R
ronnie_bonigli
Guest
I haven’t missed anything, you’ve just refused to listen to what I’m sayingThere is another thing that you have missed.
I haven’t missed anything, you’ve just refused to listen to what I’m sayingThere is another thing that you have missed.
Science of the Brain: How the Mind WorksThe brain is a very complex system, consisting of about 10 to a 100 billions of neurons, which are interconnected. The mind is the “activity” of this complex system.
Ronnie!If any formal system is inconsistent in any way, then it is completely untrustworthy and can prove ANYTHING is true, even if it is obviously false. An inconsistent formal system will prove that 1 = 0. It’s a junk system. When a human makes a mistake, he can be shown the mistake and “understand” that it is indeed in error, an inconsistent system would still say that the mistake is true, it is completely unreliable.
You, you word-smith, you.There are some of us who observe that the brain is the working of the mind.
However, that observation is off topic.
I am very glad to see your participation and your examples.But there’s a difference between mistakes and bugs. Drink a couple of glasses of wine and we introduce bugs in our system that makes us unsafe to drive. A computer program can have bugs in it but a supervisor program can cancel transactions or reload it if it fails. The program in post #15 isn’t buggy but makes mistakes which it corrects by further evolution. Programs can learn, e.g.
reuters.com/article/2007/07/24/us-babytalk-idUSN2419932120070724
stanfordscientific.org/index.php?option=com_content&view=article&id=73:a-passion-for-service&catid=42:volume-6-issue-2&Itemid=59
Welcome aboard.Those who explain away the power of reason are cutting their own throat!
I’m on a different ship.Those who explain away the power of reason are cutting their own throat! Welcome aboard.![]()
I had just said that an inconsistent formal system **does not **correct it’s mistakes. If a human mind were merely an inconsistent formal system it could not be shown where it make an error and come to ***understand ***that it was indeed an error. This is one of the implications that follow from Godel’s Theorem regarding formal systems.Ronnie!Correcting mistakes is after the fact, a system that makes mistakes can make more mistakes.
But there’s a difference between mistakes and bugs. Drink a couple of glasses of wine and we introduce bugs in our system that makes us unsafe to drive. A computer program can have bugs in it but a supervisor program can cancel transactions or reload it if it fails. The program in post #15 isn’t buggy but makes mistakes which it corrects by further evolution. Programs can learn, e.g.
reuters.com/article/2007/07/24/us-babytalk-idUSN2419932120070724
stanfordscientific.org/index.php?option=com_content&view=article&id=73:a-passion-for-service&catid=42:volume-6-issue-2&Itemid=59
That program is baby stepsand we are far more than computers but we need to compare apples with apples, on a level playing field, with a straight bat, etc.
Searle is one of those theorists though. He is arguing against traditional AI, but not comparing apples with apples. His mystical “causal powers” can be explained by complexity, that at some point syntactic becomes semantic. Us practical guys ask whether semantics are more than relationships and transforms anyway, is there any ultimate meaning?In addition to Godel’s Theorem showing there is a difference in **kind **and not **degree **between a computer system and a human mind, we can look at John Searle’s “Chinese Room”. That thought experiment shows that any system which is base on symbol manipulation can never understand (there’s that word again) what it’s doing, computers will always be philosophical zombies
It’s a big mystery as to why the cosmos is the way it is, why it’s reliable and orderly, why there’s matter at all, why complexity arises out of simplicity, why it provides a backdrop for us to exist. And why simplicity comes out of complexity - you are made of trillions upon trillions of atoms yet they are organized into one person who can have simple thoughts.The problem with that^, however, is that I think he’ll say: reason etc. may be a product of blind forces, but it is not longer subject to them; it has transcended those forces. And is independent of them now.
How would you deal with that^ Does it make sense at all?
Spock is correct. You are thoroughly confused regarding the implications of Gödel Incompleteness.Irony Alert!
Dude, it appears to be YOU who “seriously misunderstand the Gödel Theorem”
But humans cannot grasp the structure of the formal system any more than fully than a machine can (for the very reason, I suggest, that the mind is a machine, and subject to the same real-world limitations as any other machine). You’ve fallen into the trap of thinking that since humans can wrap their heads around simplistic formal systems, and transcend them, cognitively, “jumping up a frame”, that this is a process humans can deploy to arbitrary position. Manifestly, they cannot, or more precisely, we have no reason to think we can, and plenty of empirical reasons to conclude they cannot, any more than this Mac I’m typing this on can.Gödel’s First Incompleteness Theorem states that for any consistent formal system (that would be any computer) there exist propositions (called “Godel propositions”) that cannot be proven true within the system, and yet can nevertheless be proven to be true by going outside the system. And yet because the human mind can grasp the structure of the formal system and understand the meaning of its symbols, it is able to reason about them in ways that are not possible for a merely formal system.
Just noting, per above, that this is the precise point of your error, here. Humans can “stand outside of” some systems, just as a sophisticated software systems. But a human cannot “stand outside of” any given system, and neither can a sophisticated software system. In both of these respects, minds and machines are in the same circumstance.That is, any mechanistic system (anything made of matter, operating under the normal laws of physics) will have Godel propositions which it can not prove to be true, yet are true and can be found to be true by a human being standing outside that system.
