002/9781118972090.ch9
Rumfitt, I., 2000, “ ‘Yes’ and ‘No’ ”, Mind 109 (436): 781–823. DOI: http://dx.doi.org/10.1093/mind/109.436.781
Sagi, G., 2018, “Logicality and meaning”, The Review of Symbolic Logic 11 (1): 133–159. DOI: http://dx.doi.org/10.1017/S1755020317000247
Sher, G., 1991, The Bounds of Logic: A Generalized Viewpoint, MIT Press.
Sher, G., 2016, Epistemic Friction. An Essay on Knowledge, Truth, and Logic, Oxford University Press. DOI: http://dx.doi.org/10.1093/acprof:oso/9780198768685.001.0001
Sher, G., 2022, Logical Consequence, Elements in Philosophy and Logic, Cambridge: Cambridge University Press. DOI: http://dx.doi.org/10.1017/9781108981668
Speitel, S. G. W., 2020, “Logical constants between inference and reference. An essay in the philosophy of logic”, UC San Diego Electronic Theses and Dissertations. https://escholarship.org/uc/item/7256r138
Tarski, A., 1983, “On the concept of logical consequence”, pages 409–421 in J. Corcoran (ed.), Logic, Semantics, Metamathematics, second edition, Hacket Publishing Company.
Tarski, A., 1986, “What are logical notions”, History and Philosophy of Logic 7: 143–154. DOI: http://dx.doi.org/10.1080/01445348608837096
Westerståhl, D., 2019, “Generalized quantifiers”, in E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/archives/win2019/entries/generalized-quantifiers/
Pobrania
Opublikowane
Jak cytować
Numer
Dział
Licencja
Prawa autorskie (c) 2023 Sebastian G. W. Speitel
Utwór dostępny jest na licencji Creative Commons Uznanie autorstwa – Bez utworów zależnych 4.0 Międzynarodowe.
Statystyki
Liczba wyświetleń i pobrań: 867
Liczba cytowań: 0
