First principles… for fun and prophet.

[LMNO]

I'm not the Emergence scholar here, so I can't comment on that.

However, I can say that Z = "the current mix of information and ignorance that I am currently provided with."

I'm sure you can work out some sort of math, but ultimately, it doesn't matter.  Maybe Logic is just another model... It's a way of saying "this is more true than that".  The percentages are just a way of showing the gradual nature of truth in the system.

[Captain Utopia]

Any time you can evoke Emergence, the "truth" becomes the system, unrelated to the various "truth" states/predictions of the components. Since Emergence can be thought of as a metaforce which transcends domains, then the study of Emergence may be the closest we can get to a "first principle" truth. It doesn't directly contradict "the ___ which can be spoken is not the true ___", as there still remains no way (from within the system) to know the greater "truth" of the past, nor predict future events with absolute accuracy.

But to say that it doesn't matter is a tautological argument which doesn't seem to get us anywhere. My interpretation of Emergence may be tautological too, but you can derive a testable hypothesis from it, and stand to benefit as long as it holds true.

I'll let Kai kick me if I'm shitting all over the theory.

[LMNO]

Again, I can't speak to emergence, but I can point to an old thread that might clarify my main points.

In this dialogue, JPF is "Jean Paul Fartres" and ME is, well, me.

JPF: To return to the original topic of conversation, EP/ML seems to gives us the best possible platform to move forward logically, but does that result in knowledge becoming a probability?

ME: Yes.  Knowledge appears to be an evolving thing, and can often be hinged upon a frame of reference of a window of time.  While I "know" that my pen will fall "down" if I drop it, there is a very small chance it won't, for various reasons.  While the percentage of that happening is infinitesimal, it still precludes my knowledge from being 100% sure.  But for me, it's close enough that I don't worry about it.  I feel that nothing can be known 100%, and that's a good thing to me.

JPF: Truth as only a possibility?... and if that's so, then wouldn't the original assumption seem a possibility?

ME: Yes.  Maybe Logic/E-Prime (ML/EP) are simply game rules that we have arbitrarily assumed. (Side note: even the phrase "original assumption" implies a less-than-100% level of assuredness to begin with).  Those that find it useful, use it.  Some have decided that, for now, it's the best set of game rules to use.  If a better one comes along, the chances are good that ML/EP will be abandoned in favor of the new rules.  ML/EP shouldn't be thought of as "the" answer, just a set of beneficial rules.

JPF: Doesn't it erode any ultimate basis for subscribing to EP/ML since probability encompasses all probabilities? 

ME: Are you trying to do a George Bernard Shaw-style paradox?  Because it's not working.

JPF: The benefit of EP/ML is only a possibility.  Why do we have greater confidence in EP/ML? 

ME: Because when using ML/EP, the level of opinion and prejudice is made more apparent.  ML/EP shows the degree of bias in the system.  This leads to greater clarity, though (of course), not 100%.

JPF: To what degree is our confidence greater in it than our confidence in other possibilities.  Using ML, what convinces us that ML is true(r)?

ME: There is no "truth" in ML/EP.  As said before, they are merely game rules.

JPF: In short can EP/ML convince us of any truth, itself included?

ME: No, because that is not its intended purpose.

Essentially, you seem to be trying to fold ML in on itself and make it implode, but ML easily encompasses itself in a very clear manner.

In addition, you seem to be saying that if we can't get to 100% truth, then its Hassan I Sabbah (misquoted) time: "Nothing is true, everything is permitted."

But that's not what ML does. You seem to be using polar thinking on ML, "true/false", where ML behaves more like, "not true/kinda true/more true than that/pretty awfully convinced that this is most likely true".

Just because probably nothing can be 100% true doesn't mean that everything is false (unless you ask a Buddhist).


JPF: As far as possibilities are concerned, do you think that there are ways to deduce what degree of probability can be associated with any idea?

ME: So, you're looking for a mathematical equation that will give you an exact percentage? I'm not sure there's a catch-all formula, but if you really wanted to look, I'd suggest quantum physics as a start.

JPF: Does everything end up having an equal possibility of occurring or is there still a difference in possibilities?

