Quote:Original post by RPGeezus
We don't even know what it means to be a concious sentient being ourselves. The only truth, in this regard, is 'I think, therfore I am'. Of course the questions 'What is I' and 'What is Think' still go answered.

Don't think about it too hard. These questions have driven people to depression and madness. :)

The question is undecidable. You need to prove or disprove determinism first, which is provably not possible. But, if the world is nondeterministic, then the proof doesn't matter...

If the Universe is nondeterministic, then it follows that you can think. It also follows that all math and logical proofs are invalid.

If the Universe is deterministic then math and logical proofs are valid, but it means we aren't really thinking, that there is no morality, and that all decisions were pre-decided from the big bang, or before.

Any good AI class (or philosophy class) will get in to this subject.

frob.

I never understood what determinism has to do with anything. Do you care to explain or post a good link?

Quote:Original post by alvaro
I never understood what determinism has to do with anything. Do you care to explain or post a good link?

Wikipedia has a pretty good article on determinism, but it focuses more on the philosophy of the problem.

(Okay all you skilled math people, don't cringe too much at this. I know there are flaws and holes in what I am describing below. I'm trying to convey the principle.)

The basic axioms of pure sciences, such as math, are that:
* The Universe behaves the same way, everywhere
* Given the same conditions, you get the same results

This is called "determinism".

It is something we rely on in computers all the time. If we set the same starting conditions, and we run the algorithm a bazillion times, it will always give exactly the same result. If it doesn't, either the algorithm or the machine is flawed.

It is a guiding principle in the scientific method. We find a set of rules that describe the Universe as we understand it. When we find a problem with it, we improve on the rules to include the new observations.

Next point

There are many Grand Challenge problems out there. These are basically really big problems that will help lots of people if they are solved.

One Grand Challenge problem of a century ago: Is it possible to have an automatic proof verification machine?


The answer led to several odd results, including Godel's incompleteness theorms, Very simply put, it means:
* We can never have a system that finds ALL math proofs. Such a system will also generate falsehoods.
* If a set of proof is complete and proves itself to be consistant, those proofs are inconsistant.

So as long as we take the first two basic theories (universal consistancy of results) then the second set follows (some things cannot be proven).

So we divide things in to three classes:
* Stuff we can figure out. (computable)
* Stuff we could figure out with infinite time. (intractable)
* Stuff we can never figure out, even if we had limitless resources. (undecidable)

Lots of things are computable. You can count the fingers on your hand, or the leaves on a tree, or figure out your taxes. (Well, maybe not the taxes... [grin])

An intractable issue is something like breaking strong encryption algorithms with a huge crypto key. It is possible to do. If we only used the resources and knowledge we have today, a brute force attack could take longer than the expected life of the Universe. Maybe someday we'll have the resources or knowledge to solve the problem, but we don't today.

One undecidable is issue is the continuum hypothesis. If we subdivided time and space (and a few other things) into smaller and smaller pieces, do we eventually get to a single atomic unit of time or space? Or is it infinitely divisible and continuous? It is impossible to know.

Another undecidable issue is the halting problem. Simply, it is undecidable if the function defined by an algorithm will stop in finite time. There are several very small programs (some as small as 10 lines of C code) that we cannot prove will ever finish, such as finding a number with certain properties where the number may not exist. Again, it is impossible to know.


This gets us back to the original problem: Can we prove or disprove the first two issues, namely, is the Universe consistant everywhere, and do we always get the same results?

If it can be proven, then it follows that everything that happens in the Universe, has happend, and will ever do, was predetermined from the first instant of time. This includes all human thought, meaning all choices people make are not choices at all.

If it can be disproven, then it follows that absolutely nothing is certain in the Universe. It means it is possible for objects, planets, even star systems, to simply pop into existance. Or instantly be destroyed. It also means that people are capable of thought, rather than being compelled by the first instant of the Universe.

Solving the problem has been proven to be undecidable. Therefore, we cannot know the answer within the confines of the Universe.


I've oversimplified a few issues and left out few details, but most of them require more detail and math than is appropriate for a gd.net post.


The result end result is a great philosophy problem. If we don't have free will, explain moral issues like the law and punishments. If we have free will, explain what it is and how it works. Your essay is due at the beginning of class on Friday


frob.

Quote:Original post by frob
If the Universe is nondeterministic, then it follows that you can think. It also follows that all math and logical proofs are invalid.

Actually there is another possibility besides Freedom and Necessity - Chance. It only follows that you can think if the universe is nondeterministic and Freedom rules.

But if the universe is indeterministic and Chance rules, then you can't think (because everything happens by chance, not by will), and at the same time nothing can be predicted (or accurately simulated) either.

P.S. If you fully embrace the description of the universe currently given to us by physics, then it follows from quantum mechanics that the universe is indeed ruled by Chance.

Quote:Original post by Devilogic

Quote:Original post by frob
If the Universe is nondeterministic, then it follows that you can think. It also follows that all math and logical proofs are invalid.

Actually there is another possibility besides Freedom and Necessity - Chance. It only follows that you can think if the universe is nondeterministic and Freedom rules.

But if the universe is indeterministic and Chance rules, then you can't think (because everything happens by chance, not by will), and at the same time nothing can be predicted (or accurately simulated) either.

P.S. If you fully embrace the description of the universe currently given to us by physics, then it follows from quantum mechanics that the universe is indeed ruled by Chance.

Like I said, it is an oversimplification. [grin]

You're right, nondeterminism doesn't prove free will, only that free will is possible.

Chance is nondeterminism. And the problem still exists: prove it.

By the way, what kind of a proof are you asking for? A mathematical proof, or a philosophical "proof"?

Since philosophy is mathematically not a science, you can prove anything within its context. So I guess you can also prove (or disprove, whichever you like) determinism. :)

Quote:Original post by Devilogic
By the way, what kind of a proof are you asking for? A mathematical proof, or a philosophical "proof"?

Since philosophy is mathematically not a science, you can prove anything within its context. So I guess you can also prove (or disprove, whichever you like) determinism. :)

Since it's been proven to be an undecidable problem, it will have to be a philosophical proof.

I'm comfortable enough with the problem that whichever way you argue, I'll argue against it. [disturbed]

frob.

I am fairly familiar with Gödel's works, or at least I understood the proofs when I took the time to study them (my memory is a little bit fuzzy on some details now). I am also familiar with the notion of determinism. And I still don't see a connection between these things and intelligence or conciousness. I know some of these connections are made in "The emperor's new mind" by Roger Penrose, but I don't think his reasoning is sound.

I will explain my personal position. I honestly think that there is no such thing as free will in a strong sense. That doesn't mean that people don't make decissions. It just means that decission making falls within the laws of physiscs, like everything else.

The problem of conciousness is probably not a problem at all. I think the problem is with the way humans tend to think of the world. Most people have a description of the world that consists of some space populated by inanimate things and by living things. Both inanimate and living things are subject to the laws of physics, but living things have complicated behaviours that we don't fully grasp with our understanding of physiscs, so we imagine a "soul" or a "conciousness" attached to them, which is responsible for their behaviour. The question of whether a computer can have a conciousness is a human-centric questions, since "conciousness" is probably an artifact of human [poor] thinking, and not an element of reality.

The answer is then that whenever a machine has a complicated enough behaviour, humans will treat it as having a conciousness, and that will be it. Gödel and determinism have very little to do with conciousness. Belief in souls or spirits might have more to do with it.

Just my personal opinion. Feel free to attack it. That's what forums are for. :)