Dear John, (01)
I know we usually agree on most things, so here I am going to try to
tease out what if anything we might disagree about here. (02)
> First of all, I strongly endorse the 4-d view, and I believe that
> it is preferable to a 3-d view for many problems. However, I don't
> believe that there is any ontology that is ideal for all problems. (03)
[MW] Yes, that is my position too.
> JFS>> Whether you have a 3D or a 4D perspective, change still exists,
> MW> Not really. 4-Dimensionalism has the effect of making 3D change
> > seem static, because it is looked at in a different way, in 4
> > dimensions instead of 3.
> The basic laws of physics are stated in differential equations, which
> are "almost" symmetric with respect to the space and time coordinates.
> I use the term 'almost' because entropy creates an "arrow of time",
> which breaks that symmetry. In relativistic terminology, the arrow
> of time defines a *light cone* that delimits the causal influences.
> If you look in the direction of that arrow, you find increasing
> entropy. But there is no such distinction in any of the spatial
> coordinates. (04)
[MW] Again I agree, but this is not really the root of what is different
between 3D and 4D. 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
If you think about it this is necessary when you accept that things have
temporal parts. If things have temporal parts, then those temporal parts
must exist, but they are extended in time, so things that are not simply
"here and now" must exist, i.e. all spatio-temporal extents exist (at all
times, but strictly independent of time). Now when I was saying it was
natural in 4D that the set of, say cars, was the set of all cars that ever
existed, that is because it is natural for the set of cars to be the set of
all cars that exist, and since that is the set of all extents that are cars
for the whole of their lives, then that is naturally the set of all cars
that ever existed or will exist (to put it in 3D terms).
> MW> ... extensionalism in classes is quite natural when you have
> > dealt with change in the way that 4-dimensionalism does.
> I'll avoid getting into debates about what is 'natural', but I must
> emphasize that the distinction is independent of time or change.
> In my previous note, I made that point by talking about hypothetical
> issues, but the same point can also be made in terms of modal logic. (06)
[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.
> Second, the distinction can be seen very clearly in examples such as
> the types HumanBeing and FeatherlessBiped, both of which have the same
> extension, but different intensions. It's irrelevant whether those
> two types have the same extension in a 4-d universe or for all time
> in a 3-d universe. They are not provably equivalent according to
> the usual definitions of the terms. Therefore, they are different
> by intension, and only accidentally the same by extension. (07)
[MW] Again, I do not object to others choosing to follow this route,
I only say that I am not inevitably obliged to do so, and in fact do
What you say is very "natural" for someone with a background in logic
and traditional set theory which has a strong emphasis on predicates
equating to sets or types, but this is not an inevitable choice. For
example, I prefer to say that sometimes predicates do not refer to a
set (e.g. Russels paradox), and sometimes more than one predicate refers
to the same set (e.g. your example above).
> JFS>> In any perspective, you must be able to plan for the future,
> >> talk about what exists NOW, or what exists in some hypothetical
> >> time or place that might never exist anywhere in the 4D universe.
> MW> Yes. But in a 4-dimensional world view, all of this can be dealt
> > with extensionally, so why wouldn't you?
> You wouldn't in either 3-d or 4-d because it's impossible. Many more
> things are planned than are ever implemented, and many things that are
> implemented have no little or no resemblance to the plans. Therefore,
> you must be able to talk about the *type* of airplane because the set
> is very likely empty in any or all ontologies. And there is exactly
> one empty set: the set of all unicorns is identical to the set of
> all airplanes with flapping wings. (09)
[MW] This is just another case that is covered by possible worlds. Plans
are about possible worlds you wish to bring about, but often they do not
coincide exactly with the real world, and they can include entirely
worlds in which unicorns do exist, and then I can quantify across these
possible worlds and not end up with the empty set.
> MW> Well you can do the usual things with possible worlds to deal
> > with That [hypotheticals], so no great problem there.
> But we cannot observe, visit, or manipulate possible worlds. (010)
[MW] But we can talk about them and say "What if?" which is the usual use
I find for these in practice. (011)
> When we reason about possible worlds and entities on our computers,
> we are actually using intensional descriptions of the hypothetical
> entities to create 'virtual' extensions. (012)
[MW] I suggest that using possible worlds is not necessarily restricted
to this. I see the entities as existing in the possible world, and not
> Even with our actual world, it is impossible to deal with extensions
> for most of the things we talk about. Census takers are well aware
> of the difficulty of enumerating all the people in a single city.
> Imagine trying to enumerate or reason with the set of all mice,
> flies, or bacteria in a city. We must reason with intensional
> descriptions because it's impossible to deal with the extensions. (013)
[MW] Ah! OK. Here we need to distinguish between what is and what we
know. Ontologically, the set of people in a city (at a point in time)
does exist, but we may not know all the members. That does not make the
set intensional, nor does it mean the set does not exist, it only means
we do not have complete knowledge about it. (014)
This brings some practical problems, but it is not an ontological reason
> MW> They [differential equations] are just descriptions of 4D
> > objects, just as a quadratic can describe a line in two dimensions.
> Yes, indeed. Those equations are *intensional* characterizations
> of entities that might or might not exist in any world, independent
> of whether the ontology happens to be viewed in 3-d or 4-d terms. (015)
[MW] I see these as properties that all members happen to have. That
might be why a particular set is interesting, rather than another one.
> MW> However, a 3D ontology will be predisposed to an intensional
> > approach, whereas I find with a 4D ontology an extensional approach
> > is more natural.
> In all of your examples of hypotheticals and plans, you were talking
> about the intensional characterizations. So you were doing what I
> was suggesting: talking about intensions. (016)
[MW] I agree I am "talking about" the same things, but in different
Bottom Line (018)
There are a number of ontological positions that you need to choose
between, and it seems to me that we have not made all the same choices,
and this is what is resulting in the differences we have found here. (019)
The key choices that seem to me to be relevant here are:
1. Do particulars have temporal parts or not.
i.e. are particulars extended in time as well as space (or not)?
2. Extensionalism (or not) in particulars.
i.e. if particulars coincide, are they the same thing?
3. Eternalism vs presentism.
i.e. is everything that exists what exists now, or is everything that
exists include all that exists in the past and the future?
4. Extensionalism in sets/types/classes vs intensionalism
i.e. if two sets/types/classes have the same membership, are they the same. (020)
Now my choices are:
- Temporal Parts
- Extensionalism for particulars
- Extensionalism in sets (021)
>From the way you are talking you choices would seem to be:
- Temporal Parts
- (not clear from these discussions, but probably extensionalism for
- Presentism (the membership of types changes over time)
- Intensionalism (022)
Now none of these choices are a free lunch it seems to me, and various
can make sense, though I think there are some that do not, and there are
choices to be made beyond these (like possible worlds and modal logic). In
the most important thing is to be clear about the choices you have made, and
be consistent, rather than that there is only one "right" choice that can be
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