excreationist

John Page:
That article on the "Meaningful Machines" company was interesting. I wouldn't say that the computer quite "understands" language to the level that we do though... but it could be said that it can (theoretically) accurately translate language.

Peter Soderqvist

Soderqvist1: language is transformable into numbers, and vice versa, because Godel has translated Russell and whitehead's momentous book. Principia Mathematica into numbers that was part of Godel's proof regarding his Incompleteness theorem 1931! We have seen that the conclusion - philosophers are mortals- is derivable from its two premises, and is thus computable in a syllogistic framework! We also saw that the Cretan's statement; I am a liar! Is not derivable from its two premises, and is thus incomputable, in these senses human mind is some kind of a Turing Machine, but a human mind is not a Turing Machine in every respect! Since we can see some truth statement, which is not formally derived! I have found something on the Internet (Cassius J. Keyser) in other matters, but yet illustrate what I mean! Look below here emphases in bold type by me!

The European Institute For General Semantics!
"You will know that no doctrine can, without committing the unpardonable sin of circularity, undertake to define all of the terms it employs but that every doctrine must employ one or more terms regarded as being, without definition of them, sufficiently intelligible for the purposes of clear discourse. You will know that for a like reason no doctrine can furnish proof of all its propositions but that every doctrine must contain one or more propositions which it takes for granted, using them without demonstrating them. And you will know that a doctrine can have maximum clarity and cogency when and only when it has the minimum of undefined terms and undemonstrated propositions."
— Cassius J. Keyser, TAT
http://www.esgs.org/uk/und.htm

Gödel showed that within a rigidly logical system such as Russell and Whitehead had developed for arithmetic, propositions can be formulated that are undecidable or un-demonstrable within the axioms of the system. That is, within the system, there exist certain clear-cut statements that can neither be proved nor disproved. Within any given branch of mathematics, there would always be some propositions that couldn't be proven either true or false using the rules and axioms ... of that mathematical branch itself. You might be able to prove every conceivable statement about numbers within a system by going outside the system in order to come up with new rules an axioms, but by doing so you'll only create a larger system with its own un-provable statements. The implication is that all logical system of any complexity are, by definition, incomplete; each of them contains, at any given time, more true statements than it can possibly prove according to its own defining set of rules.
http://www.miskatonic.org/godel.html

Soderqvist1: Thus, if we ask a Turing Machine to compute if our arithmetical systems are complete? The machine will go on, and on in a loop (infinite regress) without halting! The question is not computable, and is thus undecidable by a Turing Machine! But mathematicians know that, that the answer to the question is that; our arithmetical systems are incomplete!

excreationist

Peter Soderqvist:
"....Gödel showed that within a rigidly logical system.... propositions can be formulated that are undecidable or un-demonstrable within the axioms of the system"

Is a human a "rigidly logical system"? Let's assume our "axioms" are our current knowledge and beliefs. How about this for a proposition - "Is there an any cheese on any other planets?" or "Is the weight of the moon, rounded to the nearest ton, an odd number or an even number?"

If humans are "rigidly logical systems" who face some undecidable propositions, what is the big deal if AI would face the same problem?

"....Thus, if we ask a Turing Machine to compute if our arithmetical systems are complete? The machine will go on, and on in a loop (infinite regress) without halting!..."

If you make it act like a human and give up after a while, then it would stop.

Peter Soderqvist

Soderqvist1: Ex creationist, you have posted this on page 4, May 14, 2003 12:46 PM: "Unfortunately I don't have enough time to do much more than skim read some things."

I am the opposite of that, because I am too busy with readings, I have too little time in order to reply!

Best regards!

excreationist

Peter Soderqvist:
I guess that would explain why you didn't reply to my previous post to you either... well that suits me. I just don't want people to have the impression that I'm not posting because my position is fatally flawed.

sodium

You seem to be asking if something is decidable computationally, but I'm not sure exactly what. But here's a more general answer.

1. If a question has an answer, then it is decidable computationally, in principle. For example, let's consider the question, "Does life have meaning?"

I can easily write a program that when faced with this input will output the answer "Yes!" I can also create one that will answer "No!" Assuming this question has an answer, one of these programs will be right. So, one of my programs, although I don't know which one, is able to answer the question using purely mechanical processes.

You might say that this kind of canned answer isn't good enough, and that the computer should be able to justify its answer. But as long as I can limit the length of this justification, there will be a program that can spit it out in response to the question. So, the problem is still decidable computationally, if it is decidable at all.

John Page

For the answer to be meaningful, the computer needs to understand the question and provide its reasoning. If not, such generated answers will be an answer to a question, not necessarily the one asked.
This may well be true, but in my Lego analogy I was trying to point out that the scope of the problem may be "outside the system and rules as defined." The issue then becomes the nature of computations (mathematical, logical, neural, set-theoretic etc.) and I think this is one of the points Soderqvist1 was pointing out.

Cheers, John

DRFseven

But isn't this exactly how humans come up with answers?

John Page

LOL.
However, if the answerer does not not understand any of the questions one might expect only a 50% correct answer rate. Some humans seem to be able to exceed this.

DRFseven

Q: Why do you think we have free will?

A: Because if I didn't I'd have to excuse criminals!