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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