Re: Problems for solutions

[Tim Gwinn <***>]

Dan,

I?d say that mechanism is not so much an opposite, or is complementary, to
life as you mention below, as it is a too-restricted paradigm for answering
the question ?why life??. A mechanistic paradigm is merely a subset, if you
will, of the Rosennean paradigm. Mechanism is just the Rosennean paradigm
with the added constraint of Church?s Thesis imposed on it. So, its not so
much that life is opposite to mechanism, as it is that some questions about
life and living things require the larger universe of discourse to be able
to state the answers (and perhaps, even to state the problem); other
questions about living things can be answered happily within the subset of
the Rosennean paradigm known as the mechanistic paradigm.

The constraint of Church?s Thesis makes mechanism a degenerate universe of
discourse, capable of limited kinds of models and explanation. Removing that
constraint brings us from the degenerate to the generic. Kercel used
hyperset theory to model impredicative structures (such as the Liar
paradox). The structures (i.e., the structures of the sets) created using
the usual predicative set theory are a subset of the universe of structures
available in hyperset theory. This is due to the nature of the Foundation
Axiom which imposes restrictions on set structures and is replaced with the
looser Anti-Foundation Axiom in hyperset theory. So, this is also a case
where what was needed was not so much the invocation of some incompatible
universe of discourse to normal set theory, but simply an enlarged universe,
which hyperset theory provides.

There is no conflict or antagonism between sets with impredicative
structures and those without in hyperset theory. Likewise, there is no
conflict or antagonism between complex models and mechanistic models in the
Rosennean paradigm. In either case, we can?t reduce the former to the
latter, but that is not really a conflict per se. To me, the potential for
conflict only arises when there is debate about if and when one can work
work entirely in the degenerate subset of the Rosennean paradigm, versus
when one must utilize the genericity of the total paradigm, in order to
answer some particular question or solve some particular problem.

Regards,
Tim


> -----Original Message-----
> From: ROSEN Forum [mailto:*** Behalf Of Dan
> Fiscus
> Sent: Tuesday, February 01, 2005 12:42 PM
> To: ***
> Subject: Re: Problems for solutions
>
>
> Tim,
>
> Good points. A comment that may or may not be relevant,
> but to me suggests the challenges to clarity are big and not
> trivial. In papers Steve Kercel has written he cites some
> people who explain the Liar's Paradox as rooted in an
> ambiguity with our sense of falseness - it can either mean
> negation or denial (the explicit details and distinctions of
> which I don't remember but need to learn). The strange
> loopiness and "bad", contradictory behavior of the Liar's
> Paradox goes away if one keeps these two meanings of
> falseness clear and distinct.
>
> I think we are dealing with a similar ambiguity with life,
> one that perhaps is tangled up with the distinction
> between complement and opposite. Rosen seems to say
> that the opposite of life is machine or mechanism. But I
> think in many minds (including mine) the opposite of
> life is/has been death, intuitively. But what if death is not
> the opposite, but the complement? If life is not a thing but
> a process (i.e. living) and if the complementary process is
> required  - like two heads of a coin, two poles of a magnet,
> two types of electrical charge, etc. cannot be fractionated
> or discussed alone, in isolation - then death or dying is
> integral to life, not the opposite. But, if machine or
> mechanism is the opposite of life it is something other - it
> is not required or integral for life, it can be fractionated,
> treated in isolation. But machine and mechanism as the
> opposite of life may then figure in another coupled
> complementary process and impredicative definition - one
> about Great Truth a la Bohr: A Great Truth is one for
> which its opposite is also a Great Truth. Life and complexity
> (in science) may be a Great Truth, mechanics and machines
> (in science) may be the opposite. Together we get Great
> Truth, alone we don't. Another reason not to slam or shun
> mechanism but to seek to resolve the conflicts (maybe not
> even needing to say one is more general and the other
> degenerate, necessarily. Perhaps more context dependent
> in value-neutral way. Not sure.)
>
> Hmm...not sure if that is any clearer or not. I guess I am
> asking whether these distinctions are part of the problem,
> like a general conflict in wars between mechanistic and
> non-mechanistic science and between humans and our
> environment, and if so if their clarification could help with
> issues like how to move forward, either in learning (science)
> or living (sustainability).
>
> Maybe "complement" is more ontic, "opposite" more
> epistemic?
>
> Dan