What I mean is: your pen is dropping. There's an infinitesimal chance of it becoming a brown dwarf and a more likely chance of it hitting the ground. Can you measure that still? Can you say that hitting the ground has a greater chance of happening than brown dwarf-morph? If so, how do you measure that with ML?

ME: Remember, these are game rules, and therefore, arbitrary. Yes, you probably can measure the probability of pen-to-brown dwarf, but I don't get that picky. I just say, "not fucking likely", and carry on with my day. Not to mention, if that did happen, knowing how improbable it was will be the least of my worries.

JPF: "not true/kinda true/more true than that/pretty awfully convinced that this is most likely true"
-- Can we provide percentages or is thaat impossible?

ME: You can, if you'd like. I'm more subjective. The point is that it's not a "yes/no" dichotomy; it's a "more than/less than" evaluation.

JPF: I guess what I want to know is: if every possible scenario is still a possibility, does that mean that 100% chance (of something happening and something not happening) is divided infinitely?

ME: I don't see why not. But much like in physics, you'll get a large chunk of the 100% divided among a handful of things, and an extremely small fraction of a percent taken up by everything else.

JPF: I was asking specifically ABOUT the more/less thing and your last paragraph answered my question.

Finally.

ME: Wait, your whole point was whether or not a system of game rules that subjectively applies percentages of truth can be divided infinitely?






Wow, that was really stupid.

...And that, my friends, is how these sorts of things usually end.

[Captain Utopia]

Knowing only one weighted neuron in a network can tell you nothing about the result, it's the interactions and mapping of multiple neurons which are weighted relative to each other that produces a truth/result greater than the "comprehension" of the individual neurons.

[LMNO]

I'm sure you think you're making a point, but I have to be honest, I'm not seeing it.

[Requia ☣]

http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

Simply put, a system cannot be both complete and consistent.  In any consistent system, there will be truths that cannot be proven.  See Godel, Escher, Bach for more detail.

I never got why thats supposed to be insightful.  We *made* the systems, they are 100% made up from human imagination.  Usually they try to match the world we live in, because that makes them useful, but they don't have to.  Those unprovable bits are the basic building blocks of the system.  It's like an architect getting excited by realizing that you can't make wood and have to get it from somewhere.

Far more interesting is the idea that its possible to have a completely proven (if inconsistent) system at all.

[Triple Zero]

no that stuff would be the axioms of a system, Gödel talks about theorems.

the difference is that axioms are given as the basic building blocks of a formal system, and are asserted as True. like wood, in your example.

the unprovable theorems can be stated, but their truth value can never be determined or proven. like uhm ... i dunno what the architectural equivalent of this would be. some kind of paradox thing.

[Cain]

Because, thanks to the influence of Plato, everyone thought they were making use of a most excellent mental faculty (ie reason) to discover the underlying, inbuilt laws of the Universe which are both Really Real, 100% discoverable and entirely comprehendable by a person of a certain amount of intellect.

[Requia ☣]

I thought the unprovable theorems thing was Turing?

[Triple Zero]

I thought the unprovable theorems thing was Turing?

nope Turing was the undecidable problems ..

...



undecidable problems, unprovable theorems, whatever this is cracking me up.

lemme help you out, these things are about formal mathematics. if there's any way to draw an analogy with reality, it's not been mentioned in this thread so far.

they're good fun proofs and if you read them and can grok the mathematical rigour, provide an excellent mindfuck, and in that way they are useful for taking a good look around in your cage (happened to me), got me started on a long journey, eventually took me to discordia, but by now I know they're not exactly suitable for drawing conclusions about reality.

they are useful, but as far as I know only as important fundamentals in formal mathematics and computer science. building blocks in order to derive other more useful and practical proofs from. and very important in that they show there are hard limits to what mathematics can do. and that is awesome.

[Captain Utopia]

Definitely awesome, but if Godel et al are not that useful for drawing conclusions about reality, then what relation do they have to First Principles?

[LMNO]

That First Principles don't exist, basically.

[Captain Utopia]

That First Principles don't exist, basically.

[LMNO]

H, come on, you MUST have seen that coming.

[Cain]

There is no spoon.

You must slurp your soup directly from the bowl.