On 23 Aug 2013, at 01:21, Ian Mclean wrote:
Details on my blog, Radical Computing.
The summary is this, we can argue that a Theory of Everything is
characterized by either syntactic, negation, or deductive
completeness or universal closure. "A theory of everything (ToE) or
final theory is a theory of theoretical physics that fully explains
and links together all known physical phenomena, and predicts the
outcome of any experiment that could be carried out in
principle." (Wikipedia: Theory of Everything)
I would say that a theory of everything should give a coherent picture
of everything, notably consciousness and matter. I know that physicist
limits this to the unfication of the know forces, but this presupposes
some physicalism, which seems to be unable to even formulate the mind-
body problem.
In fact if we suppose that the brain is Turing emulable, which is
reasonable enough given the evidences, it can be shown that physicshas
to be an emergent pattern from the way natural numbers are related to
each other (through no more than addition and multiplication). So if
we are (digital) machine, physics becomes a branch of machine or
number psychology or theology.
Either definition excludes strictly consistent theories from
consideration. Universal closure is achieved almost exclusively by
the axiom of unrestricted comprehension and universal sets which in
general entail Russell's paradox. Completeness is a more tractable
property, but as I've sketched, necessitates that a neither a Theory
of Everything nor its metasystem is strictly consistent.
I doubt very much that we can have completeness even when restricting
ourself to what number or computer program can do.
Relinquishing consistency is useful to handle semantics of natural
language, but seems to me quite a leap for a scientific study of
"everything".
This sketch is for the first part of a two part thesis on proof by
contradiction methods examining proofs by contradiction intolerance
and proofs by contradiction tolerance towards the development of
paraconsistent metasystems and methods in metamathematics and the
scientific method. Rather than argue for the impossibility of a
theory of everything whatsoever, I argue that this necessitates that
a Theory of Everything and its metasystem will be paraconsistent in
a stronger sense than Zizzi's Lq and Lnq qubit languages. The second
part of the paper will re-examine Gödel's proofs, Russell's paradox,
and diagonalization proofs with contradiction tolerant methods.
I appreciate any feedback--especially constructive criticism,
Physicalism is not compatible with mechanism. So be aware that your
theory is at the start not mechanist.
I am not sure why you want completeness. Now, the idea to use
paraconsistent logic makes sense to analyze the human psyche, or the
psyche of complex entities (machine or not machine), but I would not
apply it to fundamental questions, as it can lead to sophisticated way
to put the mind-body problem under the rug (an aristotelian tradition).
See my URL for reference to mechanism and its consequences (or see my
post to this list). mechanism leads naturally to a form of pythagorean
neoplatonism. Somehow elementary arithmetic already imposes the
existence of all possible machine dreams, with a very rich
mathematical structure, and physical realities emerge from both a
statistics on those dreams, together with modalities inherited through
diagonalization and consequence of incompleteness. In fact
incompleteness is the reason why such modalities exist, and
incompleteness is a simple (one (double) diagonalization) consequence
of Church thesis (which i make part of the "digital mechanist
hypothesis").
Note that I am not saying that mechanism is true, just that it is not
compatible with materialism, or naturalism or physicalism. I reduce
the mind-body problem, using mechanism, to the problem of the origin
and emergence of apparent physical laws from arithmetic (or any Turing
complete theory). Turing completeness, or sigma_1 completeness, is the
completeness which counts, when assuming mechanism.
Bruno
http://iridia.ulb.ac.be/~marchal/
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