Dave_Oblad wrote:I set a goal for myself to see if I could find a reality that doesn't depend on anything tangible. A purely logical and mathematical type reality. Hence my first set of rules.
That's fine, but it's not science. Like I said, what you are trying to do is really philosophy. In particular, it's metaphysics. Whether you are being successful in that task is an entirely different matter...
Dave_Oblad wrote:A paradox is self conflicting and denies it's own existence. You can't go back in time and kill your earlier self. If you did manage to perform this task then you would be dealing with branched realities in which case you didn't really kill the original version of you.
This is still too vague. All you did was to give an example of a paradox. You didn't actually give me necessary and sufficient conditions for a given proposition to be paradoxical. And, in fact, there's no reason to a priori rule out the kind of event that you have in mind, other than that you find it counter intuitive or in some way strange. It certainly doesn't necessarily result in a logical contradiction. It could be that there are good reasons to rule out the kinds of things that you have in mind, but you have not named them. Furthermore, given the lack of necessary and sufficient conditions, you haven't been clear enough about what you actually mean.
Dave_Oblad wrote:A circular argument is like: The universe came from a singularity, which came from a previous universe that collapsed, that came from a singularity, that came from a previous universe.. etc.. forever backwards in time. In other words.. I'm saying all cause/effect functions have a beginning initial state where sequence/time is concerned. I would accept this as an Axiom.
That's not a circular argument, or at the very least, is not what is usually meant by a circular argument. A circular argument is usually taken to be an argument whose conclusion is already assumed amongst the premises. A circular argument about the universe might go like this:
1. The Universe exists.
2. If the (1) then the Universe exists.
3. Therefore, the Universe exists (by Modus Ponens, from (1) and (2).)
Now, an argument like this is bad because it doesn't actually tell us anything. It is undoubtedly true that if the Universe exists then it exists. There's nothing false in the argument I just gave; nonetheless, the lack of new information is deeply troubling.
To take the idea that the Universe cannot have some kind of cyclic existence actually begs the question against any cosmological theory which posits precisely that. Therefore, not only are you using a non-standard definition of "circular", but you are also begging the question against many other theories. Most would contend that being circular is just as bad as begging the question; why do you think you can take it for granted that other theories must be wrong, without even having argued against them?
Dave_Oblad wrote:Another Axiom: True Randomness can't exist in a purely mathematical setting.
Proof? You cannot write a mathematical formula or program or statement that produces a random numerical result.
Well, that's just patently false. I can certainly construct random variables and then tell you about their properties. If what you claim here were true, then much of modern probability theory would not be possible (and, in fact, I'd be largely out of a job!)
In any event, even if it were true that randomness can't exist in mathematics, we observe true randomness in the Universe in which we inhabit. Sure, you can quote Einstein as saying otherwise (as you proceed to do), but the lesson here is more than even Einstein got some things wrong (actually, he got a lot of things wrong.) In so far as the evidence that we have available to us now, the universe is, at bottom, entirely random (though governed by deterministically evolving probability distributions, except during measurements, when even the distributions fail to evolve deterministically.)
Dave_Oblad wrote:Call them hidden variables if you wish.
Except that hidden variables have been ruled out by the violation of Bell's Inequalities....
Dave_Oblad wrote:The one thing that can't be eliminated however, is logic or math.
Dave_Oblad wrote:A logical complex formula can produce a complex answer. For every logical formula that has an absolute answer, then an absolute answer exists for that formula. Sounds redundant but is nonetheless true. There is no fixed limit on the complexity of the formula(s) and there is no fixed limit on the complexity of the result(s) for all formulas. If the solution to an equation is complex enough to support self aware intelligences, then those intelligences might debate with each other if they truly exist or not. (Hint: if they can debate.. then they do exist..lol)
My problem here is that the relationship between the existence of intelligent beings on the one hand, and the existence of complex formulae on the other, is not entirely obvious to me. One might think that one simply does not suffice for the other; that there exist complex formulae without intelligence and vice versa, and that complex formulae are not the things which suffice to produce self aware intelligences. In fact, the precise relationship between the physical world and mathematics is deeply controversial amongst modern philosophers, and has some level of debate amongst philosophically minded mathematicians and physicists. To merely claim, as you do, that complex equations support self aware intelligences is highly dubious; it should take a rather lot of convincing argument to make this point stand (none of which do you actually provide.)
