On 1/13/2012 7:29 PM, David Nyman wrote:
Hi Stephen

Thanks for responding to my post in such detail.  I'll need some time
to digest your points, although I'm not at all sure I have the
necessary background to grasp all of what you are saying.  However, I
would just like to remark at this point that my characterisation of
the sought-for ontology as "mathematical" is not because I have any
special insight into the matter (pun intended) - how could I?  Rather
it is because I observe that such an assumption seems to have become,
either implicitly or explicitly, the principal way in which physics -
the "default" ontology of modern science - is characterised.  The
determined "objectivity" of this approach may indeed obscure key
problems at the heart of the interpretation of the resulting
formalism, but it's all too easy to ignore or trivialise these when
one is in the grip of a doctrine.

As to Bruno's position, given that his point of departure is the
computational theory of mind, he argues, if I understand him, that
this consequently places particular logical constraints on his choice
of ontology from the outset.  Does this imply that you explicitly
reject CTM, or do you rather disagree about the ontological
constraints it might imply?  Or, if your own theoretical point of
entry begins from quite different basic assumptions, what would be the
most straightforward introduction to these?


Hi David,

I am coming from a very different point of view. I ask that you take a look at the non-well founded set theory stuff and see if you can figure out for yourself its implications re ontology. I very well might be reading something into it that is not there, but after having read almost all of Barwise et al's books (particularly The Liar: An Essay on Truth and Circularity <http://www.amazon.com/Liar-Essay-Truth-Circularity/dp/0195059441/ref=ntt_at_ep_dpt_4> and Vicious Circles <http://www.amazon.com/Vicious-Circles-Center-Language-Information/dp/1575860082/ref=ntt_at_ep_dpt_2> ) and studying metamathematics and philosophy (a wide swath), it seems to me that my conclusion is correct. OTOH, I know that I am missing something as I am fallible and finite. ;-)



On 13 January 2012 21:26, Stephen P. King<stephe...@charter.net>  wrote:
Hi David,

     I do appreciate your remarks and thank you for writing them up and
posting them. Let me interleave some comments in reply.

On 1/13/2012 1:43 PM, David Nyman wrote:

On 13 January 2012 17:24, Stephen P. King<stephe...@charter.net>  wrote:

I submit to you that you cannot just ignore the
universals vs. nominal problem and posit by fiat that just because one can
proof the truth of some statement that that statement's existence determines
its properties. Our ability to communicate ideas follows from their
universality, that they do not require *some particular* physical
implementation, but that is not the same as requiring *no* physical
implementation. You argue that *no* physical implementation is necessary; I

Forgive me for butting in (particularly in the light of the fact that
I too lack Bruno's erudition, only in spades) but I simply don't read
Bruno's work in the way you are representing it.  I see it like this:
we have little option but to split our theories of "what there is"
into two parts: the epistemological (i.e. the only form in which, and
the exclusive means whereby, we have any access to information) and
the ontological (i.e. some coherent theoretical framework in which to
situate what that knowledge seems to reveal, and also, ideally, one
that is able to account satisfactorily for how we are able to come by
such knowledge in the first place).

     My point is that our epistemological and ontological theories are
predicated upon our actuality (not just existence) as physical systems that
have the ability to reason. It is obviously true that if something that is
like an observer does not exist then none of this discussion would exist
either. We simply cannot remove ourselves from our theories, concepts,
models, representations, ... I am trying to point out that the same holds
for physical implementations of those theories, concepts, models,
representations, ... Consider how the notion of meaningfulness implicitly
requires at "to whom" a meaning obtains. But there is more to this

But after Kant, we can surely no longer believe that the ontological
component of this dyad can possibly give us direct access to some
ultimate ding and sich?

     Right, we can show via a logical argument that we cannot have knowledge
of any "ding and sich" by any direct means, I will not go into such for sake
of brevity, but we need some way to get around this fact. We postulate
assumptions when we are theory making and see where they take us...

  Rather, what we seek in such theories is a
mathematical schema in terms of which the relations between
"primitive" theoretical entities, which themselves explicitly lack any
further internal relations or characteristics, can be framed.

     OK, but this remark itself assumes an ontological postulate! What about
models that do not assume ""primitive" theoretical entities, which
themselves explicitly lack any further internal relations or
characteristics.."? There are theories, such as what Jon Barwise et al
discussed in his papers and books, that do not assume the well-founded axiom
(aka Axiom of regularity) or equivalent. Non-Well Founded set theory exists
and works! If and when we base our ideas about Existence, Reality and the
nature and means of knowledge on entities such as numbers, as Bruno is
doing,  then we are implicitly assuming a particular mereology (relationship
between wholes and parts) when, given the existence of alternatives (given
that we can mathematically prove their properties follow from blah blah
     My argument rest on the fact that other schemata are possible! That
there are mathematical models that do not require a notion of a "primitive"
(in the Greek sense of Atoms, as being indivisible and lacking of any
internal relations or characteristics) but instead consider entities as,
crudely explained,  composed of others. This idea has been long castigated
as implying all kinds of problems and paradox such as the Cretan Liar, Sets
that both contain and do not contain themselves, etc. But I content that all
of these pathologies follow from the failure of thinkers to comprehend the
deep implications of what it means for a statement, claim, Sigma_1 sentence,
etc. to have meaningfulness. There is always an implicit "to whom" meaning
obtains and that "to whom-ness" cannot be separated from the "ding and
sich-ness" of objects, be they planets, numbers, or Pink Polka-dotted

