eep! Aside from the typos, i think the cl snippet i posted
was actually a second order statement. Regardless however, any CL axioms would
be along those lines.
Some other corrections, Gibson's work touches on the
equivalence starting from section 6.3.2 (not 6.4), and his work can be found
Additionally, the following paper by Varzi may clarify some
additional question re the relationship between the two views:
Varzi (2007) - Promiscuous Endurantism and Diachronic
Vagueness - Ameri Philo Quart
And finally, in case people would object that this
inter-translatability (indeed, quite explicitly, not ontological
equivalence), would force one to countenance types of entities in their
ontology that they would rather not, in the 3D view, importing 4D objects actually
imports pairs of objects. Admittedly, this would restrict one's ability to
quantify over the resultant entities.
Conversely, in the 4D view, importing 3D objects would
amount to importing instantaneous slices of the object -- you never have to
directly admit the existence of things you don't want in your ontology.
[MW] I don’t think you import objects. From 3D objects in
a 3D ontology, you imply the existence of 4D objects that are equivalent, and
where it is possible you do the same in reverse, for many 4D objects you can
imply the existence of a 3D object at a time or times. Noone should be offended
unless one object has to be both 3D and 4D.
I guess, if there are no serious errors in this email and
the last, are there any practical considerations which might hinder such
interoperability (aside from the non-existence of axioms thus far)? Is
the 3D-4D debate really an issue for people developing actual ontology
[MW] Probably not at present, because most people developing an
ontology pick one or the other at the outset (or both as in BUFO for different sorts
of things). The interest comes when you want to interrelate existing
ontologies and/or use them together.
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On Tue, Mar 10, 2009 at 12:11 PM, Ali Hashemi <ali.hashemi+ontolog@xxxxxxxxxxx>
For those who are interested, check out:
- Mark Hinchliff (1996), The Puzzle of
Change. Philosophical Perspectives, 10, Metaphysics, 1996. pp.
for a nice overview of the issues at hand here.
- Trenton Merricks (1999) Persistence, Parts
and Presentism, NOUS 33:3 (1999) 421-438
we get two nice definitions of the two accounts:
(1) For any presently existing object 0, 0 endures if and
only if 0 persists
and all of O's parts simpliciter exist at the present time.
We can give a parallel account of what it is for an object
(2) For any presently existing object 0, 0 perdures if and
only if 0 persists
and some of O's parts simpliciter do not exist at the
- Storrs McCall & EJ Lowe (2003). “3D/4D
Equivalence, the Twins Paradox, and Absolute Time,” Analysis
63, pp. 114–23.
- McCall & Lowe (2006). "The 3D/4D
Controversy: A Storm in a Teacup." NOUS 40:3 (2006)
we get an argument for the equivalence of the two
perspectives. They come closest to actually positing axioms showing
The reader will have noticed that there is a close
similarity between the set
of 3D particles which constitute an enduring object O at a
time t, and the
instantaneous 4D temporal part of O at t. This fact provides
for a simple
translation scheme between the 4D temporal parts ontology
and the 3D
particle ontology. Let T(O, t) be the instantaneous 4D
temporal part of O at t,
and let <O, t> be the instantaneous 3D sum of the
particles which constitute
O at t. In 4D ontology, O is the mereological fusion of all
its temporal parts
T(O, t), one for each moment at which O exists. In 3D
ontology, O is the
set of particles which successively constitute it at each
moment O exists, a
set which “changes”, i.e. is replaced by a new
set, each time O gains a new
particle or loses an old one. To translate from the 4D to
the 3D description
of O, reduce O to its temporal parts, and replace each
temporal part T(O,
t) by the momentary sum <O, t> of particles which
constitute O at t. The
collection of all such momentary sums <O, t>, for
every time at which O
exists, yields the set of sets of 3D particles which
successively constitute O.
Conversely, to translate from the 3D to the 4D description of
O, first reduce
O to the momentary sums of particles which constitute it,
then replace each
<O, t> by the corresponding temporal part T(O, t),
then reconstruct O as
the fusion of its temporal parts.
I haven't been successful at finding people who disagree
with McCall and Lowe's observations, the closest is in a phd thesis found here:
Gibson (2007) Time, Objects, and Identity - pihlisci
archive, Oxford PhD (section 6.4).
He argues, (rightly imo) that their appeal to particles is
unnecessary and potentially distracting. He also seems to assert that their
position is of ontological equivalence, tho McCall and Lowe never explicitly
state this. These two points aside, Gibson's major quibble arises from the
equivalence between 4D-3D being based (implicitly) on linking X with "the
life of X." Based on this, Gibson notes that the parts of one's life are
not equivalent to X himself. I don't agree with this line of reasoning as it
seems to me he is conflating several senses of life to derive this apparent
oddity, the sense of life required for the mapping to work is exactly that
which captures X and his properties as the parts of X's life. Whether this is
too technical a definition to be palatable is another issue, which imo, doesn't
affect engineering / business considerations. If it is so objectionable, let's
call it not "life of X", but "X through his life."
Anyhow, I thought I'd post this to the forum and see what
people have to say.
For the record, I don't believe that the 3D-4D translation
provided in McCall and Lowe (2006) is ontological equivalence. Moreover, for
someone developing ontologies for practical applications, i think logical
equivalence suffices. Anyone disagree?
Finally, as many have pointed it, we haven't really come
across any ontology which has formalized these notions of perdurance and
endurance. I would imagine if one wanted to actually enforce a 4D view in an
ontology, they'd need a second order axiom, otherwise, they could use CL's
ability to quantify over explicit relations via an axiom similar too
whenever you have a relation (i.e. Rel1) you want to
be restricted to the 4d view, you would state:
(forall (Rel1) (4DRel Rel1))
then you would have to have something akin to:
... t) (time t) (argument ...) )
with appropriate axioms to define what an argument is.
Though this style is coming perilously close to mixing meta concepts with the
Yet without a set of axioms, whether at the metaontology
level or within the ontology, it is nigh impossible to develop a mapping
through which one could prove, at least, logical equivalence between the two
As Michael Gruninger pointed out though, there is high similarity
between the notions of 3D-4D and time intervals and time points. While the
latter are clearly not ontologically equivalent, their extensions may be mapped
to logical equivalence over particular domains.