Does this theory have any validity whatsoever?
- Yes
- No
- Maybe
- Not a clue
- Huh?
Hello! I was wondering if anyone could help me with a problem which I have been working on.
Define Q to be the set of all items which satisfy axioms A1,A2,A3,…An, where n is a positive integer. An axiom is defined to be a string of symbols phi a, phi b, phi c, and so on. There is nothing which is an element of a symbol. The union of all the symbols of the set of axioms must be finite. Call the union the alphabet of Q. Now, earlier I stated Q to be the set of all items which satisfy the axioms. That makes no sense if the axioms are just a string of symbols, so we need to introduce a “meaning†function. This function isomorphically maps a set of symbols from the alphabet to an item y. The item y is defined as an item/concept either in this universe or derived from something which is in this universe, or is derived from something that is derived from something that is in this universe, and so on. I term this property being an element of degree n of the universe, where n indicates how many times the “derived from something†is iterated. In other words, y must be something not 100% abstract – somewhere along the way, it had to be derived from something real by an arbitrary deductive method. It could be one from model theory, proof theory, or other standard type of deduction. For our purposes, a universe is defined as any thing which responds to a “mind†,i.e., Turing machine. The Turing machine receives its input from the universe, and its ouput alters the universe. Thus, the universe is any permutation of anything whatsoever that is consistent with the given Turing machine. Anyway – Q is thus the set of anything isomorphic in some sense to y. Furthermore, There has to be at least one Turing machine which is an element of Q. Up till this point, all of the statements have been assumptions, ones which certainly could be satisfied. Any terminology, such as universe, mind, etc., are simply terms which make clear what thoughts led to these definitions. All , however, are still simply abstract possibilities and may very well not correspond to the actual things at all. Now, what I am attempting to prove is that if we know that a “mind” M is an element of Q (say, if Q is the set of all minds) that the mere fact that M fully believes that the abstract formulation ,called a.f., (a set of axioms) is the set which Q is based on, and that we know both the equations of M and a.f., then we can derive what the actual axioms are. The proof is not meant to be within the original “axiomatic” system, but to be simply a result from standard set theory and logical postulates. Here is my idea: We know that M maps his perception of the universe ( an approximation of some sorts based on the actual state of the universe) to an “idea†(defined to be some string of symbols). The truth function maps strings to [0,1]. And equivalent maps a string to another string with the same meaning (note that it is reflexive). So, we know what all of these functions map to – thus we can find their inverse. So, because of M’s belief, we have T(M(a.f. is equivalent to Q))=1
M(a.f. is equivalent to Q) = Inverse of T(1)
a.f. is equivalent to Q = Inverse of M(Inverse of T(1))
Now we are stuck – or are we? We have equivalent expressed in a different form the rest. So, change it to Equivalent(a.f.), which is the same as Equivalent(Q). Thus
Equivalent(a.f.) = Inverse of M(Inverse of T(1))
a.f. = Inverse of Equivalent(Inverse of M(Inverse of T(1)))
Now we take the set of all beta which could take place of a.f. in the equation. Call the set Y. We have established that Q must be an element of Y. However, it must also be an element of all beta which satisfy beta = Inverse of Equivalent(Inverse of M^2(Inverse of T(1))), where the two indicates iteration (Call this set Y2.) This is true because M thinks that he thinks that a.f. is equivalent to Q. In fact, Q must be in Yn for all n. Therefore, Q is an element of the intersection of Yn for all n. It also must have M as an element. So, we have greatly limited the possibilities already. It is my belief that for any a.f., there will only be one possibility for Q – but I cannot prove it, try as I might. I would greatly appreciate it if you looked over what I have so far, and then give some tips for what to do now.
To explain…Well, it is a sort of…mathematical toy universe to find methods of mathematically modeling consciousness. It essentially assumes that the mind is a Turing machine (or other sort of mapping from senses to ideas to bodily actions) and that there exists an axiomatic definition of consciousness. Those, along with a few other assumptions, are used to try to methodize ways of “solving for” the axioms of consciousness if one knows the equation of one mind and the fact that the mind we know believes that a certain set of axioms of his own are equivalent to the actual axioms of consciousness. I think that I have come up with a method of doing such a thing (in the toy universe). In reality, not only may the assumptions not be true, but also it would seem impossible to know the equation of the particular mind in the first place. Yet, I think that simply the possibility of it is interesting and important enough to shed light on what the method of doing such a thing would be in other toy universes. The method that I think might work is described at the bottom of my first post
Quote: ‹ Select › ‹ Expand ›
So, we know what all of these functions map to – thus we can find their inverse. So, because of M’s belief, we have T(M(a.f. is equivalent to Q))=1
M(a.f. is equivalent to Q) = Inverse of T(1)
a.f. is equivalent to Q = Inverse of M(Inverse of T(1))
Now we are stuck – or are we? We have equivalent expressed in a different form the rest. So, change it to Equivalent(a.f.), which is the same as Equivalent(Q). Thus
Equivalent(a.f.) = Inverse of M(Inverse of T(1))
a.f. = Inverse of Equivalent(Inverse of M(Inverse of T(1)))
Now we take the set of all beta which could take place of a.f. in the equation. Call the set Y. We have established that Q must be an element of Y. However, it must also be an element of all beta which satisfy beta = Inverse of Equivalent(Inverse of M^2(Inverse of T(1))), where the two indicates iteration (Call this set Y2.) This is true because M thinks that he thinks that a.f. is equivalent to Q. In fact, Q must be in Yn for all n. Therefore, Q is an element of the intersection of Yn for all n. It also must have M as an element. So, we have greatly limited the possibilities already. It is my belief that for any a.f., there will only be one possibility for Q – but I cannot prove it, try as I might
I am hoping that I could find some assistance in proving my idea and its effectiveness, and then, of course, generalizing the possible results to closer aproximations of reality. I realize that even this may seem to be as clear as mud, but I hope that this clarifies what I am trying to do.
