To: |
"Patrick Cassidy" <pat@xxxxxxxxx> |
---|---|

Cc: |
ontolog-forum@xxxxxxxxxxxxxxxx |

From: |
Pat Hayes <phayes@xxxxxxx> |

Date: |
Thu, 20 Mar 2008 12:50:19 -0500 |

Message-id: |
<p06230901c40848bcf611@[10.100.0.20]> |

At 11:31 PM -0400 3/19/08, Patrick Cassidy wrote:
PatH, Yes, of course. You have to understand these axioms in the
context of our discussion. Im not suggesting for a moment that the
above axioms form a coherent ontology, or conform to a coherent
single view of the world. They don't: that is the point of them. They
are supposed to illustrate that there are TWO, DIFFERENT, INCOMPATIBLE
views of the world. One perspective, which we are calling 4D, treats
the x in (x at t) as something extended along the time-dimension,
which can have temporal slices of it taken. The other, which we are
calling - misleadingly - 3D, treats such entities as continuants. The
only way this second view could make sense of the notation (x at t) is
that is simply a poorly chosen way of saying "the continuant x,
at t"; and according to this view, this is the
same
continuant as that x at any other t. So if this _expression_ really
does denote a continuant, then the above axiom would be true. Now, I
will admit that a dyed-in-the-wool 3D modeler would probably never
write an axiom like this, and might even regard it as ill-formed; but
we are considering the case where two different ontological
perspectives meet, and so it may be that the 3D ontologist is obliged
to deal with the 4D ontologist's syntax, no matter how aberrant it
appears to be; and if they did have to deal with it, this is what they
might say about it.
Yes, of course it is. That is the point. Thus it appears that the above set of axioms still does not serve as a demonstration of contradiction between 3D and 4D. Of course it does. Those two senses ARE the contradiction between
3D and 4D.
PatH provided a second set of axioms, below. But there is still an And you will get different answers (and different axioms) from
different people. That was the point I was trying to make from the
beginning of this discussion.
No, they were vividly clear, but there were TWO DIFFERENT
meanings.
This is an illustration Yes, OF COURSE it is. , _expression_ the time at which the age is calculated is not in fact expressed, Yes, but this only makes sense if (x at t) = x. Hence the other
axiom, which I supplied.
In the set of axioms, the "t" in ((age (x at t)) is taken to have the same (x at t) is a timeslice (which I now recognize it is not It is in one ontology, but not in the other. Are you beginning to get the point? ), or the "t" in (x I am dazzled by your extraordinary ability to not get the point.
The two senses for (x at t) ARE the incompatibility between 3D and 4D.
You have understood the problem, and immediately concluded that there
is no problem.
IT DEPENDS WHICH VIEWPOINT YOU ADOPT. In 4D, it is a timeslice of
the 4-dimensional entity x. In 3D, it is either meaningless or simply
a rebarbative way of saying "x, at t". These two
interpretations are INCONSISTENT with one another. Which was the point
I have been trying to get through to you from the beginning of this
conversation.
course, the Pat in Pat-at-t1 and Pat-at-t2 are the same Pat; and also of Quite. A true 3D modeler would leave it out altogether or refuse
to deal with it. But if they were forced to, in order to communicate
with a 4D modeler who uses such expressions, the best they could do,
and still stick to their own ontological rules, would be to treat it
as referring to x.
Quite.
. . . in which case it would appear to be a timeslice of some 4D "x". Not if x is a continuant, it would not. Continuants
cannot
have timeslices. They are a different fundamental constituent of
reality than 4D things. They have no 4D extent. They are inherently
3D, but continue to exist through time. I myself find all this close
to incoherent, but it is what true 3D modelers say (and indeed what
has been set into stone in for example the OBO foundry
ontologies.)But Spoken like a true 3D modeler; but to a true 4D modeler, this is
like saying that 3=265 because 3 is part of 265. It is obviously
false. So if you follow 3D rules (such as this substitution) with 4D
axioms, you will quickly reach inconsistencies. Which was my
point.
True; but it does relieve the 4D modeler of that obligation. So
now, tell me again (since you seem to have navigated from a 4D to a 3D
perspective) how these two points of view can be combined into a
single ontology?
exactly the same thing as "the Eiffel Tower", with some obiter dicta different points in time. The _expression_ (x at t) can be interpreted as a You seem to have talked yourself into being an endurantist
again.
Another way to find an interpretation of (x at t) is to think of a WHICH grammar? There are at least two under discussion here.
argument. But the category of 'continuant' simply does not occur in a 4D
ontology. There is no such thing.
Yes, it would be a contradiction, but it would be a contradiction Well, its not clear that this is ever a
logical
contradiction. It isn't in an untyped logic such as CL, in any
case.I would think of this as a syntactic error Which might well be appropriate in a 3D (perdurant) ontology, but
most emphatically is not in a 4D one, in which
any entity
extended in time can be time-sliced., but you may consider domain an entity that is not in its domain or range. First, that is wrong; but more to the point, it is
not
being used outside its range in the 4D framework. Yes, of
course, one can obtain consistency by restricting the 4D framework to
only apply to the occurrent sub-universe of the 3D world, but that is
obviously not satisfactory to the 4D modeler. The entire point of
using that framework is to be allowed to use a single coherent way of
talking about temporal relationships which applies uniformly
to all spatiotemporally extended entitiesThis is not diagnostic of an inconsistent ontology. The contradiction generated by trying to use 'physicalPart' on an AbstractObject - it cannot make any sense An aside, but in fact it can. CL manages to express arbitrary
ontologies in an untyped logic.
, not because implied in 4D) on use of that relation. In 4D, no such restriction is implied. In fact, no such
restriction is
acceptable. All you have done here is imposed a
3D distinction onto the 4D ontology, crippling it in the
process.It does not appear to me that this example demonstrates a logical Again, I am dazzled by your obduracy.
Pat
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