Re: A possible structure isomorphic to reality
On 09 Dec 2010, at 20:43, Brian Tenneson wrote: Is there any first order formula true in only one of R and R*? I would think that if the answer is NO then R R*. What I'm exploring is the connection of to [=], with the statement that implies [=]. The elementary embeddings preserve the truth of all first order formula. So it should be obvious that if A B, then A [=] B. In B there might be elements or objects or set of objects obeying relations which are not consequences of the first order relations. I think that all standard models of first order theories of finite structures (like numbers, hereditarily finites sets, rational numbers, etc.) are elementary equivalent with their non standard models. You need second order logic to describe what happens in those models. But I have not invest on model theory since some time. Are there any other comparitive relations besides elementary embedding that would fit with what I'm trying to do? What I'm trying to do is one major leg of my paper: there is a superstructure to all structures. But sets and categories have been seen that way. This leads to reductionism in math, in my opinion. Yet category theory provides ubiquitous non trivial relations between many mathematical objects. But Lawvere failed to found mathematics on the category of categories. And categories with partial objects, like those which populate so much computer science, are, well, quite close to abstract unintelligibility (for me, but who knows). Category impresses me the most in knot theory, and the buildings of models for weak logics (linear logic, intuitionist logics, quantum linear logic). What super means could be any comparitive relation. But what relation is 'good'? You ask a very difficult question. You might appreciate morphism of categories (functor), or of morphism of bicategories, or n-categories, if you want powerful abstractions. But assuming mechanism, and the 'everything goal': I would insist on the relations of 'dreaming', or partial emulation between numbers relatively to universal numbers. The infinite dynamical mirroring of the universal numbers. That just exist if we assume the axiom of Robinson arithmetic, and we are embedded or better: distributed, or multi-dreamed by or in it (with our richer axioms!) and all, this with notions of neighborhoods and accessibility between our consistent extensions (that you can extract from studying what can and cannot prove sound löbian numbers about themselves. See my papers for more on that, and good basic books are Boolos 1979, 1993, Smullyan, Rogers, etc). It depends on what you are searching for. If you want to include psychology and theology, expect some universal mess diagonalizing against all complete reductions. Bruno On Dec 9, 8:12 am, Bruno Marchal marc...@ulb.ac.be wrote: On 09 Dec 2010, at 05:12, Brian Tenneson wrote: On Dec 5, 12:02 pm, Bruno Marchal marc...@ulb.ac.be wrote: On 04 Dec 2010, at 18:50, Brian Tenneson wrote: That means that R (standard model of the first order theory of the reals + archimedian axiom, without the term natural number) is not elementary embeddable in R*, given that such an embedding has to preserve all first order formula (purely first order formula, and so without notion like natural number). I'm a bit confused. Is R R* or not? I thought there was a fairly natural way to elementarily embed R in R*. I would say that NOT(R R*). *You* gave me the counter example. The archimedian axiom. You are confusing (like me when I read your draft the first time) an algebraical injective morphism with an elementary embedding. But elementary embedding conserves the truth of all first order formula, and then the archimedian axiom (without natural numbers) is true in R but not in R*. Elementary embeddings are *terribly* conservator, quite unlike algebraical monomorphism or categorical arrows, or Turing emulations. Bruno -- You received this message because you are subscribed to the Google Groups 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 athttp://groups.google.com/group/everything-list?hl=en . http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups 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 . http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this
Re: A possible structure isomorphic to reality
Just to be clear on this: On 09 Dec 2010, at 20:43, Brian Tenneson wrote: Is there any first order formula true in only one of R and R*? So yes, there is one: the weak pure archimedian formula AF: AF: for all x there is a y such that (xy) (not your: for all X there is a Y such that (Y is a natural number and XY), because this is a second order formula. You cannot defined natural number in first order logic (actually you cannot defined finite in first order logic). I would think that if the answer is NO then R R*. You would be right. But AF is true in R, and false in R* In R* there is an object infinity which is such that there is no y such that infinity y, making AF false. Bruno What I'm exploring is the connection of to [=], with the statement that implies [=]. Are there any other comparitive relations besides elementary embedding that would fit with what I'm trying to do? What I'm trying to do is one major leg of my paper: there is a superstructure to all structures. What super means could be any comparitive relation. But what relation is 'good'? On Dec 9, 8:12 am, Bruno Marchal marc...@ulb.ac.be wrote: On 09 Dec 2010, at 05:12, Brian Tenneson wrote: On Dec 5, 12:02 pm, Bruno Marchal marc...@ulb.ac.be wrote: On 04 Dec 2010, at 18:50, Brian Tenneson wrote: That means that R (standard model of the first order theory of the reals + archimedian axiom, without the term natural number) is not elementary embeddable in R*, given that such an embedding has to preserve all first order formula (purely first order formula, and so without notion like natural number). I'm a bit confused. Is R R* or not? I thought there was a fairly natural way to elementarily embed R in R*. I would say that NOT(R R*). *You* gave me the counter example. The archimedian axiom. You are confusing (like me when I read your draft the first time) an algebraical injective morphism with an elementary embedding. But elementary embedding conserves the truth of all first order formula, and then the archimedian axiom (without natural numbers) is true in R but not in R*. Elementary embeddings are *terribly* conservator, quite unlike algebraical monomorphism or categorical arrows, or Turing emulations. Bruno -- You received this message because you are subscribed to the Google Groups 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 athttp://groups.google.com/group/everything-list?hl=en . http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups 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 . http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups 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.
