>Indeed. And of course, change occurs in the real world and is
>described by both 3-d and 4-d ontologies, but in different ways. This
>is so obvious that nobody felt any need to say it. (01)
Some of this discussion of change and 3d and 4d seems to be covering (very)
old ground. (02)
It is my impression that in the philosophical tradition that in time gave
rise to the short names 3d and 4d (I think these are only decades old), it
is usual to say that the 4d view denies the existence of change. (03)
See. For example, http://plato.stanford.edu/entries/change/
Where it has the nice comment: (04)
It is on the face of it extremely implausible to deny change, but extreme
implausibility has not always deterred philosophers. The Eleatics (C5th
BCE), particularly Parmenides, appear to have been the first to do so. (05)
More recently - McTaggart, J.E., 1908, "The Unreality of Time," - with
Series A and B. And then a plethora of authors in the last few decades. (06)
As this and other entries in the site explain, the issue is how we explain
the changes we see - and 3d and 4d are alternatives. (07)
see also http://plato.stanford.edu/entries/temporal-parts/ - Change] (08)
Take the definition of an ontology as the set of things that exist, and we
start compiling our list .... (09)
Then in the traditional Aristotle 3d view, there are objects that are
changes. For example, my movement from A to B. (010)
In the 4d view, my movement from A to B consists in my being 'at' A at time
t1 and 'at' B at time t2 (Russell characterised this as an at-at
description). (011)
One can of course, and philosophers like to do it, take elements of the 3d
and 4d view and concoct gerrymandered positions, where something that looks
3d has 4d elements. (012)
One may also take issue with the basic claim about change. But from a
historical point of view, I think there is a good (overwhelming?) case for
saying that the 4d position has been characterised for some time as denying
the existence of change (in the sense described above). (013)
One can add the gloss that 4d-ists (Parmenideans) did not really mean that
change could not be described in a 4d view - but it seems to me odd to claim
that 4d has not been characterised as denying the existence of change, and
also to miss an insight into how the position arose, if not into what it is. (014)
BTW Pat's comment copied in at the top "of course, change occurs in the real
world" would seem to give precedence to the 3d view that changes should be
on our ontology list. But I have taken it out of context. (015)
Chris (016)
>-----Original Message-----
>From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
>bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
>Sent: 12 September 2008 18:16
>To: [ontolog-forum]
>Subject: Re: [ontolog-forum] Thing and Class
>
>
>On Sep 12, 2008, at 1:11 AM, John F. Sowa wrote:
>
>> Dear Matthew and Pat,
>>
>> MW> The real difference is that 3D sees that what exists now is all
>>> that exists, whilst 4D sees the past and the future as part of
>>> what exists as well as the present. This is what it means to stand
>>> outside time.
>>
>> I agree with that description, but you seemed to suggest that the
>> notion of change does not exist in a 4-d view, but I think that
>> we were using different definitions of 'change'.
>
>Indeed. And of course, change occurs in the real world and is
>described by both 3-d and 4-d ontologies, but in different ways. This
>is so obvious that nobody felt any need to say it.
>
>>
>>
>> MW>> all spatio-temporal extents exist (at all times, but
>>>> strictly independent of time).
>>
>> PH> Agreed, and a nice analysis. Putting the same point in logical
>>> terms, the universe of discourse shouldn't be in a state of flux,
>>
>> I have no quarrel with that, but it has nothing to do with the
>> definition of the concept of change.
>
>BUt that, unlike the 'concept of change' , is what the thread was
>about until you introduced this irrelevant aside. I think you can take
>it that most of us don't need elementary calculus explained to us
>again, John.
>
>> According to the most common
>> definition, if time slices at t=0 and t=1 are identical, there is
>> no change.
>>
>> Another way to say it: if the partial derivative with respect
>> to the time coordinate is 0, there is no change; otherwise, there
>> is change in that region of space-time. The existence of change
>> does not imply that the global 4-d universe is in flux. It just
>> means that there is some region in the universe where the derivative
>> with respect to time is not zero.
>
>Quite.
