Abstract
There are two fundamentally different attitudes to the methods of formal logic in the logical tradition at least since Frege. On one hand, a logical formalization of some part of mathematics, or some other domain, is meant to articulate conceptually essential features of that domain as it exists. The formalization is fundamentally the result of a conceptual investigation, and not just the application of a certain technique for transforming informal notions into formal ones. Logical analysis is clarification of given concepts and conceptual relationships. And in this conception of logic, it is taken for granted that logical and conceptual problems, arising in some domain, concern something about which one can be absolutely right or wrong.
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References
As presented in Quine, V.v.O.: Word & Object, The M.I.T. Press, Cambridge, Ma., 1960.
Frege, G., “What is a function?”, in Geach, P. and Black, M. (eds.), Translations from the Philosophical Writings of Gottlob Frege, Basil Blackwell, Oxford, 1952, p. 116.
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In his article Booles rechnende Logik und die Begriffsschrift’, Frege explains: “Meine Begriffsschrift hat ein weiteres Ziel als die Boolesche Logik, indem sie in Verbindung mit aritmetischen und geometrischen Zeichen die Darstellund eines Inhaltes ermöglichen will.” in Frege, G., Nachgelassene Schriften, Felix Meiner Verlag, Hamburg, 1969, p. 51.
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In§13of the Begriffsschrift Frege explains: “We have already introduced a number of fundamental principles of thought in the rust chapter in order to transform them into rules for the use of our signs. These rules and the laws whose transforms they are cannot be expressed in the ideography because they form its basis.” van Heijenoort
In his criticism of the formalists in the Grundgesetze (§90) Frege says explicitly that the formalist interpretation of the formal system of the Begriffsschrift is a possible, though incorrect, interpretation.
This point is elaborated in Stenlund, S.: Language and Philosophical Problems, Routledge, London and New York, 1990.
Wright, G.H.von,: ‘Logic and Philosophy in the Twentieth Century’, in Prawitz, D., Skyrms, B., WesterstAhl, D., (eds.), Logic, Methodology and Philosophy of Science, Proceedings of the 1991 International Conference,North-Holland, (to appear).
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Stenlund, S. (1994). The Limits of Formalization. In: Prawitz, D., Westerståhl, D. (eds) Logic and Philosophy of Science in Uppsala. Synthese Library, vol 236. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8311-4_24
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DOI: https://doi.org/10.1007/978-94-015-8311-4_24
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