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Infinity and a Critical View of Logic

Charles Parsons

Inquiry: An Interdisciplinary Journal of Philosophy 58 (1):1-19 (2015)

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Introduction to special issue on ‘critical views of logic’.Øystein Linnebo, Frode Kjosavik & Mirja Hartimo - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 65 (6):631-637.details Critical views of logic are presented. These are views that are critical of logic in a sense akin to the way in which Kant is critical rather than dogmatic about traditional metaphysics. Such approaches differ from the Fregean ‘logic-first’ view. In accordance with the latter, logic is often regarded as epistemologically and methodologically fundamental. Hence, all disciplines – including mathematics – are considered as answerable to logic, rather than vice versa. In critical views of logic, by contrast, the logical principles (...) Download Export citation Bookmark
The Many and the One: A Philosophical Study of Plural Logic.Salvatore Florio & Øystein Linnebo - 2021 - Oxford, England: Oxford University Press.details Plural expressions found in natural languages allow us to talk about many objects simultaneously. Plural logic — a logical system that takes plurals at face value — has seen a surge of interest in recent years. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between (...) Download Export citation Bookmark 17 citations
Kant on the possibilities of mathematics and the scope and limits of logic.Frode Kjosavik - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 65 (6):683-706.details ABSTRACT I suggest how a broadly Kantian critique of classical logic might spring from reflections on constructibility conditions. According to Kant, mathematics is concerned with objects that are given through ‘arbitrary synthesis,’ in the form of ‘constructions of concepts’ in the medium of ‘pure intuition.’ Logic, by contrast, is narrowly constrained – it has no objects of its own and is fixed by the very forms of thought. That is why there is not much room for developments within logic, as (...) Download Export citation Bookmark 1 citation
Replies.Øystein Linnebo - 2023 - Theoria 89 (3):393-406.details Thin Objects has two overarching ambitions. The first is to clarify and defend the idea that some objects are ‘thin’, in the sense that their existence does not make a substantive demand on reality. The second is to develop a systematic and well-motivated account of permissible abstraction, thereby solving the so-called ‘bad company problem’. Here I synthesise the book by briefly commenting on what I regard as its central themes. Download Export citation Bookmark 2 citations
Weyl and Two Kinds of Potential Domains.Laura Crosilla & Øystein Linnebo - forthcoming - Noûs.details According to Weyl, “‘inexhaustibility’ is essential to the infinite”. However, he distinguishes two kinds of inexhaustible, or merely potential, domains: those that are “extensionally determinate” and those that are not. This article clarifies Weyl's distinction and explains its enduring logical and philosophical significance. The distinction sheds lights on the contemporary debate about potentialism, which in turn affords a deeper understanding of Weyl. Download Export citation Bookmark 2 citations
Husserl on Kant and the critical view of logic.Mirja Hartimo - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 65 (6):707-724.details ABSTRACT This paper seeks to clarify Husserl’s critical remarks about Kant’s view of logic by comparing their respective views of logic. In his Formal and Transcendental Logic Husserl criticizes Kant for not asking transcendental questions about formal logic, but rather ascribing an ‘extraordinary apriority’ to it. He thinks the reason for Kant’s uncritical attitude to logic lies in Kant’s view of logic as directed toward the subjective, instead of being concerned with a ‘“world” of ideal Objects’. Whereas for Kant, general (...) Download Export citation Bookmark 4 citations
Critical Plural Logic.Salvatore Florio & Øystein Linnebo - 2020 - Philosophia Mathematica 28 (2):172-203.details What is the relation between some things and the set of these things? Mathematical practice does not provide a univocal answer. On the one hand, it relies on ordinary plural talk, which is implicitly committed to a traditional form of plural logic. On the other hand, mathematical practice favors a liberal view of definitions which entails that traditional plural logic must be restricted. We explore this predicament and develop a “critical” alternative to traditional plural logic. Download Export citation Bookmark 6 citations

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