Logical Forms: Validity and Variety of Formalizations

Georg Brun

doi:10.12775/LLP.2023.016

Autor

Georg Brun Institute of Philosophy, University of Bern https://orcid.org/0000-0001-9884-0566

DOI:

https://doi.org/10.12775/LLP.2023.016

Słowa kluczowe

logical form, formalization, validity, invalidity, substitution

Abstrakt

Formalizations in first-order logic are standardly used to represent logical forms of sentences and to show the validity of ordinary-language arguments. Since every sentence admits of a variety of formalizations, a challenge arises: why should one valid formalization suffice to show validity even if there are other, invalid, formalizations? This paper suggests an explanation with reference to criteria of adequacy which ensure that formalizations are related in a hierarchy of more or less specific formalizations. This proposal is then compared with stronger criteria and assumptions, especially the idea that sentences essentially have just one logical form

Bibliografia

Baker-Plummer, D., J. Barwise, and J. Etchemendy, 2011, Language, Proof and Logic, 2nd ed., Stanford: CSLI publications.

Baumgartner, M., and T. Lampert, 2008, “Adequate formalization”, Synthese 164: 93–115. DOI: ="http://dx.doi.org/10.1007/s11229-007-9218-1

Brun, G., 2004, Die richtige Formel. Philosophische Probleme der logischen Formalisierung, 2nd ed., Frankfurt a. M.: ontos. DOI: http://dx.doi.org/10.1515/9783110323528

Brun, G., 2014, “Reconstructing arguments. Formalization and reflective equilibrium”, Logical Analysis and History of Philosophy 17: 94–129. DOI: http://dx.doi.org/10.30965/26664275-01701006

Castañeda, H. N., 1975, Thinking and Doing. The Philosophical Foundations of Institutions, Dordrecht: Reidel. DOI: http://dx.doi.org/10.1007/978-94-010-9888-5

Cheyne, C., 2012, “The asymmetry of formal kogic”, pages 49–62 in M. Peliš and V. Punčochář (eds.), The Logica Yearbook 2011, London: College Publications.

Curtis, G. N., 1993, The Concept of Logical Form, PhD thesis, Bloomington: Indiana University.

Davidson, D., 1980, “The logical form of action sentences”, pages 105–122 in Essays on Actions and Events, Oxford: Oxford University Press. DOI: http://dx.doi.org/10.1093/0199246270.003.0006

Epstein, R. L., 1994, The Semantic Foundations of Logic. Predicate Logic, New York: Oxford University Press.

Halbach, V., 2013, The Logic Manual, Oxford: Oxford University Press.

Kleene, S. C., 1974, Introduction to Metamathematics, 7th reprint, Groningen/Amsterdam: Wolters-Nordhoff/North-Holland.

Montague, R., 1970, “Universal grammar”, Theoria 36: 373–398. DOI: http://dx.doi.org/10.1111/j.1755-2567.1970.tb00434.x

Peregrin, J., and V. M. Svoboda, 2017, Reflective Equilibrium and the Principles of Logical Analysis. Understanding the Laws of Logic, New York: Routledge.

Punčochář, V., 2023, “Logical forms, substitutions and information types”, Logic and Logical Philosophy. DOI: http://dx.doi.org/10.12775/LLP.2023.017

Quine, W. V. O., 1996, Word and Object, Cambridge, MA: MIT Press.

Sagi, G., 2020, “Logic in natural language. Commitments and constraints”, Disputatio XII/58: 277–308. DOI: http://dx.doi.org/10.2478/disp-2020-0014

Sainsbury, M., 2001, Logical Forms. An Introduction to Philosophical Logic, 2nd ed., Oxford: Blackwell.

Schurz, G., 1995, “Most general first order theorems are not recursively enumerable”, Theoretical Computer Science 147: 149–63. DOI: http://dx.doi.org/10.1016/0304-3975(94)00229-C

Schurz, G., 2001, “Rudolf Carnap’s modal logic”, pages 365–80 in W. Stelzner and M. Stöckler, Zwischen traditioneller und moderner Logik. Nichtklassische Ansätze, Paderborn: mentis. DOI: http://dx.doi.org/10.30965/9783969756966

von Savigny, E., 1976, Grundkurs im logischen Schließen., München: Deutscher Taschenbuch Verlag.

Wittgenstein, L., 1989, Logisch-philosophische Abhandlung. Tractatus logico-philosophicus. Kritische Edition, Frankfurt a. M.: Suhrkamp.