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 blog.sigfpe.com
A Neighborhood of Infinity: Self-referential logic via self-referential circuits
| | lawrencecpaulson.github.io
Inductive definitions
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| | pavpanchekha.com
What is Modal Logic?
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| | www.umsu.de
Bacon on higher-order logic :: Wolfgang Schwarz
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| | [AI summary] The discussion centers on the interpretation of higher-order logic and the role of metaphysical domains. Andrew Bacon argues that higher-order logic doesn't require a metaphysical commitment to domains of objects, properties, or propositions. Instead, he emphasizes the use of stipulative definitions and logical connections between sentences to interpret expressions. He contrasts this with the idea that models must be interpreted in a way that reflects a metaphysical structure of reality. The conversation also touches on the nature of provability operators and their relationship to logical frameworks, highlighting the distinction between formal languages and their interpretations in different contexts.
| | math.andrej.com
Mathematics and Computation | Am I a constructive mathematician?
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| [AI summary] The discussion revolves around the philosophical and methodological pluralism in mathematics, emphasizing that mathematics is a human-made construct with historical developments rather than an absolute, universal truth. Key points include the idea that different mathematical frameworks (e.g., classical vs. intuitionistic logic, paraconsistent logic) represent distinct 'worlds' of mathematics, each with its own standards and validity. The conversation highlights the importance of acknowledging these pluralistic perspectives without assuming a single, unifying foundation. It also touches on the role of context, the evolution of mathematical concepts, and the implications of relativism for the future of mathematics. The discussion underscores that ...