>
>>
>>
>> MW>> And interestingly, I again use possible worlds as an alternative
>>>> to modal logic. Not that I object to others using modal logic, but
>>>> I do not see that I am obliged inevitably to do so.
>>
>> PH> Again, I agree that this is the best approach. I think this is
>>> widely accepted, by the way: John McCarthy made the same point many
>>> years ago :
>>> http://www-formal.stanford.edu/jmc/modality/modality.html
>>
>> I believe that what John McC, Matthew, and Pat are recommending is
>> very close to Dunn's semantics for modal logic.
>
>Not McCarthy or me, I am quite sure; and given his stance on 4-d
>extensionality, I doubt if Matthew is either.
>
>>
>>
>> Most AI work with "possible worlds" is actually based on metalevel
>> reasoning about sets of propositions that describe those worlds,
>> not with the worlds themselves.
>
>Wrong. It is based on - it actually uses - inferences made in a theory
>which refers directly to the worlds. Any planner which has an explicit
>notion of time-interval or time-point or 'situation' (as in sit.
>calc., not situation theory) or world-state or context, is reasoning
>in a theory whose semantics is more Kripkean than Dunnian. (For an
>early exposition of the relationship of situation calculus to Krikpe,
>see section 4 of McCarthy & Hayes 1969.) None of this is based on
>METAlevel reasoning about sets of propositions. Of course, like all
>reasoning, it is PERFORMED by sets of sentences, but it is not ABOUT
>them.
>
>> Starting with any Kripke model
>> K=(W,R,Phi), where W is the set of words, R is the accessibility
>> relation among worlds, and Phi is the evaluation function, those
>> sets can be derived:
>>
>> 1. For each word w in W, define the facts of w as the set of all
>> propositions p that are true in w: {p | Phi(w,p) = True}.
>>
>> 2. Define the laws of w as the set of all propositions p that are
>> necessarily true; i.e., p is true in all worlds accessible from w.
>>
>> 3. Define the accessibility relation R(w, w') as True iff every
>> proposition p that is necessarily true in w is also true in w'.
>>
>> This construction replaces every world in a Kripke model with a set
>> of laws and facts in a Dunn-style model. Any theorem that can be
>> proved about a Kripke model is also true of the corresponding Dunn
>> model. But Dunn's version is more *usable* because it makes the
>> laws and facts available for further analysis and manipulation.
>
>Nonsense. Not only is Dunn's version not more usable, it is not in
>fact used. The laws and facts are stated explicitly as sentences in
>theories using Kripke-style semantics. Check out any of the hundreds
>of papers on planning using a situation-calculus style of
>representation.
>
>> PH> John's way follows Dunn's theory and is based on intensional
>>> descriptions. The far more commonly used view uses Kripke's
>>> possible-worlds account of modalities. Kripke's is widely accepted
>>> as the standard, and certainly gives a more usable semantics...
>>
>> Not true. Nobody actually implements "possible worlds"
>
>I never said they did. They implement systems which reason, using
>formalisms which refer to possible worlds. Remember, we are talking
>here about SEMANTICS, not implementation.
>
>> . What they
>> implement and reason with and about are sets of statements of the
>> laws and facts of those worlds.
>
>Yes, exactly. And the question is, what is the appropriate SEMANTICS
>for those statements? Answer: they REFER TO possible worlds. They do
>not refer to sets of sentences; they are not in a METAtheory.
>
>> Since the above construction can
>> map any Kripke model into such sets, most people who implement such
>> systems pay lip service to Kripke's version, but they actually use
>> something that is much closer to Dunn's version.
>
>They - and here I speak as one of them - use Kripke-style semantics
>when doing semantic analysis. They do not, as a broad rule, use Dunn-
>style semantics. In fact, I do not know of any significant body of
>work in AI planning based on Dunn-style semantics. I believe you are
>the only writer who argues for Dunn's model in this context.
>
>Pat
>
>>
>>
>> For further discussion of these and related issues, see
>>
>> http://www.jfsowa.com/pubs/laws.htm
>> Laws, Facts, and Contexts
>>
>> http://www.jfsowa.com/pubs/worlds.pdf
>> Worlds, Models, and Descriptions
>>
>> John
>>
>>
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