Timeline for Why hasn't mereology succeeded as an alternative to set theory?
Current License: CC BY-SA 2.5
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| Mar 15, 2011 at 14:34 | comment | added | Jeremy Shipley | My main point in answering the question is that mereology is more restrictive. Although it is true that interesting mathematics arises from adopting restrictions (intuitionism, constructivism), more restricitve frameworks are not likely to supplant less restrictive frameworks as widely adopted working foundations, in my opinion. | |
| Mar 15, 2011 at 14:31 | comment | added | Jeremy Shipley | You might be right Carl. I was thinking of Russell who, in some writings on physical space, had points only as logical fictions. I'm not sure, however, that even with that approach you can get set theory. It will be more like a homogeneous set whose parts are homogeneous and some parts are singletons (which have no parts). For a philosopher discussing this see David Lewis "Parts of Classes." | |
| Mar 15, 2011 at 12:08 | comment | added | Carl Mummert | As a quibble, locale theory can certainly prove a result that is analogous to Tychonoff's theorem without AC, but because Tychonoff's theorem implies AC over ZF it's impossible to prove the actual Tychonoff theorem in ZF or in any constructive theory that is a subtheory of ZF when viewed from a classical standpoint. | |
| Mar 15, 2011 at 12:03 | comment | added | Carl Mummert | I thought that points were definable in mereology as objects that have no proper parts (after you get rid of the empty set's object). What's the obstruction that prevents mereology from getting set theory as a definitional extension in that way? | |
| Mar 15, 2011 at 4:21 | comment | added | Jeremy Shipley | Thanks! I didn't mean to suggest it was a bad idea. | |
| Mar 15, 2011 at 3:56 | comment | added | Andrej Bauer | Locale theory is topology without points. It proves Tychonoff theorem without using choice. In fact, it is a good idea to consider spaces as more than just bags of points. | |
| Mar 15, 2011 at 2:18 | history | edited | Jeremy Shipley | CC BY-SA 2.5 |
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| Mar 15, 2011 at 1:58 | history | answered | Jeremy Shipley | CC BY-SA 2.5 |