  Of course, this bare mathematical depiction cannot be reconciled with any
aspect of experience without recombination with the epistemological
component, which in most theories typically entails a
sleight-of-thought that is still, to say the least, almost entirely

     I agree! This, I argue, is the underlying reason why I am making a big
deal about implementation. The fact that depiction is required in some form,
reconcilable or not with any concept of aspects of experience - we are not
aware of experience directly! -, is my point that we cannot mistake
"independence of any particular physical implementation" with  "independence
from physical implementation" for such would render concepts to be just
another set of free floating entities that, like ghosts, require some
secularized and de-anthropomorphized version of the "God in the gaps"
explanation to be coherent. This is almost identical to a long standing
criticism of Platonism, that given the existence of the Ideal Forms, how can
we, as finite entities, have any knowledge of them? Does knowledge come for
free? I don't believe that it does! Descartes version of Dualism failed for
similar reasons.
      Bruno's "Result" shows that there cannot be any physical primitives. I
agree with this and believe it. But this is not an establishment of
sufficiency of any form of concept primitive, especially when theories based
on non-well foundedness can be shown to be coherent (e.g. give us a means to
form theories and explanations that are useful in weaving together our
thoughts about the world)!

If the foregoing is even vaguely true, then surely your debate with
Bruno cannot be about whether either matter or numbers "really exist",
because the very notion of "real existence" transcends anything about
which we can theorise or have experience.

     I agree, but do you understand that we have already moved past that
point? Do you understand my argument that we must not conflate the existence
on an object (concrete or abstract) with the definiteness of its properties?
If you have read a lot of literature on the problem of interpretation of QM
this might be clear... How do we reconside the properties of linear
algebraic entities with our experience of a classical appearing world?

  Since mathematics delimits
any possible ontological characterisation,

     Wait! What? How does mathematics, the internal machinations of thinking
entities, "delimit... any possible ontological characterization"? Surely the
tacit and accepted ontological ideas that a sapient entity uses to reason
leave traces in the mathematics of a class of such sapient entities,
otherwise coherence in communication would be impossible, but to elevate the
ontological status of mathematics to endow it with such a power smacks of a
bit of misunderstanding of mathematics. The fact is that mathematics is not
one set of finitely specifiable axioms that forms a unique and TRUE T.O.E.
of all that exists. Many mathematicians have proven that there are multiple
versions of mathematics that have differing axioms, all internally

  the debate can in
consequence only be about the derivation, priority and hence relative
"primitiveness", of the mathematical "entities" thus characterised.
In fact, this is an implicit assumption, so far as I can see, amongst
physicists, who have until quite recently assumed that the
mathematical structure of physics, as currently known, simply was the
relevant "primitive" structure.

     Sure and we see where that trajectory of thinking leads; to theories
that are void of empirical content. We are left with "proof from authority"
to rest our reasons for belief in such theories. I reject such as a return
to the absurdity of Scholasticism. If our theories cannot be tested against
empirical facts, even if in principle, and thus by implication do not
require physicality to be real then we are back to debating how many angels
(superpartners) can dance on the heads of pins (orbifolds), and the winners
of debates are decided by the rhetorical skills of certain people.

However, attempts to reach beyond the puzzles of current theory have
already led some, like Tegmark, to an explicitly mathematical
characterisation of physical ontology.

     I see Tegmark as having seen some of the same idea that I am considering
and discussing ... not that I agree with all of Tegmark's ideas...

   Bruno's work, it seems to me,
is in the same spirit, with the critical distinction that he believes
that, unless the epistemological component is placed at the centre of
the theory, the appearances cannot ultimately be saved.

     I am not trying to save appearances, I am trying to find coherence and
integrity in our thinking. How can a theory which prohibits its own
implementability in a physical object be considered to be coherent? If a
result makes a claim that it cannot be communicated, how am I to know of it,
much less understand it? This is exactly what thinking that the physical
world is just the "dreams of numbers" necessitates. My debate with Bruno
seems to center around questions about the ontological properties of numbers
and while I agree that they "exist", I do not grant that this mere existence
necessitates any ability or specific property.

it is inaccurate to say that "physical representation" is not a core
aspect of his theory - it is absolutely central, just not primitive,
in the sense that the theory seeks to derive it as an aspect of a more
fundamental (in fact, in Bruno's contention, the MOST fundamental)
mathematical framework .

     Then if I follow that reasoning then I am lead to thinking that you
agree with me; ideal monism is an insufficient explanatory model/theory. I
invite you to read any of Bertrand Russell's discussion of neutral monism
(see 1 for more). He was much more erudite than this poor sap of an amateur.



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