MoL-2020-05: What Structural Objects Could Be: Mathematical Structuralism and its Prospects

MoL-2020-05: Călinoiu, Teodor Tiberiu (2020) What Structural Objects Could Be: Mathematical Structuralism and its Prospects. [Pre-print]

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This thesis covers structuralism in the philosophy of mathematics, focusing on non-eliminative versions thereof and zooming in on three fresh and promising contemporary articulations. After introducing the topic and essential piece of terminology, we follow a quasi-historical route to modern mathematical structuralism: starting with Paul Benacerraf’s seminal articles and after drawing a taxonomy of views playing out in the contemporary field, we discuss eliminative structuralism alongside introducing useful ideology, and we formulate eliminativist discontents which feed a line of reasoning which is crucially invoked by non-eliminativists to motivate their view. Moving thus on to non-eliminativism, we introduce Stewart Shapiro’s early articulation thereof: Sui Generis Structuralism, followed by an extensive discussion of many of the the problems and ensuing objections leveraged against it. Gathered together, all these concerns constitute the canon we use to assess the three newly emerging articulations of positionalist non-eliminativist structuralism. After taking a motivated detour through non-positionalist non-eliminativism, we introduce in some detail Øystein Linnebo and Richard Pettigrew’s Fregean Abstractionist Structuralism, Edward Zalta and Uri Nodelman’s Object Theoretic Structuralism and Hannes Leitgeb’s Graph Theoretic Structuralism. Assessing each of these views against our canon, we find that, for the most part, each of these is successfully replied. Our thesis is that in spite of sustained criticism, there is still fuel in the realist’s tank, meaning that each of the three views is left standing following their assessment against the canon, albeit this claim will be qualified in Conclusion.

Item Type: Pre-print
Report Nr: MoL-2020-05
Series Name: Master of Logic Thesis (MoL) Series
Year: 2020
Subjects: Logic
Depositing User: Dr Marco Vervoort
Date Deposited: 17 Aug 2020 12:52
Last Modified: 17 Aug 2020 13:11

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