On 12/28/2012 2:48 PM, Bruno Marchal wrote:
Hi Roger,

On 28 Dec 2012, at 13:53, Roger Clough wrote:

Thanks for the clarification, I was wrong about 3p.
But according to Leibniz, 1p is always in God's eye,
but our personal pov is never undistorted or perfectly clear,
and operates down here, which is why I classified it as
being contingent.

3p have necessities and contingencies, but they have also their divine and terrestrial aspect. Here, Divine just means True, and Terrestrial just means effectively believed (and true as I study ideally correct machines).

Dear Bruno,

Thank you for this post! I still have hope that your ideas will filter down to the engineers. ;-)

So there is an OUTER GOD, which is the ONE, and which is 3p, in the comp theory, as it is the collection of true arithmetical propositions.

This is an important definition, but one has to be careful *not* to treat the One as an observer. Most realists, ISTM, treat this One as an observer and a source of 3p truth, but there is no such thing in the absence of the knower, the "inner god".

There is a knower, and it is the INNER GOD, it is the one "available" in the mystical experience. For the ideally correct machine it is both terrestrial and divine (S4Grz = S4Grz*).

OK. This makes consciousness seem to be an ontological primitive! I argue that this is an illusion since if we try to define the inner god as a 1p and isolate, it becomes such that cannot be even named.

The Noùs, i.e. the "accessible" 3p, and the Matter splits into divine and terrestrial parts.

    This is where Pratt's dual aspects show up, no?

Eventually we get 8 person points of view, which gives 8 ways to see arithmetical truth from inside:

TRUTH (outer God) 0p
INTELLIGIBLE (by Man)                INTELLIGIBLE (by God)         3p
SOUL (inner God) 1p

Intelligible MATTER (by Man)   Intelligible MATTER (by God)   3p
sensible MATTER (by Man)       sensible MATTER (by God)    1p

This sum up an interpretation of Plotinus in term of the naturally existing intensional variant of self-reference. This gives eight different logics/mathematics.

if Gödel's incompleteness theorem was false, or if Church thesis was false, the 8 hypostases would collapse into effective truth. But things are not that easy for the machine looking inward.

But we can "slow" the collapse by linking computations to physical implementation. This is where you and I seem to collide in our thinking. :_( I think it is merely a mutual lack of understanding...

I have no 2p, as I am not studying the private life of couples of machines :)

Ah, but it is in couples that we recover finite context and, ultimately engineering. I wish to discuss with you the cyclic gossiping idea that I use, it gives us a nice semi-formal model to examine the effects of interactions between pairs of machines in a combinatorial way. See, for instance http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1097-0037(199610)28:3%3C135::AID-NET2%3E3.0.CO;2-O/abstract


Gossiping and broadcasting are two problems of information dissemination described for a group of individuals connected by a communication network. In gossiping, every person in the network knows a unique item of information and needs to communicate it to everyone else. In broadcasting, one individual has an item of information which needs to be communicated to everyone else. A variation of gossiping, called cyclic gossiping, recently introduced by Liestman and Richards, is studied here for certain classes of graphs."



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