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www.lesswrong.com | ||
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unstableontology.com
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| | | | | (note: one may find the embedded LaTeX more readable on LessWrong) The Löwenheim-Skolem theorem implies, among other things, that any first-order theory whose symbols are countable, and which has an infinite model, has a countably infinite model. This means that, in attempting to refer to uncountably infinite structures (such as in set theory), one "may... | |
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www.umsu.de
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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. | |
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pavpanchekha.com
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relatedwork.blogspot.com
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| | | WARNING: the following contains a whole lot of pedantry about proving theorems at a level of detail such that you could likely convince a co... | ||
