From: "Stathis Papaioannou" <[EMAIL PROTECTED]>
and which is not so
muddled as the crypto-idealist suggestions that any 'mathematical
structure'
or any 'program' defines a possible world.
Why that last phrase? There is a great elegance and simplicity in the idea
that all mathematical structures exist necessarily, with the anthropic
principle selecting out those structures with observers. There is also an
inevitability to it, even if you believe that as a matter of fact there is
a
real physical world out there. All it takes is one infinite computer to
arise in this physical world and it will generate the mathematical
Plenitude.
Let me start with a brief definition of idealism and of platonism.
Idealism is the doctrine that mind, not matter, is fundamental. Platonism, I
think it can be said, is the doctrine that only universals are real.
Platonism has often been viewed as a form of idealism by people who think
that universals are only in the mind. One doesn't have to view things that
way; for example, the Aristotelian view was that universals are always
exemplified or instantiated in some material substance. The people who
placed universals in the mind were generally not idealists, they were
nominalist materialists. In any case, even if it can be debated as to
whether platonists were idealists, they were generally not materialists.
I think it is clear enough that the belief that everything that exists is a
mathematical structure is a platonism. If it were meant to be a materialist
proposition, it would be posed in an Aristotelian fashion, as the statement
that everything that exists is a material structure with mathematical
properties.
As for the idea that everything is a program, again it is clear from the
context (e.g. the discussion thread which spawned this one) that some
idealized ('mathematical') notion of program is intended, and not 'program'
in any concrete sense. Incidentally, as a quasi-mathematical concept, an
idealized program is an unusual construct in that its constituent entities
are often assigned some *semantic* properties. That's not something you find
anywhere else in mathematics, and it can add a special twist to a
mathematical idealism (or 'platonic materialism') based specifically on
computer-science concepts. (This is not so much a consideration in a
computational idealism based on Turing machines, where the presence of
stealth intentionality at the fundamental level is at a minimum, if it's
there at all.)
I think I can safely say that these theories are muddled because they are
saturated through and through with age-old ontological questions, and yet
their proponents do not seem to notice this at all. The debate between
materialism and idealism, realism and nominalism, is an old one and appears
to have arisen spontaneously in all the major civilizations, so one may
conclude that it revolves around some question as basic and legitimate as
'why does anything exist at all?', and is not just a symptom of some
cultural idiosyncrasy. It also looks as if the basic issues still exist even
in the age of mathematized atomism (the major difference between the atomism
of Democritus and the atomism of Feynman is that the latter features exact
equations of motion). Whether the old debates have something to teach us, in
thinking about these new idealisms, I don't know (because I have not
actually studied the intellectual history), but it seems likely.
So much for the accusation of crypto-idealism. (I don't actually object to
idealism in a theory, by the way, I just prefer that people be aware that
it's there, and of some of the implications.) I also want to say something
about theories of plenitude, by which I mean theories according to which all
possible Xs exist, or even that all possible Xs *necessarily* exist.
Stathis, can you tell me *why* it is that all mathematical structures would
'exist necessarily'? I can see why it would be intellectually convenient
*if* that were true, but can you actually explain the *mechanism* of
'necessary existence'?
The theological use of the concept is illuminating. The universe exists, I
don't know why. Maybe God made it; but then why does God exist? I can go
into infinite regress; or I can suppose that some things exist for a reason
other than that they were caused to exist by some agency external to them.
For example, maybe they just had to exist, as a matter of logical necessity
(although I can't right now exhibit the exact reason). Thus, I believe, the
idea of a 'necessary existent' was born - it was perceived that *if there
were such a novel mode of causation*, it would offer a third way between an
infinite regress of gods, and a First Cause whose own existence was just an
uncaused brute fact (and therefore presumably contingent). This genealogy of
the concept does not in itself disprove the possibility that such a mode of
causation actually exists, of course.
I think the one thing that can be said for entertaining the idea of
existential necessitation (to give it a name) is that it is a stimulus to
thought. *If* there is a reason why anything at all exists, perhaps one is
more likely to discover it by brooding on the idea of existential
necessitation, rather than by assuming that there is only 'intra-worldly'
causation (that is, causal relations among contingently existent entities).
I could probably write another essay critiquing your last statement that
'All it takes is one infinite computer to arise in this physical world and
it will generate the mathematical Plenitude', except that I cannot guess
what hidden premises lie behind it. 'All it takes' - is an infinite computer
really such a small request?! Also, just because something is infinite
doesn't mean that every finite possibility is in it somewhere - this is
obvious even for real numbers.
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