Hmm. OK, then, in what sense is this resulting, er,
structure of extensions an ontology? And why are you not just being vacuous
here, and urging that there should be many alternative, mutually inconsistent,
ontologies? We can arrange for that with a very low cost to the government.
(2) [[PC]] >> [No, “space
is flat” is meaningful from Euclid’s postulates, which is why I
appended “(Euclidean)”.
[PH] > In Newton's
physics, space has no 'shape' at all. The idea isn't meaningful. In fact, it
isn't meaningful in any physics: what Einstein's general relativity provides is
a curved space-time; and Newton's entire framework doesn't even mention the
notion of space-time. Until the late 19th century, no human mind had ever even
conceived of space-time as a meaningful notion.
With the benefit of hindsight, we can now characterize the
abstract product of Newtonian space with Newtonian time as 'flat', but my point
is that this hindsight is only available because we are already within the
post-Einsteinian (actually post-Minkowskian) world in which this way of talking
and thinking makes sense. No pre-1850 ontology, no matter how sophisticated,
would have mentioned a flat space-time coordinate system.
[[PC]] The flatness of space is implied by Newton’s
equations. At that time, space and time were considered different things,
and if an ontologist were to axiomatize space back then (or “flat”
Newtonian space today) it would be using Euclid’s postulates.
(3) [PH]> >> This seems vanishingly unlikely. This first requirement
forces this common theory
>> to be as small as
possible, but you believe that it will be as large as any theory
>> every conceived by the
human mind.
[PC] >> No, the theory encoded by the FO is only as
large as the number of primitives and their deductive closure. But
extensions can be infinitely large, since there is no limit to the number of
complex concept representations that can be constructed as combinations of the
primitive concept representations.
[PH] > Since these complex concepts are all defined, they
are all eliminable. The extensions have the same expressive power as the FO. So
the FO itself already has the expressive power of every other theory.
[[PC]] Well, if “largeness” is the same as
“expressive power” in your terminology, then, yes. I am
accustomed to thinking of size as something different.
(4) [PC] >> I recall that PH and I had a long exchange last year or so at
the end of which I thought that we agreed that 4D and 3D assertions could be
translated into each other. Did I get a wrong impression, or is PH
misinterpreting what I am saying?
[PH] > You got a wrong impression. But the point is not
just about translation. I recently had a discussion with Barry Smith about
this. Barry's view of the way to reconcile 3-D with 4-D (apologies for the
terminology) is that the 4D perspective simply classifies everything as an
occurrent. That is the most natural way to express it from his perspective, and
it is in a sense accurate. For Barry, people are continuants, and the 4D-ers
say they are occurrents: a simple difference of ontological opinion, like
me saying I'm Irish and Barry saying I'm American.
> That would be one way to reconcile the two point of
view, but it has the demerit that if the basic ontology accepts the
distinction, there have to be two 'me's: the occurrent and the continuant. And
this is a problem for the 4Ders such as myself, because from our point of view,
this bifurcation of entities into two halves is an ontological mistake. From
this point of view, there simply is no meaningful distinction to
be made between continuants and occurrents; that all the so-called
continuants are in fact occurrents. From this point of view, there is no
disagreement between Barry saying I am a continuant and me saying I am an
occurrent; we aren't disagreeing about any matter of fact, or indeed about
anything.
> The problem lies higher up the classification chain: it
is the notion, fundamental to Barry, that the occurrent/continuant distinction
is basic ("upper") and also sharply dichotomous, so that nothing can possibly
be in both categories. To me, in contrast, the distinction is vacuous or, at
most, amounts merely to a syntactic preference for writing certain
time-dependent facts in one style rather than another.
> Now, it is possible to translate between these points of
view, but not to reduce them to a single one. They are not two branches
extending from a common trunk: they are more like two completely separate
plants which are about the same height. They give different accounts of
Pat Hayes the person: in one viewpoint, there are two of me: me the continuant
and me (my lifespan) the occurrent, and all the vocabulary for talking about me
has to be duplicated. One cannot simply say that the 4D perspective is got by
equating these (though that would be intuitively correct) as the ontology
itself would prohibit this equation.
[PC] >> If some person PH is classified in one ontology as
4D and in another as 3D, clearly the ontologies cannot be combined under the
assumption that the label PH applies to the same thing in the two cases.
It isn’t.
[PH] > Ah, but you see, it IS. That is the critical
point. Lets agree that I am what I am, the facts of my life are what they are,
and so on. Nobody will dispute any of this, let’s suppose. Still, two
philosophers can disagree about how all this stuff should be encoded in an
ontology. But they are both talking about the same person, the actual Pat Hayes
in the actual world. (If they aren't, there is something badly wrong with their
ontologies.) The two ontologies conceptualize me differently, but it is simply
factually wrong to claim that I am two persons, just because two philosophers
disagree about how best to describe me. Everyone agrees that I last for a time
and occupy space and have properties which vary with time, and so on. They just
disagree about how to formulate this in a logic. But neither of them thinks
that there are two Pat Hayeses, and any ontology which says there are is just
flat wrong. http://www.ihmc.us/users/phayes/PatHayes
denotes me, the actual me, here in the actual world.
