Timeline for Why hasn't mereology succeeded as an alternative to set theory?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 6, 2023 at 10:54 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Apr 17, 2017 at 13:16 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
Updated reference and added new reference
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| Jan 26, 2016 at 22:13 | comment | added | Emil Jeřábek | All right. I wasn't quite serious in the last comment. | |
| Jan 26, 2016 at 19:15 | comment | added | Joel David Hamkins | To the barricades! Errr....I mean...I view the ontology of set theory as built in a cumulative hierarchy, by which sets arise as collections of previously created objects, and on this view, one does not seem ever to arrive at a universal set. Thus, rather than being a way to avoid paradox, ZFC instead expresses the fundamental situation. In any case, in our paper we are quite explicit that there are many other approaches to mereology, even though we happen to focus on the theory of $\subseteq$ as it is understood in ZFC set theory (although much weaker theories suffice for our analysis). | |
| Jan 26, 2016 at 17:01 | comment | added | Emil Jeřábek | I see. Well, of course there is a universal set. Its existence was denied in ZFC as a way around paradoxes in naive set theory, but there is no reason to cripple the universe in a similar way for mereology when no such paradoxes arise. | |
| Jan 26, 2016 at 16:17 | comment | added | Joel David Hamkins | Meanwhile, David Lewis (1991) treated the case of class-based mereology, which is an infinite atomic Boolean algebra as you mention. | |
| Jan 26, 2016 at 16:15 | comment | added | Joel David Hamkins | @EmilJeřábek There is no universal set, so it is not a Boolean algebra, but an atomic unbounded relatively complemented distributive lattice, which is finitely axiomatizable. | |
| Jan 26, 2016 at 15:58 | comment | added | Emil Jeřábek | Hmm. As far as I can see, the natural axioms for $\subseteq$-based mereology are those of an infinite atomic Boolean algebra, which is indeed a complete decidable theory, but not finitely axiomatizable, so presumably you do it differently? | |
| Jan 26, 2016 at 11:11 | vote | accept | godelian | ||
| Jan 26, 2016 at 11:11 | comment | added | godelian | That a decidable theory cannot be foundational is a beautiful argument. It reveals the richness one gets from incompleteness. | |
| Jan 26, 2016 at 2:03 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |