Povich, Mark (2024) The Symbolic Approach to the Omega Rule. In: UNSPECIFIED.
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Abstract
According to the ω-rule, it is valid to infer that all natural numbers possess some property, if 0 possesses it, 1 possesses it, 2 possesses it, and so on. The ω-rule is important because its inclusion in certain arithmetical theories results in true arithmetic. It is controversial because it seems impossible for finite human beings to follow, given that it seems to require accepting infinitely many premises. Inspired by a remark of Wittgenstein’s, I argue that the mystery of how we follow the ω-rule subsides once we treat the rule as helping to give meaning to the symbol, “…”.
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| Item Type: | Conference or Workshop Item (UNSPECIFIED) | ||||||
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| Keywords: | determinacy, categoricity, infinitary inference, Wittgenstein, foundations of mathematics, | ||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic |
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| Depositing User: | Mr. Mark Povich | ||||||
| Date Deposited: | 11 Jun 2024 17:18 | ||||||
| Last Modified: | 11 Jun 2024 17:18 | ||||||
| Item ID: | 23553 | ||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic |
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| Date: | 2024 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/23553 |
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