Ferreirós, José (2023) Conceptual Structuralism. Journal for General Philosophy of Science, 54. pp. 125-148. ISSN 0925-4560

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Abstract

This paper defends a conceptualistic version of structuralism as the most convincing way of elaborating a philosophical understanding of structuralism in line with the classical tradition. The argument begins with a revision of the tradition of “conceptual mathematics”, incarnated in key figures of the period 1850 to 1940 like Riemann, Dedekind, Hilbert or Noether, showing how it led to a structuralist methodology. Then the tension between the ‘presuppositionless’ approach of those authors, and the platonism of some recent versions of philosophical structuralism, is presented. In order to resolve this tension, we argue for the idea of ‘logical objects’ as a form of minimalist realism, again in the tradition of classical authors including Peirce and Cassirer, and we introduce the basic tenets of conceptual structuralism. The remainder of the paper is devoted to an open discussion of the assumptions behind conceptual structuralism, and—most importantly—an argument to show how the objectivity of mathematics can be explained from the adopted standpoint. This includes the idea that advanced mathematics builds on hypothetical assumptions (Riemann, Peirce, and others), which is presented and discussed in some detail. Finally, the ensuing notion of objectivity is interpreted as a form of particularly robust intersubjectivity, and it is distinguished from fictional or social ontology.

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Item Type:	Published Article or Volume
Creators:	Creators Email ORCID Ferreirós, José josef@us.es 0000-0002-4837-3071
Subjects:	Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics > Methodology Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics > Practice Specific Sciences > Mathematics
Depositing User:	Dr José Ferreirós
Date Deposited:	23 Jan 2025 18:14
Last Modified:	23 Jan 2025 18:14
Item ID:	24588
Journal or Publication Title:	Journal for General Philosophy of Science
Official URL:	https://link.springer.com/article/10.1007/s10838-0...
DOI or Unique Handle:	10.1007/s10838-021-09598-8
Subjects:	Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics > Methodology Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics > Practice Specific Sciences > Mathematics
Date:	2023
Page Range:	pp. 125-148
Volume:	54
ISSN:	0925-4560
URI:	https://philsci-archive.pitt.edu/id/eprint/24588

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