On Sep 13, 2008, at 7:43 AM, Matthew West wrote: 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.
[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
not.
But here I think John is right, and that you are obliged, whether you
like it or not :-), to accept this distinction.
[MW] When I am obliged to I will of course accept it, but I am not quite done yet. Perhaps my mistake above was to make a general point, rather than to address the specific example. Under 4D featherless biped and human being do not have the same extension. Because under 4D we include things from the past as well as the present (not to mention things in possible worlds)
Well, just to be clear, including mythological entities into the universe is a decision which is orthogonal to the 3d/4d debate. But I agree with your approach here.
then featherless biped will include (from history) T. Rex, and from
mythology those creatures with a goats hind legs and a human torso and head.
My argument would be that for anything that is not provably equivalent,
there
is at least some possible thing in some possible world that is a member of
one but not a member of the other.
That seems to be the key. Your stance, then, is that intensional differences will always be revealed as extensional differences in some possible world: and if we agree to quantify panoptically over all entities in all possible worlds, then it will be an extensional difference. Ergo, intensional differences ARE extensional differences, if one casts ones extensional net widely enough. Good point, though to be fair to the rest of the philosophers, they are usually referring to extensions in the actual world (maybe an eternalist one, but still without unicorns in it.) Perhaps a more interesting example is one from mathematics, where (in a
flat 2D plane) the set of equilateral triangles is the same as the set of
equiangular triangles. Since we are dealing with universals here, possible
worlds does not come into it. However, in this case, though my geometry is
a little rusty, I anticipate that it can be proved that these are
equivalent,
so they are just alternative definitions of the same thing.
Well, then, you seem to be an extensionalist. A strict intensionalist position would be that there is a clear difference of meaning between 'equiangular' and 'equilateral', so these are two distinct categories, even if it is provable in geometry that they have the same exemplars. There are all kinds of intermediate positions available: on one view, categories which necessarily have the same exemplars must be the same, and then one can have further discussions about what counts as 'necessary' and so on. But the basic dividing issue seems to be whether or not one believes that a category (class, concept) is determined by its exemplars or not. The other differences arise from varying positions on what counts as an exemplar, etc..
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.
Of course, but that is the point. Extensionality *is* the decision to
identify predicates with sets.
[MW] Perhaps I am not clear enough. My objection is having to accept something set like whose membership can change with time. It may be my error to conflate that with intensionality.
I think it is, yes. Personally I have no objection to set-LIKE things which are dynamic: after all, everyday collections like flocks of sheep seem to have this character. But my point was that to call these sets is simply an error.
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).
A healthy intensionalist position regarding predicates. However, you
do need to say what it is they DO refer to, if its not a set. Common
Logic solves that problem for you, by the way.
[MW] That is useful. However, my definition of nonsense is a predicate that does not refer to anything. Could you remind me how Common Logic solves the problem please?
Well, it assumes up-front that distinct predicates can have the same extension. And what predicate symbols refer to is in CL are simply elements of the universe of discourse. So there are predicates, which are first-class elements of the universe about which you can make any axiomatic theory you like, and their extensions, which are sets. And CL cleanly maintains the distinction for you, without needing to make any special effort in the ontology. You don't have to get your knickers in a twist trying to say what an intensional predicate *is*: you can just write axioms about them. CL brings them from the realm of philosophy into that of axiomatic ontology.
.... Bottom Line
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.
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)?
Physical (spatiotemporal) particulars. The number 7 is a particular
but isn't spatiotemporal. Here's another way to say it: can something
occupy space without occupying time? Yes (continuants) or no ("4-d")?
[MW] Yes. At present ISO 15926 treats numbers as classes, and I appreciate that is not the only, and may not be the best approach.
Hmm. I would prefer to treat numbers as numbers, myself. 2. Extensionalism (or not) in particulars.
i.e. if particulars coincide, are they the same thing?
Do you mean spatiotemporally coincide? Like a bottle and the glass it
is made of?
[MW] Yes, but the bottle and the glass it is made of will only coincide accidentally. The usual case is that the temporal extent of the glass is greater than the temporal extent of the bottle, and indeed the bottle is a state of the glass. This also means that bottle is not a subtype of glass-object (the whole of its life), but state-of-glass-object
Its not hard to imagine a scenario in which the thing and the piece of stuff exactly coincide in 4-d. Consider for example a bottle made of some heat-formed polymer, which is made by blowing a gas into a hot mold, and comes into existence in the form of a bottle; and then ends its life by being incinerated in a flash furnace. Here the bottle and the piece of stuff of which it is made occupy the exact same 4-d history, but some folk would still want to distinguish them. For example, someone might want to assert a property of one but not the other. I agree its much less plausible to want to make the distinction in cases like this, but I can see a pragmatic reason for doing so, which is that we make the distinction in the more usual cases, perhaps for good extensionalist reasons, so why should we be forced to not make it here?
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?
Also possibilism: even hypothetical things exist. But this 'exists'
has to be taken with a pinch of salt, or at least clarified, as it
really doesn't mean what people ordinarily mean when they talk about
the world in English. We say things like, "The hadron supercollider
didn't exist in the sixteenth century." I suggest a better (less
confusing and contentious) way to say it is, the logic admits all
possible, future and past entities in its universe: they all
*logically exist*. But only a small fraction of the things that
*logically exist* ACTUALLY exist (i.e. in the actual world, now). So
actual existence is a predicate (or a type, if you like) in the
logical description. To 'logically exist' simply means that it is a
thing that can be referred to, can be discussed, can be given a name.
So this is really only another way to say that all names refer, which
is the basic semantic assumption of logic.
[MW] Well I'm nearly with you here. For me actually exist means everything in our universe, for all time, and not restricted to now. That would be a further restriction.
Speaking like an ontologist, I agree. But when you aren't doing ontology, do you really talk this way? Would you say that Julius Caesar exists, in the same sense that (unfortunately) Sarah Palin does? ....
Now my choices are:
- Temporal Parts
- Extensionalism for particulars
- eternalism
- Extensionalism in sets
I agree except for the second. Don't you want to be able to
distinguish the bottle from the glass out of which it is made? Or have
I misunderstood what you mean by this?
[MW] No you have not misunderstood, but I can distinguish between the bottle and the glass (see above) and when I can't it does not matter, because any statements I would make about it as one would also be true of it as the other.
An intensionalist is going to say: but it may be true to say of the bottle that it could have been made of polythene; but it is nonsense to say that a piece of glass could have been made of polythene. I know how you will get past this objection, but it illustrates that you have to be careful when you say 'any statement'.
But this is philosophical debate, and IMO somewhat irrelevant for Working Ontology :-)
Pat
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