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

Hi StephenThanks 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? David

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. ;-)`

Onward! Stephen

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 disagree. 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 discussion.... 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 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 Unicorns. 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 opaque. 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 consistent. 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. Consequently, 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. Onward! Stephen

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