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Laws of Thought and Laws of Logic After Kant

Patton, Lydia (2018) Laws of Thought and Laws of Logic After Kant. Logic from Kant to Russell.

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Abstract

George Boole emerged from the British tradition of the “New Analytic”, known for the view that the laws of logic are laws of thought. Logicians in the New Analytic tradition were influenced by the work of Immanuel Kant, and by the German logicians Wilhelm Traugott Krug and Wilhelm Esser, among others. In his 1854 work An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Boole argues that the laws of thought acquire normative force when constrained to mathematical reasoning. Boole’s motivation is, first, to address issues in the foundations of mathematics, including the relationship between arithmetic and algebra, and the study and application of differential equations (Durand-Richard, van Evra, Panteki). Second, Boole intended to derive the laws of logic from the laws of the operation of the human mind, and to show that these laws were valid of algebra and of logic both, when applied to a restricted domain. Boole’s thorough and flexible work in these areas influenced the development of model theory (see Hodges, forthcoming), and has much in common with contemporary inferentialist approaches to logic (found in, e.g., Peregrin and Resnik).


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Patton, Lydiacritique@vt.edu0000-0003-2751-1196
Keywords: logic, Boole, algebra, model theory, inferentialism
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
General Issues > History of Philosophy of Science
Depositing User: Dr Lydia Patton
Date Deposited: 04 Mar 2019 02:34
Last Modified: 04 Mar 2019 02:34
Item ID: 15788
Journal or Publication Title: Logic from Kant to Russell
Publisher: Routledge
Official URL: https://www.routledge.com/Logic-from-Kant-to-Russe...
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
General Issues > History of Philosophy of Science
Date: 2018
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/15788

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