Re: advice needed for Star Trek talk
Bruno:
I stand corrected on steps 6 and 7. I believe I understand your UDA
diagrams. Before I can comment, I need to decide waht progrmas are and
are not Turing emulatable, and if the brain runs a program, parallel
programs, or something else.
Ronald
On Dec 7, 4:10 pm, Bruno Marchal marc...@ulb.ac.be wrote:
On 06 Dec 2010, at 19:00, ronaldheld wrote:
Bruno(and others)
I am going to do this in two posts. The first is my interpretation
of your UDA. Since the Brain is a Turing emulatable program running on
a biological platform(to start), steps 1-5 are not controversal. Step
6 scan(and annilates) the body and only places the program on another
physical hardware platform, for a finite amount of time. Step 7 is the
usual scan and annihilate,
Well, step 6 and 7 use step 5 where you don't need to annihilate the
original anymore.
A (classical) teleportation without annihilation is a duplication
where the original is considered annihilate and reconstituted at his
original place wihout delay.
You need that to understand that if you do an experience of physics,
you have to to consider into account all computations in the UD
execution to predict your future experience (including looking at a
measuring apparatus needle'. OK?
and then looks for the program in the UD
still on some physical platform?
Yes. At step seven, you have already that DM entails indeterminacy,
non locality and even (exercice) non clonability of anything
'physically' observable. (mechanism accepts the 3-duplicability of the
person which is not something physically observable (yet inferable)).
Step 8 removes the physical universe
and had the UD running in Arithmetical Platonia?
Yes. The UD is somehow given by the true sigma_1 arithmetical
propositions (with shape like ExP(x) P decidable) together with their
many proofs. This can be derived from a well known result asserting
that the computable functions are representable in Robinson (tiny)
arithmetic, or you can use the beautiful work of Putnam, Juila
Robinson, Davis, and Matiyazevitch). This makes it Turing universal,
and makes the UD emulated in Platonia (or in any model of Peano
Arithmetic, that is a tiny part of arithmetical truth).
If I basically understand this correctly, then I will interpret UDA
from my(physicla scineces POV).
Normally the reasoning does not depend on any points of view (that is
why is a deductive reasoning or a proof). The step 8 is more
difficult, and I might resend the Movie Graph Argument (MGA) already
sent. Step 8 explains the necessity of immateriality. It explains that
the physical supervenience thesis cannot work, unless you accept the
idea that an inactive piece of material has an active physical
activity in a computation, and still say yes to the doctor, like
Jack Mallah apparently. To avoid this I add sometimes that the
survival, when saying yes to the doctor, is done qua computatio, and
I am working to make this more precise. It is always possible to put
some magic in the notion of matter to build a fake comp hypothesis
saving primary matter, but then you can save any theology, and it
seems to me quite an ad hoc move. But I am interested in hearing your
Physical Science point of view.
Bruno
Ronald
On Dec 2, 10:55 am, Bruno Marchal marc...@ulb.ac.be wrote:
On 02 Dec 2010, at 15:51, ronaldheld wrote:
Bruno:
I looked at UDA via the SANE paper. I am not certain the the mind is
Turing emulatable, but will move onward.
OK. It is better to say brain instead of mind. The doctor proposes an
artificial digital brain, and keep silent on what is the mind, just
that it will be preserved locally through the running of the adequate
computer.
Using Star Trek transporter
concepts, I can accept steps 1 through 5.
Nice. Note that the Star trek transporter usually annihilates the
original (like in quantum teleportation), but if I am a program (a
natural program) then it can be duplicated (cut, copy and paste apply
to it).
Step 6 takes only the mind
(the program, or the digital instantaneous state of a program)
and sends it to a finite computational device or the entire person
into a device similar to a Holodeck,
It is just a computer. A physical embodiment of a (Turing) Universal
Machine. Assuming the mind state (here and now) can be captured as
an instantaneous description of a digital program, nobody can feel
the
difference between reality and its physical digital emulation, at
least for a period (which is all what is needed for the probability
or
credibility measure).
where the person is a
Holocharacter?
A person is what appears when the correct program (which exists by
the
mechanist assumption) is executed ('runned') in a physical computer.
I am not certain a UD is physically possible in a
finite resource Universe.
You don't need this to get the
