Talk:Whitehead's point-free geometry
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Pointless topology
[edit]I'd like to see a few sentences comparing/contrasting this to pointless topology. linas 15:25, 13 November 2007 (UTC)
Is C5 mistaken?
[edit]Here's C5 as it stands:
- C5.
![{\displaystyle \forall xy\exists z[Czx\land Czy].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9261758ee29d57845c721de2e9481cfdc40f7113)
It says that given any two regions, there exists a region connected to both of them. I cannot find a counterpart to C5 in Casati & Varzi (1999). Instead, I find there the axiom:
- C13.
![{\displaystyle \forall z\exists xy[Czx\land Czy].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d40e419bfd3355fba56e111326822061c025973a)
C13 says that there are at least two regions connected to any given region. In other words, there can be no "restaurant at the end of the universe." Casati & Varzi (1999: 66) attribute their C12-C14 to Process and Reality, then announce that their study will make no further use of them. (It is well-known that Whitehead botched the mereotopology that grounds his later metaphysical work, so that sound mereotopology begins with Clarke's 1980s papers.)
Which of C5 and C13 should this entry include?132.181.160.42 (talk) 19:32, 21 December 2007 (UTC)
Incomplete G6
[edit]shouldn't G6 be
![{\displaystyle \forall x\exists yz[y<x\land x<z].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b6a2370ec127330a41bce949a38c5efb840483c2)
instead of
![{\displaystyle \exists yz[y<x\land x<z].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/be32198602ad5edbf0e42cf01ea2949124378130)
i just wanted to make sure before i edit it Pjbeierle (talk) 22:57, 5 November 2009 (UTC)
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