Timeline for Syntax/semantics conflation leads to infinitary logic
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 4, 2023 at 18:14 | comment | added | Lave Cave | Would $\exists x \in S; \phi (x)$ be equivalent to $\vee_{x \in S} \phi(x)$ and fix this problem? | |
| Jan 4, 2019 at 9:17 | comment | added | Peter LeFanu Lumsdaine | @ Mallik: In the “internal language” setups @Andrej is speaking of, you don’t lose those distinctions again; rather, you get a powerful analysis of what the early approach was doing, from a modern point of view on syntax. An example that doesn’t need familiarity with categorical logic is what’s classically known as the complete or elementary diagram of a structure. The general idea is: you’re using a language including names for elements of the structure. So no need to throw out the progress; you can have the best of both worlds. | |
| Jan 4, 2019 at 7:43 | comment | added | Monroe Eskew | @Mallik if you find the problems of contemporary model theory interesting, then you certainly lose something by dropping the distinction between structures and languages. | |
| Jan 4, 2019 at 3:53 | comment | added | Mallik | I'm not familiar with the examples from categorical logic, but Andrej's answer suggests that losing the distinctions between having infinitely many constants in the language and infinitely many elements in the domain is not necessarily a drawback of a theory. Are there also obvious situations where it would it be a problem? | |
| Jan 3, 2019 at 10:30 | history | answered | Peter LeFanu Lumsdaine | CC BY-SA 4.0 |