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 of physicists (where model = a theory, like a toy model), and model in the sense of the logician, where model = the reality studied (like a woman serving as model for a painter, or the mathematical structure (N, +, x) for PA or RA).

Logicians and physicists use the word "model" in the complete opposite sense, and this leads often to complete deaf dialog.

This makes even more problem with computationalism, where an observer accept that some "theories/brains/finite-describable-objects" fits the reality. When you say "yes" to the doctor, it is because 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 a model-theory correspond to a model-reality, a bit like in Brouwer fixed point theorem, where a map of a territory is shown to have a point on it matching the real point in the territory, provided the map is not ripped in two disconnected parts, but only transformed continuously. The point is that in some contexts some overlap can exist between a theory and its (or one of its) model, between description and realities, like with the painting of a painting of a pipe (cf Magritte).

Things get confusing also if, like Brian, (but also logicians in some circumstances) people makes a model (a "reality") into a (non effective) theory. This can be justified for some technical reason, when working on super non effective structure, but is really out of topic, imo.

Bruno

What makes a theory effective?
I'm going to be less precise given that my audience has changed in a way I do not know.
Given a couple of assumptions, which are essentially that (1) reality is independent of humans (which will imply that a model (in the logical sense) can be a TOE as defined in this thread) and (2) a model every model can be embedded within endows that model with a universality that makes it a candidate for being reality. This is then a brief description of reality, though I couldn't hope to give all the details about reality.  I am also working on the hypothesis that a TOE can be given in an finite/infinite presentation such as found in ZF with axioms and axiom schemata.
Question: what is the theory with no assumptions?  I know that in logic, the consequent closure of the empty set of statements is the set of tautologies, which is not really what I'd call an effective theory.
But what about if we remove all assumptions?  Sounds like chaos to me. This is connected to all this as I can explain.

In fact, I can prove (1) on the grounds that there is no largest number.  It took me a while to find this argument.





-- 
silky

http://dnoondt.wordpress.com/  (Noon Silk) | http://www.mirios.com.au:8081 >

"Every morning when I wake up, I experience an exquisite joy — the joy
of being this signature."

http://iridia.ulb.ac.be/~marchal/




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