The Cosmological Argument
Gene Ward Smith
>In article <15...@ucbvax.BERKELEY.EDU> gsm...@brahms.UUCP (Gene Ward Smith) writes:
>> We can do this a little differently: we can look at everything that exists
>>and the relation "<" of ontological dependence ...
>>Zorn's lemma says that there are maxima under ontological dependence.
>Extrapolating logic and set theory outside our universe is questionable,
>at best. I see no reason why any theoretical god need be bound by some
>descriptive laws invented by men to describe the behavior of
>mathematical sets that they created to describe the universe around
>them.
Well, I agree with you, sort of. But I think logic and set theory are
more universal than you think. In particular, set theory was invented to
talk about mathematical reality (sets of real numbers, etc.) and not
the universe around us.
>In particular, I cannot see why we should grant Zorn's Lemma.
>Mathematicians generally prefer to have proofs that do not depend on the
>Axiom of Choice or its equivalents.
Most mathematicians could care less, a few strange ones do. By the way,
there is an old joke to the effect that the existence of God is equivalent
to the Axiom of Choice: since Zorn's lemma => God exists and God exists =>
God can do the choice routine, and hence the Axiom of Choice is true.
>I feel that somehow any theoretical god is belittled by being dependent
>for its very existence on Zorn's Lemma.
This is not what the argument says, so I wouldn't worry about it.
ucbvax!brahms!gsmith Gene Ward Smith/UCB Math Dept/Berkeley CA 94720
"*That* the world is, is the mystical." -- Ludwig Wittgenstein
John Chambers
> universe = R0 < R1 < R2 ... where "<" means "explains" or "causes to be".
> We may assume X < Y < Z => X < Y. Let us suppose also that X < Y & Y < X is
> impossible; that is, two *different* things cannot provide mutual explanations
> for the other's existence.
Leaving aside the rest of this for others to hack apart, I'll
jump into the fray by attacking this point. At first glance,
this seems like an intuitively reasonable assumption, but that
just goes to show how feeble a think intuition is. Biologists
quite frequently invoke arguments in which X < Y & Y < X.
How so? Well, consider the evolution of the ornate reproductive
structures we call "flowers". It seems quite clear that these
evolved in response to the pollinating behavior of insects (and
possibly a few birds). On the other hand, the insects' behavior
clearly evolved as to take advantage of the existence of flowers.
Thus we have:
X = Insects visit flowers, consuming nectar and/or pollen,
and incidentally cross-pollinate the flowers.
Y = Plants produce flowers that announce the presence of
nectar and pollen.
It seems quite clear that X < Y, and also Y < X. That is, without
the presence of pollinators, flowers wouldn't have evolved; without
the presence of flowers, insects would do little if any pollination.
This is usually referred to as "co-evolution".
A similar situation exists with the evolution of edible fruit,
which are devices that plants use to trick large animals (mostly
birds and mammals) into scattering the plants' seeds and fertilizing
them as they sow them. Fruit evolved because there were animals
around willing to eat them; the animals eat them because the
plants supply them.
Perhaps I should put "because" in quotes. The concept of "causation"
here is a bit different than what most theologians and philosophers
have dealt with. Note especially that this interpretation of the
concept doesn't require purpose and/or intelligence on the part of
the agents.
--
John M Chambers
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