Definitions:
Q:=all items that satisfy “axioms” A1,A2,A3,…An, where:
n is a positive integer
each “axiom” is a string of “symbols” s(a),s(b),…s(q), where
there does not exist anything which is an element of a “symbolâ€
the union of all of the symbols must be finite
logical symbols (first order predicate, modal, etc.) are all symbols
logical axioms of a deductive system are included
M is an element of Q
M is a Turing machine, or some similar function
M: A |-> s(x)s(y)s(z)… |->B(A)
A: Universe |-> approximation (Universe)
Universe:=anything consistent with the M – M’s input is from U(niverse)M and the output changes UM – it changes with respect to a “time variable†, and every element of it must also satisfy the
s(x)s(y)s(z)… are all “symbolsâ€
B: A |-> Universe’
We could postulate that there is a string of symbols in between the two processes A and B for the same reason that we cannot really know that anyone else thinks: we see only inputs and outputs
Earlier, we defined Q as all items that satisfy the “axioms†– yet nothing can satisfy a set of symbols. Thus, we define:
“Meaning": symbols |-> p
p is an element of UM, or derived/abstracted from UM, or derived/abstracted from something that was derived/abstracted from UM…etc.
derived – logically deduced using logical axioms
abstracted- if P(v)=c for all v an element of G, then the abstracted version applies it to a different set than G
For further use,
T(truth):symbols |-> [0,1]
Equivalent: f |->h
Meaning(f)=Meaning(h)
Here is one that I am not quite sure how to define as a function (it really shouldn’t , but) There Exists: Set x string |->the statement â€string an n element of setâ€
Assumptions:
We know that there exists the string Q is equivalent to R, where R is some set of “axioms†from some set of “symbolsâ€, within M’s processing
We know M
We know R
Method:
By assumption, T(ThereExists(BM(Q Equivalent R)))=1
ThereExists(BM(Q Equivalent R)) is an element of T^-1(1)
BM(Q Equivalent R) is an element of ThereExists^-1(T^-1(1))
(Q Equivalent R) is an element of BM^-1(ThereExists^-1(T^-1(1)))
Now, we know that Q Equivalent R means Equivalent(R) and Equivalent(Q), so
Both Q and R are elements of Equivalent^-1(BM^-1(ThereExists^-1(T^-1(1))))
We know that M “thinks†that it “thinks†that Q is equivalent to R, So
Both Q and R are elements of Equivalent^-1(BM^-2(ThereExists^-1(T^-1(1))))
We can continue the line of reasoning, ending with “Both Q and R are elements of the intersection of Equivalent^-1(BM^-n(ThereExists^-1(T^-1(1))))for all nâ€
Conjecture:
Q and R are the only elements of the intersection of Equivalent^-1(BM^-n(ThereExists^-1(T^-1(1))))for all n
Significance if correct:
If M is interpreted as Mind, A as the senses, its symbol-string as ideas, and B as the bodily output (be it in a following thought or physical action), and Q is the set of all minds, then one arrives at the statement that one can determine Q from a mind and its beliefs. An application might be to use an artificial intelligence which passes every Turing Test and is conclusively sentient and take its program and beliefs on the mind to program every possible mind. Using a more formalized Calculus of Self ( aleph.se/Trans/Cultural/Phil … ntity.html ) , it becomes apparent that the creation of another mind of yours would allow you to experience what the computer you experiences. In other words, if you program Bob’s computer mind to perceive being chased by a shark, then a part of Bob in real life will perceive it. The identity of Bob’s mind could be determined by some method of correlating brain signals with the computational processes occurring in the computer. In fact, if you were to program the “Bob†algorithm to run on, say, 30 different computers then the majority of him would perceive that shark. The only part that wouldn’t be would be a small twinge of his thoughts. Of course, it can be fairly safely assumed that any program of any mind would require vast computational resources, so parallel processing would probably be in order. All of this is assuming, however, that the human brain would not overload and go insane under the simultaneous perceptions. If no one would go insane, then one could (as long as there is some factor of “desire†in Q’s axioms) program a sort of LifeLight (see Pendragon, The Reality Bug). Horrible ethical issues would be created, but would probably be solved. Some interesting experiments could also be created. What if the program it is based on is not really sentient? What if enough mind duplications are formed that they form a sort of “Meta-mindâ€, much as the neurons of the brain collectively emerge into consciousness? Then again, the whole idea could be wrong and I have just wasted half an hour of my life.
Thank you very much for looking over this! I promise that it is all much easier to understand with symbols 
. I myself can barely understand it with the words! I hope that you will be able to help! Bye!