On Oct 8, 2009, at 2:49 AM, Matthew West wrote: (01)
> Dear Pat,
>
>>> Dear John,
>>>
>>>>
>>>> MW> ... if I want to talk about 2 eyed sheep and 4 legged sheep
>>>>> and determine if they are necessarily the same, then I need
>>>>> only use sets that that go across all possible worlds.
>>>>
>>>> But those sets are purely imaginary.
>>>
>>> MW: Lewis would disagree with you. He claims that they are real
>> and
>>> not
>>> imaginary, hence modal realism. This is really a feature of 4
>>> dimensionalism though. In 3D only the present exists, and neither
>> the
>>> future or past do, whereas with 4D both the past and the future
>>> exist as
>>> well as the present. I am therefore not surprised that he chooses
>> to
>>> claim the possible worlds exist too. On the other hand I am
>>> indifferent,
>>> since it seems to me to make no difference.
>>
>> A point that might be relevant is that the 4D approach gives a
>> natural
>> account of what a possible world is. Lewis had to simply propose
>> that
>> they existed, a stance that was never widely popular, to put it
>> mildly. But if we accept that 4D histories - spatiotemporal
>> envelopes
>> of events and physical existence - are real, and if, as seems very
>> natural, we assume that they can stand in a relationship of
>> containment to one another, ie have a mereology, and if we make a
>> few
>> very natural assumptions about this relationship, then one can show
>> mathematically that there must be maximal elements in the space of
>> 4D
>> histories (maximal ideals in the order structure), and these play
>> exactly the required role of possible worlds. So a possible world
>> is
>> simply a largest chunk of 4D space. Which is a very nice picture,
>> seems to me.
>
> MW: Yes, I had worked that out too. I also like extend this to
> think of
> branching worlds. So, for example, that all the possible worlds from
> here have up to here as a part, and have different parts hereafter.
> That
> gives another level of aggregation around all that is possible from
> here
> (or wherever else you choose to branch from). (02)
Indeed, but (what I especially like) is that it gives many other ways
to 'branch', eg outwards spatially from a locally described situation,
or backwards in the time-direction, when figuring out how something
that did happen could have happened. (03)
>>
>> Matthew, do you know if this has been developed by anyone and
>> written
>> up? I had meant to write it years ago, but never got around to it.
>> If
>> I havnt been gazumped yet, I might put it on the list of things to
>> write when I retire.
>
> MW: I'm writing a book at the moment, and it will cover this to some
> extent (I hope) but at a popular rather than academic level. Chris P
> is
> the person to ask if it has already been written up properly
> somewhere.
> He's read everything and is a sponge for this stuff.
>
> Chris, Can you give us chapter and verse? (04)
I'd be grateful, yes. (05)
Pat (06)
>
> Regards
>
> Matthew West
> Information Junction
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