Dear Matthew and Chris P., (01)
In my previous note, I forgot to comment on the following point: (02)
MW> One of the attractions to me of 4D with possible worlds is that
> you do not need types, because 4D essentially makes things timeless
> and unchanging, and possible worlds allows you to deal with the
> intentional. (03)
There are very strong reasons for distinguishing sets and types,
independently of your ontology for time and space. (04)
For example, the set of all unicorns and the set of all motherless
cows happen to be identical, namely the empty set. But their
definitions are not equivalent. (05)
There are also many sets that have a type constraint on their members,
such as the set of all cows in Nebraska. It is very difficult to
specify that set by enumerating its members, but if you see any cow
in Nebraska, you immediately know that it is a member of that set. (06)
CP> Agree with Matthew about the 4D stuff.
>
MW>> Interestingly here it is membership that is the root primitive,
>> rather than set or type... (07)
The term 'instance' is used with types: x is an instance of a type T
and a member of the denotation of T. (08)
Even if you use a 4D ontology for the physical universe and you
avoid the word 'time' for talking about computations, it is
convenient to talk about "states" in an abstract machine.
Those states correspond to the possible worlds or situations
in the physical world, but they are independent of any
implementation, physical or imaginary. (09)
In a typed programming language, the instance associated with
a particular name always has the same type, even though its value
may change. In an "untyped" or "typeless" language, a name may
be associated with values of different types in different states. (010)
So let's be very precise in our terminology. The type/set
distinction is independent of religious convictions about the
nature of space and time. (011)
John (012)
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