Function and Argument in Begriffsschrift

0481510 - FLÚ 2018 RIV GB eng J - Článek v odborném periodiku
Badesa, C. - Bertran-San Millán, Joan
Function and Argument in Begriffsschrift.
History and Philosophy of Logic. Roč. 38, č. 4 (2017), s. 316-341. ISSN 0144-5340. E-ISSN 1464-5149
Institucionální podpora: RVO:67985955
Klíčová slova: identity * Frege * logic * function * argument
Obor OECD: Philosophy, History and Philosophy of science and technology
Impakt faktor: 0.294, rok: 2017

It is well known that the formal system developed by Frege in Begriffsschrift is based upon the distinction between function and argumentas opposed to the traditional distinction between subject and predicate. Almost all of the modern commentaries on Frege's work suggest a semantic interpretation of this distinction, and identify it with the ontological structure of function and object, upon which Grundgesetze is based. Those commentaries agree that the system proposed by Frege in Begriffsschrift has some gaps, but it is taken as an essentially correct formal system for second-order logic: the first one in the history of logic. However, there is strong textual evidence that such an interpretation should be rejected. This evidence shows that the nature of the distinction between function and argument is stated by Frege in a significantly different way: it applies only to expressions and not to entities. The formal system based on this distinction is tremendously flexible and is suitable for making explicit the logical structure of contents as well as of deductive chains. We put forward a new reconstruction of the function-argument scheme and the quantification theory in Begriffsschrift. After that, we discuss the usual semantic interpretation of Begriffsschrift and show its inconsistencies with a rigorous reading of the text.
Trvalý link: http://hdl.handle.net/11104/0277050