Free, Bound variable + misc

A notion I was thinking of using before is already defined in maths...

A free variable is a symbol which has an external use. A bound variable has a particular use within the expression and so has no external meaning. Bound variables have closure of meaning while free variables must link to the outside.

A closed expression (a black box) can only replicate "all" the output of a open expression, it cannot determine "which" value a free variable takes.

This is the concise way of expressing the problem I had with "Aime" my 1996 AI experiment. Aime was written in a hermetic box seeking whether "feedback" could explain consciousness. It became apparent very quickly that anything that operates within a closed box has no meaning to the outside world.

Arguing further now, an AI machine must be able to link with its environment in order to mix with other agents ... i.e. as required by the Turing test.

Now any computer program, being just a collection of bits, is a number. There are a finite number of programs (given that no-one is ever going to write for ever, and no machine could ever write for ever).

One of those programs is the Mind Machine (MM) and we assume that humans have found it. Now the MM takes some input. There must be a finite amount of input for the MM to discover itself ... given that humans have done so. So that input is also a finite number. So the MM and the input data together form another single finite number.

Now we have to give the MM a machine on which to run else we would need to code how to build it, another number. And another number to build that machine and so on forever. So we give it a machine. Maybe like in Hitchhikers Guide to the galaxy it needs to build a new machine * x before it can get started

OK some problems here since maybe working out the start data is non-computable... anyway that is a start on a method of proof...

Miscellaneous ...

Vertical/lateral thinking - step by step proof/deduction forward and leaps followed by working back.

Could there ever be "artificial life". That is a question very closely related to this blog and one that will become more central after this initial work is done. Can the mind be artificial is the current project since we can use self-reference more easily to test ideas.

Hermeneutics seems more relevant as time is progressing to. I just need to find a nail for the coffin of deductive/logical/mechanical process thinking to show that fixed within rules we cannot escape to investigate those rules.

Rules btw might be the foundation to work with. Even set theory has rules that define what is a good and a bad formulation and process.

So the question is what rules define the rules? or if we define a rule how do we know that the rule is being followed? or if we define the word "rule" how do we know that it is being used correctly?

All these questions come down to the old point that the question "what is reason?" can't be answered without reason so it presupposes the answer.

Or the famous Anthropic principle http://en.wikipedia.org/wiki/Anthropic_principle which I would want to expand to the mind. We need a mind before we can even do the investigations into Life (carbon or anything else) and existence.

btw the issue of can things be their own foundations didn't get anywhere in set theory. I wanted to show that T <> {T} but the following suggests its quite consistent...

Consider a U = {T, A} where T = {T}
so T' = A

Now P(U) = { {}, {T}, {A}, {T, A} }

and consider a new universe of the elements of P(U) = U1

Given the definitions above this universe has 3 members U1 = {T, {A}, U}

so now T' = { {A}, U}

I was hoping for a contradiction. But actually if T' = A = { {A}, U} then

A = { {A}, U }

So A u T = { T, {A}, U } which is a perfectly consistent universe! I think...

anyway my brain hurts now so off to pub :-)