A single point with parts?

[dl...@mitre.org]

BFO-2020 defines fiat point as "..fiat boundary that consists of a single point."  with an axiom of "'has continuant part at all times' only 'fiat point'". What would constitute a (proper) part of a single point?  The only interpretation I could make of this requires introducing granularity, something like "a single point at one level of granularity might have parts at a finer level of granularity" which seems a bit of a stretch.

[Barry Smith]

I do not believe that that axiom implies that a fiat point must have proper parts

However, for those of you who are interested in an ontology in which points do have proper parts, see

Zeno's Paradox for Colours 

and for a much longer version, with formal details 

Boundaries: An essay in mereotopology

BS

On Wed, Aug 4, 2021 at 2:39 AM dl...@mitre.org <dl...@mitre.org> wrote:

BFO-2020 defines fiat point as "..fiat boundary that consists of a single point."  with an axiom of "'has continuant part at all times' only 'fiat point'". What would constitute a (proper) part of a single point?  The only interpretation I could make of this requires introducing granularity, something like "a single point at one level of granularity might have parts at a finer level of granularity" which seems a bit of a stretch.

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[dl...@mitre.org]

Could a fiat point have a proper part? An improper part would be the point itself but wasn't clear what a proper part would be.

[Ludger Jansen]

Am 04.08.2021 um 15:21 schrieb Barry Smith:

I do not believe that that axiom implies that a fiat point must have proper parts

Indeed not.

It is an ONLY axiom, implying that IF the thing in question has a part, THEN the part is a fiat point. This is equivalent with EITHER the thing in question has NO part, OR all proper parts are fiat points.

Best
L

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PD Dr. Ludger Jansen
Institut für Philosophie
Universität Rostock
D-18051 Rostock

[dl...@mitre.org]

Yes, I understand that it is an only axiom but if a single point does have a part what would it that part be?

[Alan Ruttenberg]

It is the intention that there are no proper parts of a fiat point. While we augmented the temporal theory to have intervals and instants, we have not done similar for self-connected continuants. In the temporal theory the axioms for temporal-instant were added and it's provable those don't have proper parts. I anticipate that we will address this issue for continuants  in a future version. Still, it is easy enough to fix fiat-point assuming the common reading of "point'.

We need an axiom analogous to that used for temporal instants: The only part of a fiat-point is itself.

(forall (fp t p)
 (if (and (instance-of fp fiat-point t)
     (continuant-part-of p fp t))
    (= p fp)))

I have added this as https://github.com/BFO-ontology/BFO-2020/issues/20 For spatial regions it's clear that the current ones must allow for disconnected parts, since we have spatial regions that object aggregates occupy. In a future version, following the approach in BFO-2020 I think we would create subclasses of the x-dimensional-spatial-regions that are connected. For sites it's not clear what the answer should be. Barry needs to decide. It's an open question as to whether we need to distinguish connected from disconnected boundaries. "surface","line", and "point" seem to be used to mean connected, so if that is the case we would interpose x-dimensional boundaries as the possibly disconnected superclasses. Barry should weigh in on whether he intended otherwise for the current boundary terms. If we had an axiom that every spatial region has a boundary that would force the issue, but we don't currently. Alan

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