On 03 Jan 2011, at 17:26, Brian Tenneson wrote:

Ah, ok. Well, as your friend checked my proof, what I was/amworking on is an effective theory.

`You and most mathematician and logicians manage to have checkable`

`proofs, but they usually don't work in a formal setting, so it makes`

`no sense to say that their proofs are recursively enumerable, unless`

`they add (in a footnote) that what they do can be formalised in ZF, or`

`NBG, as it is usually the case. Mathematicians and logicians don't`

`work in formal systems. Logicians works *on* formal system, but their`

`meta-theories are the usual informal high order mathematics (and`

`easily implemented in ZF or NBG, but never actually done so).`

Bruno

Bruno Marchal wrote: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 senseof physicists (where model = a theory, like a toy model), andmodel in the sense of the logician, where model = the realitystudied (like a woman serving as model for a painter, or themathematical structure (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, itis because you believe that the artificial brain does capture(locally, with respect to your current environment) the realthing (your conscious you). In that case *you* are a fixed pointwhere a model-theory correspond to a model-reality, a bit like inBrouwer fixed point theorem, where a map of a territory is shownto have a point on it matching the real point in the territory,provided the map is not ripped in two disconnected parts, butonly transformed continuously. The point is that in some contextssome overlap can exist between a theory and its (or one of its)model, between description and realities, like with the paintingof a painting of a pipe (cf Magritte).Things get confusing also if, like Brian, (but also logicians insome circumstances) people makes a model (a "reality") into a(non effective) theory. This can be justified for some technicalreason, when working on super non effective structure, but isreally out of topic, imo.BrunoWhat makes a theory effective?That its proofs are checkable. That its set of theorems isrecursively enumerable.I'm going to be less precise given that my audience has changed ina way 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(in the logical sense) can be a TOE as defined in this thread) andI don't see this. I prefer to use "theory" for something finitelypresentable (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'thope to give all the details about reality.In that case the model (N, +, x) is the "TOE" that your aresearching. It is rather a ROE (realm of everything), and theembedding relation is simulation (emulation or partial emulation).My point is that we have no choice in the matter once we assumethat 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 isthe set of tautologies, which is not really what I'd call aneffective theory.The set of (classical tautologies) is effective. But the emptytheory 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-- silkyhttp://dnoondt.wordpress.com/ (Noon Silk) | http://www.mirios.com.au:8081>"Every morning when I wake up, I experience an exquisite joy —the joyof being this signature."http://iridia.ulb.ac.be/~marchal/--You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.http://iridia.ulb.ac.be/~marchal/ --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-l...@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.--You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-l...@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

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