Dear Matthew, (01)
Some comments on your comments from different, but related notes: (02)
JFS>> Making a clear distinction between actual sets and hypothetical
>> or imaginary sets would be useful. (03)
MW> In ISO 15926 we used the term "class" for this. An overloaded
> term I know. But I'd rather not start inventing new ones. (04)
I would recommend an adjective. Instead of using two different nouns,
such as 'set' and 'class', it is much clearer to use one noun 'set'
as the general term and add different adjectives to distinguish
which kind of set you are talking about. (05)
JFS>> But those sets [in possible worlds] are purely imaginary. (06)
MW> Lewis would disagree with you. He claims that are real
> and not imaginary, hence modal realism. (07)
Lewis was using the term 'realism' in contrast with 'nominalism'.
A strict nominalist, for example, would say that the so-called
laws of nature are merely summaries of observations. But realists
would say that any law that has been sufficiently tested, such as
the Law of Gravity, is based on something real -- i.e., the law
is an indication that there exists some *real* mechanism that is
responsible for the observations. (08)
When people like Lewis say that there are such things as "real
possibilities", they use examples such as the following: (09)
If I hold a pencil in my hand, I predict, with a degree of
certainty that I would back with a wager of any amount you
care to bet, that if I let go of the pencil, it will fall
to the floor. (010)
Many people who are realists about physical laws would say that
the possibility that the pencil would fall to the floor is real.
In short, it is a "real possibility". I am willing to accept
that terminology. (011)
However, saying that there are real possibilities does not imply
that those possibilities are actualized. When I drop that pencil,
the "mere possibility" becomes an actuality. Until then, its
mode of existence is not the same as what non-philosophers would
call "real". Despite my willingness to accept the term 'real
possibility', I would still call an unactualized possibility
"imaginary". (012)
If you prefer a different word, please suggest one. But it's
important to recognize that real, but unactualized possibilities
are not "really real" in the sense that ordinary people use. (013)
JFS>> Therefore, any use of set theory for representing physical
>> entities must recognize that a set at one instant of time is not
>> "exactly the same" set of supposedly "exactly the same" things
>> at any other instant. (014)
MW> However, 4D neatly sidesteps this with states/stages/temporal
> parts. The temporal part is unchanging and always a member of
> the sets it is a member of. This is why 4D and set theory fit
> well together. (015)
I'm sorry, but that is not a solution. Note that the person I
quoted about the difference between the baby in the cradle and
the grown man was Alfred North Whitehead. He had also developed
one of the most detailed and elaborate 4D ontologies. In that
quotation, he just happened to use a short illustration, but
the point he was making is completely independent of 3D vs 4D
ontologies. In fact, time is irrelevant to his argument. (016)
For the record, I'll repeat the quotation before the example
of the baby in the cradle: (017)
ANW> In logical reasoning, which proceeds by use of the variable,
> there are always two tacit presuppositions -- one is that the
> definite symbols of composition can retain the same meaning as the
> reasoning elaborates novel compositions. The other presupposition
> is that this self-identity of each variable can be preserved when the
> variable is replaced by some definite instance. (018)
The fundamental distinction is between mathematical entities and
physical entities: (019)
1. The great developments in 20th century logic and set theory
were applied to purely mathematical topics. For those subjects,
there is no need for epistemology or scientific methodology to
determine whether two variables refer to "the same thing". (020)
2. But things in the real world (and I mean "really real") are
messy, and determining identity is nontrivial. Just note
the difficulties in criminal investigations and court trials.
The same kinds of complexities arise in scientific experiments
and engineering measurements. (021)
I agree that a 4D view is conceptually cleaner than a 3D view
for many of the theoretical discussions. But it's essential
to note that the only direct knowledge we have is of the
immediate present. The past is known only from memory or
from records whose reliability has to be determined. And
the future is totally unknown. (022)
When dealing with the real world, you can't do ontology
without getting into all the problems of epistemology. (023)
PH>> There are some cases that have been discussed in (at least)
>> moral philosophy, involving identical twins, which at a very
>> early stage of fetal development, in some cases, were one
>> blastula. If life begins at conception, this is a difficulty. (024)
MW> What I like about 4D is that it allows this to be explained without
> giving rules that forbid it as a matter of principle, but which also
> does not make or force a choice about which twin, or either or
> neither or both split from which. It just allows the situation to
> be described. (025)
No. The entropy gradient defines a time arrow through a 4D extent that
clearly identifies before and after. Theologians since Thomas Aquinas
talked about 4D views, and they don't let you off the hook. (026)
John (027)
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