Hi David,

On 1/14/2012 12:51 PM, David Nyman wrote:
On 14 January 2012 16:50, Stephen P. King<stephe...@charter.net>  wrote:

The problem is that mathematics cannot represent matter other than by
invariance with respect to time, etc. absent an interpreter.
Sure, but do you mean to say that the interpreter must be physical?

What else would have such properties? If a system has no physical manifestations, how can we even know that it exists?

I don't see why.

What alternatives are there? Free floating minds? What means would exist to allow them to distinguish themselves from what they are not?

  And yet, as you say, the need for interpretation is

Not just interpretation but something more basic. There is a requirement of communicability. If I cannot communicate an idea to you, can you even consider its properties or truth valuation?

  Now, my understanding of Bruno, after some fairly close
questioning (which may still leave me confused, of course) is that the
elements of his arithmetical ontology are strictly limited to numbers
(or their equivalent) + addition and multiplication.

And the entire time that this questioning and thinking was going on there where physical systems in the background doing their thing of manifesting patterns invariant to changes of some particular physical property, but that they where there and necessary is my point. We cannot even have digital substitution if there is no material to substitute. 0 replaced by 0 is still 0.

  This emerged
during discussion of macroscopic compositional principles implicit in
the interpretation of micro-physical schemas; principles which are
rarely understood as being epistemological in nature.

This is where Bruno's result is important and I do not wish to detract anything at all from those epistemological implications, but that we can completely abstract away the "stuff" that acts at least as an interface between our minds as such is to cut our minds loose from even the mere possibility determining what one is and what one is not.

Hence, strictly
speaking, even the ascription of the notion of computation to
arrangements of these bare arithmetical elements assumes further
compositional principles and therefore appeals to some supplementary
epistemological "interpretation".

I suppose that that is the case, but how do mathematical entities implement themselves other than via physical processes? We seem to be thinking that this is a solvable "Chicken and Egg" problem and I argue that we cannot use the argument of reduction to solve it. We must have both the physical and the mental, not at the primitive level of existence to be sure, but at the level where they have meaning. This is why I argue for a form of dualism that transforms into a neutral monism, like that of Russel, when taken to the level of ding and sich. At teh level of ding and sich difference itself vanishes and thus to argue that matter or number is primitive is a mute point. We must be careful that we are not collapsing the levels in our thinking about this.

In other words, any bare ontological schema, uninterpreted, is unable,
from its own unsupplemented resources, to actualise whatever
higher-level emergents may be implicit within it.  But what else could
deliver that interpretation/actualisation?  What could embody the
collapse of ontology and epistemology into a single actuality?  Could
it be that interpretation is finally revealed only in the "conscious
merger" of these two polarities?

I agree!!!! We might even go so far as to claim that consciousness obtains in the juxtaposition of the polarities, but my claim against Bruno is that the poles (of mind and body) vanish when the radius of the sphere (to follow the analogy) goes to zero.



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