Timeline for To be is to be an element?
Current License: CC BY-SA 4.0
6 events
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| Aug 31, 2021 at 0:38 | comment | added | Frode Alfson Bjørdal | @PeterLeFanuLumsdaine It indeed has such a provenance. The terminology I opted for has bearings upon how we think about some important problems. Yes, there are many free logics, with non-denoting terms. The approach I suggest has advantages, it seems. To wit: (1) The mere subsistence, and thus also non-existence, of proper classes, combines well with the idea that classes merely abbreviate formulas. (2) It provides a nice semantics for fictional characters, by including them in the domain of discourse, while making statements as SH is F and SH is not-F false (if we have choice-negation). | |
| Aug 30, 2021 at 18:46 | comment | added | Peter LeFanu Lumsdaine | What you describe sounds formally just like a two-sorted set/class theory (e.g. Gödel–Bernays and similar) but with different terminology, saying “$a$ exists” for what would conventionally be read as “$a$ is a set”. Is this what you have in mind, or if not, what difference besides terminological are you thinking of? Systems with terms denoting not-necessarily-existing things have certainly been defined (e.g. Fourman/Scott’s partial logic), but in all such systems I know, “$a$ exists” is equivalent to “$\exists x\ (x=a)$”, i.e. what you’re calling “$x$ subsists”. | |
| Aug 30, 2021 at 17:40 | review | Close votes | |||
| Sep 7, 2021 at 3:07 | |||||
| Aug 30, 2021 at 17:04 | history | edited | Frode Alfson Bjørdal | CC BY-SA 4.0 |
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| Aug 30, 2021 at 16:52 | history | edited | Frode Alfson Bjørdal | CC BY-SA 4.0 |
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| Aug 30, 2021 at 16:46 | history | asked | Frode Alfson Bjørdal | CC BY-SA 4.0 |