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www.cs.uic.edu | ||
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www.lesswrong.com
The Löwenheim-Skolem theorem implies, among other things, that any first-order theory whose symbols are countable, and which has an infinite model, h... |
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www.umsu.de
[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. |
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lawrencecpaulson.github.io
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www.logicmatters.net
I didn't at all intend to return to my Introduction to Gödel's Theorems (which I've not really read for a dozen years, apart from correcting a small handful of typos in the PDF). But I had occasion to look something up, and - hey, ho! - I've found myself over the last week beginning to [...] |
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