[PC] >> In one case, it is a 4D entity whose lifetime is
PH4D and in the other case it is a 4D entity whose lifetime is PH4D, where the
‘lifetime’ is in the FO even if that concept is not in the 3D
ontology (actually, I use a “dimension-neutral object” to relate
the two). When the ontologies are translated or merged
[PH] > If you merge them, they will be inconsistent. I
agree that in many cases one can translate between the two points of view, but
its not easy and not always possible at all. I've never seen a program that can
do it.
[PC] >> , the different entities PH3D and PH4D are both
present, and assertions about the properties of one in 3D-speak can be
translated into assertions about the properties of the other in 4D-speak.
[PH] > Yes, though not always in the other
direction.
[PC] >> The problem here again appears (from
the description) to be an attempt to use the same term to refer to 2 different
entities –a terminology clash.
[PC] well, my point is that a 3D entity and it corresponding
4D entity are truly different though intimately related things, though they are
labeled by the same term by different people. One philosopher may
insist that only 4D entities exist, and another philosopher may insist that
only 3D entities exist. These are different **belief systems** about
their real world. As far as an ontological engineer should be concerned,
what “exists” is only what is or can be represented in an ontology,
and ontologically speaking, both 3D and 4D entities exist in that sense.
We can model the belief systems of those ontologists, by asserting the
“non-existence” in the sense that the philosophers are using, and
since both of those belief systems assert the non-existence of something that
is in the ontology, then whether these belief systems are or are not
inconsistent with the base FO (which has both kinds of entities) depends on how
one interprets the philosophers’ view of “exist”.
If it is identical to the logical “exists’ applying to axioms in
the ontology, there would be an inconsistency, and both belief systems would be
inconsistent – moved into a module in the “inconsistent”
set. The ontology would still be able to express assertions about the 3D
and 4D entities. IF the ontologists’ “exists” is
something different – existence in the real world, or in some ideal
world, then both theories individually would be consistent with the base FO,
though inconsistent with each other. Then they could be put into
different logically inconsistent extensions of the FO.
[PH] > But my point is that there is only one entity, in
fact. And it is important for an ontology to be able to say this, and clearly
draw appropriate conclusions. If I am in a room and nobody else is in it, there
is one person in the room. Not two people, one of them 4-d and one of them
3-d.
From an ontological point of view, I would say there are at
least two entities: a PH3D and a time-slice of PH4D. In fact, there are
an infinite number of time slices of PH4D, though one is likely to be concerned
only with one of them.
(5) [PC] >> , The FO needs to be permissive to
serve its purpose of translation. Where there are logical
inconsistencies, one or both of the candidate entities needs to be moved to an
extension (which can be logically incompatible with other extensions).
This decision would be taken by a vote of the executive committee for the FO
project.
[PH] > I cant help expressing my amusement at the
naiveity of this casual remark. Patrick, have you ever been on a standards
working group?
I have attended
meetings of some groups, and am aware of the difficulty of finding
consensus. But a practical project of this kind cannot depend on
consensus, there has to be a simple majority up-or-down vote on issues of
controversy, and very quickly. Anyone who cannot bear to participate
under such conditions doesn’t have to – that will be clear before
any organization work gets under way. I expect there will be enough people
oriented toward a practical solution to form the large community that is
required for this project. If not, the project will never start –
no harm done. This isn’t naïve, it’s practical and realistic.
(6) [PC] >> At this point we seem to be getting
redundant. I believe that these can all be described by a single set of
primitives, and apparently PH doesn’t think so. It
can’t be resolved here, and needs to be the subject of a proper
experiment.
[PH] > I know they cannot, and the 'experiment' is
already done. Those various temporal theories can all be expressed in
terms of three concepts: time-point, time-interval and duration. Duration
cannot be reduced to the other two (there's a model-thoeretic argument in the
paper) and the other two can be reduced to oine in some, but not all, of the
theories. That gets you down to two or at most three concepts, known to be
irreducible to smaller sets. And still, there are many variations possible in
the ontologies.
I am getting confused here. Your first sentence says the
time theories *cannot* be expressed by a small set of primitives, and
the seocnd sentence says they *can* be expressed by a set of three
primitives. I am clearly misundersanding something you are saying –
we must be using words in different senses.
Enough questions for now.
Pat
Patrick Cassidy
MICRA, Inc.
908-561-3416
cell: 908-565-4053
cassidy@xxxxxxxxx