Titlebook: Objects, Structures, and Logics; FilMat Studies in th Gianluigi Oliveri,Claudio Ternullo,Stefano Boscolo Book 2022 The Editor(s) (if applic

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Introduction,e realist, who holds that mathematics is about discovering and describing properties of entities which exist independently of our knowledge, is opposed by the anti-realist who does not share his conviction.

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Aristotle’s Problemd their thoughts, language, and practices. This paper has two goals. First, to show that this definition fails to distinguish platonism from various forms of . in the philosophy of mathematics, according to which mathematical objects depend for their existence and properties on non-mathematical ones

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Hofweber’s Nominalist Naturalismuzzle and two traditional responses to it—the Substantival Strategy and the Adjectival Strategy—we outline Hofweber’s proposed version of Adjectivalism. We argue that two key components—the syntactic and semantic components—of Hofweber’s analysis both suffer from serious empirical difficulties. Ulti

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Exploring Mathematical Objects from Custom-Tailored Mathematical Universesnate toposes in which mathematics plays out slightly differently. For instance, there are toposes in which the axiom of choice and the intermediate value theorem from undergraduate calculus fail. The purpose of this contribution is to give a glimpse of the toposophic landscape, presenting several sp

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Structural Relativity and Informal Rigour. Structural relativity is the idea that the kinds of structures we isolate are dependent upon the logic we employ. We bring together these ideas by considering the level of informal rigour exhibited by our set-theoretic discourse, and argue that different foundational programmes should countenance

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Ontological Dependence and Grounding for a Weak Mathematical Structuralismc Structural Realism (OSR). On that view, quantum particles . for their identity on quantum entanglement structures but are defined as not entirely structural .. A similar approach can be applied to mathematical structuralism, where Weak Mathematical Structuralism (WMS) provides a novel, more modera

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Predicativity and Constructive Mathematicsgeneralised inductive definitions. I begin by offering some motivation for an enquiry in the predicative foundations of constructive mathematics, by looking at contemporary work at the intersection between mathematics and computer science. I then review the background notions and spell out the above

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