Dave_Oblad wrote:Since there are an infinite number of equations.. then there are an infinite number of solutions.
That's not necessarily true. It could be that every formula in your system produces an answer from a finite list of solutions. What you have to prove here is that for an infinite number of equations in your system, you have an infinite number of solutions. The simplest way to do this that I can think of is to show that your formal system is one to one; i.e. for every formula there exists a unique solution.
However, there's a problem here. You have not specified for us what formal system you're working with. You can't just say "mathematics" because that's not sufficiently precise. Mathematics consists of a large number of different formal systems, many of which are distinct and entirely independent of the others. What you need to do is to specify for me which of these formal systems you are using, prove that there exists an infinity of formulae in that system, then prove that the infinity of formulae imply an infinity of solutions. I can think of a number of formal systems for which that is true, and many of them are useful for doing physics, but it seems that you would have to take an extra step. You would have to argue somehow that one of these formal systems (or perhaps some union of them) actually describe the universe precisely and without error (i.e. that reality ultimately just reflects some formal system like that.) You haven't done any of these things.
Dave_Oblad wrote:The tiniest percentage that spawn intelligences becomes an infinite number because any percentage of infinity... is still infinity.
That's definitely not true. Most people would take 0% of infinity to be 0 (though I have to confess that we're not really being sufficiently precise here. We should be talking about cardinalities or measures on sets and not percentages of infinity, which honestly doesn't really make any sense.)
Dave_Oblad wrote:No universe/reality can mathematically exist with an initial state that includes an infinity. This makes the initial state imprecise and thus no true solution can exist.
Example in programming:
A = 1 to Infinity. (Ok.. as in Case: A=A+1)
A = Infinity to 1. (Bogus, imprecise initial state)
That's simply not true, and, in any case, you need to argue for this; you can't just accept it.
Dave_Oblad wrote:You can take any Virtual Reality Video Game (like "Doom") and convert it entirely (Program, Cpu, Memory, AI, etc) to a pure Boolean form of math. Call this an equation or formula if you like. But in this form.. real monsters do roam the halls.
So because I can encode a representation of an Imp in binary, it is implied that Imps exist? That's just patently absurd. That's a particularly wild eyed brand of Pythagoreanism that I doubt even the staunchest mathematical realist would take seriously.
Dave_Oblad wrote:Time doesn't truly exist either. For all realities, all other realities are simultaneous with a duration of instantaneous.
Just because you combine intelligent sounding words together doesn't make something meaningful or coherent. "For all other realities, there exist an infinity of subjective qualifications." "For all other realities, all other realities are orthogonal to their perpendiculars." Etc. This is just dubious word play.
Dave_Oblad wrote:I know some folks have a hard time wrapping their minds around these concepts.. especially when they are convinced that the reality they exist inside of is somehow more real than just mere mathematics and logic.
Actually, I think something like that is true, though I find all of the arguments which you have presented for this to be entirely too vague and, frankly, just outright fallacious.
Dave_Oblad wrote:This is not philosophy, it's absolute logic.
Except that logic is a branch of philosophy. What you are attempting to do is what is known as formal metaphysics.
Unfortunately, philosophy is a poor reputation, mainly due to what passes colloquially as "philosophy". When people use the word "philosophy" outside of academia, they are usually referring to the kinds of ruminations that 16 year olds have while smoking copious amounts of marijuana. They think of New Age hippy movements and the like. I would like to most emphatically say that this is not what I mean when I say "philosophy". This business of trying to set up a formal system to reason about the nature of reality, which is what I believe you are attempting, is what professional philosophers identify as formal metaphysics. It is not science, and differs quite explicitly from science in a number of ways. However, I think that if you actually read about the other myriad attempts to do what it is that you are attempting, you would be deeply captivated. Therefore, I highly encourage you to pick up the books I recommended in my previous post. At the very least, try checking them out from a local library. What have you really got to lose?