Applications, applicability, and Frege’ s Constraint. Some remarks on Contemporary Platonism

Journal title PARADIGMI
Author/s Andrea Sereni
Publishing Year 2014 Issue 2013/3
Language English Pages 20 P. 91-110 File size 114 KB
DOI 10.3280/PARA2013-003007
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Le idee di Frege sulle applicazioni e l’applicabilità dell’aritmetica, e della matematica in generale, suggeriscono un certo numero di requisiti che un resoconto filosofico dell’aritmetica (della matematica) dovrebbe soddisfare. I punti rilevanti di tali requisiti sono enucleati e precisati e viene discusso come essi possano essere valutati dai sostenitori di posizioni platoniste contemporanee, sia di quelle sul versante latamente razionalista: il neo-logicismo di Hale e Wright e lo strutturalismo ante rem di Shapiro, sia di quelle sul lato empirista e naturalista: il platonismo indispensabilista e il platonismo "di default" di Burgess e Rosen. L’autore conclude offrendo alcune formulazioni deboli del Frege’s Constraint che, appropriatamente formulato, mostra di poter essere soddisfatto anche da posizioni non logiciste e non platoniste.

Keywords: Applicability of Mathematics, Frege’s Constraint, Neo-logicism, Structuralism, Empiricist platonism, Naturalist Platonism.

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Andrea Sereni, Applications, applicability, and Frege’ s Constraint. Some remarks on Contemporary Platonism in "PARADIGMI" 3/2013, pp 91-110, DOI: 10.3280/PARA2013-003007