On 02 Jan 2011, at 18:01, Brian Tenneson wrote:

Bruno Marchal wrote:On 02 Jan 2011, at 11:31, silky wrote:On Sun, Jan 2, 2011 at 8:31 PM, Brian Tenneson <tenn...@gmail.com>wrote:In the case of a TOE, the model IS reality.Okay, I won't reply further, this has become irrelevant noise.I suspect the traditional confusion between "model" in the sense ofphysicists (where model = a theory, like a toy model), and model inthe sense of the logician, where model = the reality studied (likea woman serving as model for a painter, or the mathematicalstructure (N, +, x) for PA or RA).Logicians and physicists use the word "model" in the completeopposite sense, and this leads often to complete deaf dialog.This makes even more problem with computationalism, where anobserver accept that some "theories/brains/finite-describable-objects" fits the reality. When you say "yes" to the doctor, it isbecause you believe that the artificial brain does capture(locally, with respect to your current environment) the real thing(your conscious you). In that case *you* are a fixed point where amodel-theory correspond to a model-reality, a bit like in Brouwerfixed point theorem, where a map of a territory is shown to have apoint on it matching the real point in the territory, provided themap is not ripped in two disconnected parts, but only transformedcontinuously. The point is that in some contexts some overlap canexist between a theory and its (or one of its) model, betweendescription and realities, like with the painting of a painting ofa pipe (cf Magritte).Things get confusing also if, like Brian, (but also logicians insome circumstances) people makes a model (a "reality") into a (noneffective) theory. This can be justified for some technical reason,when working on super non effective structure, but is really out oftopic, imo.BrunoWhat makes a theory effective?

`That its proofs are checkable. That its set of theorems is recursively`

`enumerable.`

I'm going to be less precise given that my audience has changed in away I do not know.

We argue in an interdisciplinary field.

Given a couple of assumptions, which are essentially that (1)reality is independent of humans (which will imply that a model (inthe logical sense) can be a TOE as defined in this thread) and

`I don't see this. I prefer to use "theory" for something finitely`

`presentable (finite or recursively enumerable).`

(2) a model every model can be embedded within endows that modelwith a universality that makes it a candidate for being reality.This is then a brief description of reality, though I couldn't hopeto give all the details about reality.

`In that case the model (N, +, x) is the "TOE" that your are searching.`

`It is rather a ROE (realm of everything), and the embedding relation`

`is simulation (emulation or partial emulation). My point is that we`

`have no choice in the matter once we assume that brains work like a`

`digital machine at some level of description.`

I am also working on the hypothesis that a TOE can be given in anfinite/infinite presentation such as found in ZF with axioms andaxiom schemata.Question: what is the theory with no assumptions? I know that inlogic, the consequent closure of the empty set of statements is theset of tautologies, which is not really what I'd call an effectivetheory.

`The set of (classical tautologies) is effective. But the empty theory`

`as all models, the structure of which depending of the meta-theory. It`

`is the trivial theory satisfied by all structures.`

But what about if we remove all assumptions? Sounds like chaos tome. This is connected to all this as I can explain.In fact, I can prove (1) on the grounds that there is no largestnumber. It took me a while to find this argument.

`"1)" follows from comp, which assumes arithmetical realism (used in`

`"there is no largest number").`

Bruno

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