On 11 Jan 2014, at 15:43, Stephen Paul King wrote:

Dear Bruno,

  You wrote:
"AR provides the neutral monism!
Comp is neutral monism. Neither mind, nor matter are taken as primitive. Both emerge from the additive-multiplicative structure of arithmetic (AR), and that structure provides the neutral stuff."

Ontological neutrality is that there are no particular properties or orders.


No. Not in the most common standard sense.
Also, if your ontology is so unstructured, how do you use it to derive the other things? It does not make sense to me.



AR has a particular set of properties and an order, thus it cannot be considered as neutral.

Neutral monism, in the philosophy of mind, means that we don't presuppose neither mind, nor body, and that we account of both of them from something else (here the arithmetical reality).



It must includes all possibilities and orderings equally.

It contains all computations, and much more, indeed. That is why it can work at all.



Numbers have particular properties and orders so how is it that you can think of them as being a neutral monism?

Because they are neither belonging to the mind, nor to the physical reality. In all theories you have to assume something from which you can account for other things. The nothing theory assumes some notion of things, like set theoretical axioms, or a energy vacuum, etc.



No Bruno, you are advocating a form of Idealism,

Then you make the numbers into a product of the human mind, but with comp, the human mind is handled by purely arithmetical notion (like relative universal numbers, computations, etc.).

Explaining the number with the human mind is a non-comp attempt to explain the simple by the very complex. It is like "God did it", or a ignorance-gap type of explanation.

Comp defines computations and machines from arithmetic. It is a much more fertile way to proceed, as we do agree on the few properties of numbers. But nobody agrees on term like mind, human mind, becoming, which are fuzzy philosophical jargon.



almost like Berkeley, but unlike Berkeley you do not fall prey to Mr. Johnson's criticism by appealing to the "kickability" of prime numbers,

OK.


the truth of theorems (within theories), etc. Nice move, but it is still flawed.

It is not a move. It is derived from an assumption. If numbers exists only in the human mind, then all machines exists only in the human mind, and I am not sure I can say "yes" to digitalist doctor in that case.

Bruno






On Sat, Jan 11, 2014 at 3:53 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:

On 11 Jan 2014, at 06:05, Stephen Paul King wrote:

Dear Brent,

I will try a crude summary and hope to not be misunderstood... It starts with the Stone duality, a well known isomorphism between Boolean algebras and totally disconnected compact Hausdorff spaces. The former are identified with minds (logical, computational, numerical, etc) and the latter with physical objects (what is more "physical" that a space that looks exactly like Democritus' "atoms in a void"?. This solves the mind-body linkage problem of Descartes' dualism. The paper then discusses how interactions between pairs of minds (generalizations of Boolean algebras identified as "states") is mediated via pairs of bodies (generalizations of Stone spaces to include mass, spin, charge, potentials,... physics identified as "events"). A crude diagram of this relation for the evolution of a single entity is:

... -> Body -> Body' -> ...
           |             |
... <- Mind <- Mind' <- ...

where the "|" symbol is the Stone isomorphism, "->" is the physical evolution of one event to the next and "<-" is the logical arrow of implication.

Mathematics as considered my most people usually ignores evolution of logical structures, such as Boolean algebras, and so the difference between mind and mind' is not considered. Now that computers are commonplace, the idea that logical structures evolve makes a lot more sense! A computation is the transformation of information and since logical structures capture the relations of the information, it is natural to consider this theory.

In this theory, minds and bodies (including brains!) are not separable substances but are isomorphs that have "dynamics" whose "arrows" point in opposite directions. Physical process moves forward from event to event' in sequences of time according to thermodynamics, etc. and logic "looks" backward to ensure that any new state is consistent with previous states. This implies an elegant solution to the measurement problem of QM! Differences between states and parameters of time can be subdivided as finely as one wishes; even to the smoothness of continua. It is what the logical 'side of the coin" does to select physical events that won me over to Pratt's theory: a physical transition from event x at time t to event x' at time t' is allowed if and only if the state x'* at t' does not imply information that would contradict prior states at t^-1, t^-2, etc. Basically, events will occur iff they do not imply a contradiction of previously allowed events. This automatically solves the White Rabbit problem by disallowing events that imply logical contradictions. It also gives a slightly different take on computational universality: individual logical structures are associated with equivalence classes of physical functions and physical systems are associated with equivalence classes of logical structures. The equivalences are, respectively: equivalent function and semantical equivalence. Thus computations and the physical processes are not ontologically isolated from each other, but universality obtains because there is no a priori bijective map between the set of particular physical systems and the set of particular Turing universal computations.

?



It seems that Pratt abandoned the theory because of a lack of interest in the community but still hosts the papers on his website. Maybe in hope that some one might come along, like me, that can make sense of it and develop it further. It does not consider SR at all, which bothers me a little bit, but that can be fixed using ideas such as those of Kevin Knuth, IMHO.

It is a nice idea, but it does not take into account the FPI (he is unaware of it), and so does not address the comp mind-body problem.



Its main prediction is that neither ghosts (logics that cannot be associated with any physical structure) nor zombies (bodies that cannot be represented by an internal self-referencing logical structure) exist. This argues against both material and mental monism. (Thus my conflict with Bruno's AR!)

AR provides the neutral monism!
Comp is neutral monism. Neither mind, nor matter are taken as primitive. Both emerge from the additive-multiplicative structure of arithmetic (AR), and that structure provides the neutral stuff.

Bruno





On Fri, Jan 10, 2014 at 9:02 PM, meekerdb <meeke...@verizon.net> wrote:
On 1/10/2014 2:23 PM, Stephen Paul King wrote:
Dear Brent,

Vaughn Pratt's dualist theory is consistent with QM and does show a mechanism that prohibits White Rabbits. It is intelligible to anyone that puts forth the effort to comprehend it.

Can you summarize it?

Brent

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