No, and that signals a thorough confusion of both what Gödel was on about directly, AND what the ramifications of his insight are. If what you were saying were true, you’d necessarily be able to prove this mathematically, which is one of the neat features of understanding Gödel – when you grasp what he’s saying, it makes your sentence above there manifestly untenable. His whole point is that what you refer to as “kind” is a meaningless, concept. Complexity as a matter of degree will produce this confusion at large scales. It will ‘look mysterious’, and even "different in kind’ in a simplistic way, but that is shown to be unsupportable by just contemplating the implications of the mind as VLSP.Human minds work in a way that is IN PRINCIPLE different in ***kind ***and not degree, from mechanistic systems such as computers or dogs.
That’s not the case. You’re suggesting that any inconsistency is tantamount to complete inconsistency. If I formalize some rendering of naive set theory, I will have something formally inconsistent – susceptible to paradoxes like Russell’s Paradox or Berry’s Paradox. But those paradoxes do not negate the consistency of the productions that are consistent, non-paradoxical. Axiomatic set theory and ZF and other formalizations that implement axiomatic relief to steer around Russell’s paradox share a huge overlap with the old naive set theory; this is the foundation of basic mathematics.If any formal system is inconsistent in any way, then it is completely untrustworthy and can prove ANYTHING is true, even if it is obviously false.
This does not follow. I can conceive of inconsistent systems where that would be produced as a contradiction, but for others, that will never be produced, and can’t be produced per the rules of the system, even if other consistencies do obtain. That’s the import of Russell’s Paradox. It didn’t invalidate naive set theory as a whole. Far from it. It was a disturbing, fascinating… “hole” in an otherwise highly consistent and useful system that foreshadowed discoveries that Gödel and others would later shed more light on.An inconsistent formal system will prove that 1 = 0.
There’s no reason an inconsistent system wouldn’t or couldn’t be just as corrigible (and possibly much more corrigible if it is not encumbered with the complications of vain emotions, etc.). I think you’ve got a major breakdown happening in your concept of what “inconsistent” entails. It’s not “a complete loss” or “utterly inconsistent”. In formal terms, inconsistent just means “not perfectly and completely consistent”. It’s a logic error to say that if a system is not perfectly consistent, it is not and cannot be consistent at all.It’s a junk system. When a human makes a mistake, he can be shown the mistake and “understand” that it is indeed in error, an inconsistent system would still say that the mistake is true, it is completely unreliable.
I’m not sure where you’re coming from with a lot of this, even Russell himself said you can prove anything true in an inconsistent formal system, and then went on to use an example where he “proved” that Russell and the Pope were the same person.That’s not the case. You’re suggesting that any inconsistency is tantamount to complete inconsistency. If I formalize some rendering of naive set theory, I will have something formally inconsistent – susceptible to paradoxes like Russell’s Paradox or Berry’s Paradox. But those paradoxes do not negate the consistency of the productions that are consistent, non-paradoxical. Axiomatic set theory and ZF and other formalizations that implement axiomatic relief to steer around Russell’s paradox share a huge overlap with the old naive set theory; this is the foundation of basic mathematics.
It’s also worth pointing out that “true” and “false” are problematic terms, here. I understand what you might mean in saying naive set theory is “false” because of Russell’s Paradox, but what is really discovered their is inconsistency. Russell’s Paradox holds that the set of all sets that are not members of themselves is a member of itself IF AND ONLY IF it is NOT a member of itself. Which is “false” there? That R is a “member of itself”, or it is NOT a member of itself?
“False” doesn’t mean anything in that context. It’s just a contradiction produced by the symbolic calculus of set theory being applied.
This does not follow. I can conceive of inconsistent systems where that would be produced as a contradiction, but for others, that will never be produced, and can’t be produced per the rules of the system, even if other consistencies do obtain. That’s the import of Russell’s Paradox. It didn’t invalidate naive set theory as a whole. Far from it. It was a disturbing, fascinating… “hole” in an otherwise highly consistent and useful system that foreshadowed discoveries that Gödel and others would later shed more light on.
Just as a way to show yourself you are mistaken, you might see how you do in taking naive set theory and getting it to produce 1=0.
-TS
You’re confusing “an inconsistent formal system” with “any inconsistent formal system”. Not all inconsistent formal systems are alike or have the same productions which is I think the point you are stumbling on, consistently, here. I don’t doubt that a system that “proves” Bertrand to be the Pope is an example of inconsistency. But it doesn’t follow that any inconsistent system can produce that, which seems to be an idea you are holding to.I’m not sure where you’re coming from with a lot of this, even Russell himself said you can prove anything true in an inconsistent formal system, and then went on to use an example where he “proved” that Russell and the Pope were the same person.
There’s no authority invoked in anything I’ve posted. You don’t need to rely on any authority claims here to grasp where your understanding broke down. Have to step out for a bit, but will come back and layout a simple formal system that we can see to be both inconsistent (that is, not completely consistent), and which yet cannot just produce any arbitrarily selected proof.Btw To just ramble on an on and keep telling someone they’re wrong on your authority is kind of a weak argument
I find that when I come across an arrogant person, one who does not know that he is not half as smart as he thinks he is, it is best to just point him in the right direction rather then continue to engage his overblown hubrisYou’re confusing “an inconsistent formal system” with “any inconsistent formal system”. Not all inconsistent formal systems are alike or have the same productions which is I think the point you are stumbling on, consistently, here. I don’t doubt that a system that “proves” Bertrand to be the Pope is an example of inconsistency. But it doesn’t follow that any inconsistent system can produce that, which seems to be an idea you are holding to.
-TS