The Foundations of Cognitive Theory

[marplots]

Another aspect of the Turing test is that the AI can also give incorrect answers (as well as "I do not know"). The Chinese speaker in the room is free to make a mistake in matching the question.

Which was one of my objections. I could not distinguish, from outside, a machine that merely returns the question submitted exactly and an uncooperative human who understood Chinese.

Which is, again, a criticism of the Turing test. We want to see the "guts" and if those inner workings tell us something about cognition itself. "Trickery" may pass the test, but doesn't advance the field.

 

[barehl]

Now, whether that argument is sound or not, I'm trying not to weigh in on, since I want to avoid being sidetracked to hear what barehl has to say. But that is the argument. It's not a Turing Test. The Room doesn't have to convince someone that it is strongly intelligent, merely that it understands Chinese.

I would say that you described it pretty well. Searle argued that a CR could act functionally indistinguishable to a person who understood Chinese but that it wouldn't contain any real comprehension. A corollary of this would be that the Turing Test would not require cognition.

Dennett argued that a CR would not be able to function in a way that was indistinguishable to a person who actually understood Chinese. With Cyc in hindsight, there is some weight to Dennett's assertion.

I was starting with a proof that no pattern matching system could function adequately, similar to Dennett's claim but with a more solid argument. Then we move on from there to set theory which is still inadequate.

Yeah, I'll drink to that. It's like wrestling a falsifiable test out of an MDC applicant.

As I've already told you, my ideas are falsifiable in a number of ways.

Hofstadter wrote 737 pages of foundational material in 20 chapters without an actual theory in G.E.B. And, Hofstadter didn't understand most of what makes up cognition. But, you seem to think that I can explain cognition in a couple of paragraphs.

Still, why don't you try us?

You're asking me to work on the book?

 

[barehl]

No, barehl: My way of showing that the assertions in the OP are wrong is to

[*]Start with the same premises except using a different simpler language.

Actually, you didn't. You specified that the language consisted of a bounded set of questions. Clearly (and pathetically obviously) you could use brute force and make an exhaustive solution set for any finite set. I'm not sure why you think this is a new idea or that you are adding anything to the conversation. But, more importantly, this idea has nothing to do with an unbounded set which is what real language is.

You could similarly and equally incorrectly falsify a number of mathematical concepts by starting with a bounded set of numbers.

 

[barehl]

You are right. But the Turing test has a finite number of questions.

ETA: Also think about neural networks as the implementation of the AI. A neural network would learn Chinese in a similar way as we do. It would not look up the answer as a one-to-one match to the question. It would have been taught that the answer to "What number comes after n" is "n + 1". So the number of answers to the questions in the Turing Test would be a function of how well "educated" the computer program is.

This is not going to sink in but...what the hell.

N+1 is not possible as a construct with either pattern matching or set theory. You are talking about mathematical theory which includes addition.

 

[barehl]

Theorem. The set of finite strings over a finite non-empty alphabet is countably infinite.

Yes, that's an excellent proof and you are correct with what you said. Basically, you could view an alphabet as a collection of numbers of that base. So, if you have 26 letters, you could view it as a base-26 number system. We can add punctuation the same way. But, however many characters we use, this symbol system can be represented by a number system of the same base if we wanted to keep the symbol count the same. If we used fewer numbers such as base-10 for an alphabet then it would take more numbers but is still representable. And, yes, this would be countable. Considering that enumeration is also the basis of computational theory I can't imagine what argument could be used to challenge it. However, what is decidedly discouraging is that you think I'm not aware of this.

But, what I've just described isn't what I was talking about. You are viewing this as a box of questions where no question would be repeated. I'm talking about questions per instance which is a box of questions for each instance. I'm guessing that isn't making any sense to you. If we had a single box of questions then we could have one sentence of "Does the cow have spots?"

So, we start with a simple problem. John owns a Holstein. Holsteins are cows with spots. Does the cow have spots?

This does not have an answer with pattern matching unless the question is self referential. Such as, "Does the spotted cow have spots?" The problem with trying to answer this question is that we cannot create a reference to a single instance with pattern matching alone. We could answer this question if it was more general such as, "Do cows have spots?"

We can do better with set theory because we can create a set for a single instance. The information above is adequate to create a set that will give us an answer. But there is actually more than that. We could handle a question such as, "Does John's cow have spots?" This question is again not answerable with pattern matching.

I have a hard time trying to figure out what I have to explain to get basic concepts across. If we were only talking about a set of questions as a string of symbols then it would be countable and each question could have a reasonable answer. However, as soon as we instantiate any topic, the questions become uncountable and reasonable answers are not possible. If we move up to set theory then we can answer a larger number of questions. In other words, using set theory we can reduce some classes of questions from uncountable to countable.

 

[annnnoid]

Yes, that's an excellent proof and you are correct with what you said. Basically, you could view an alphabet as a collection of numbers of that base. So, if you have 26 letters, you could view it as a base-26 number system. We can add punctuation the same way. But, however many characters we use, this symbol system can be represented by a number system of the same base if we wanted to keep the symbol count the same. If we used fewer numbers such as base-10 for an alphabet then it would take more numbers but is still representable. And, yes, this would be countable. Considering that enumeration is also the basis of computational theory I can't imagine what argument could be used to challenge it. However, what is decidedly discouraging is that you think I'm not aware of this.

But, what I've just described isn't what I was talking about. You are viewing this as a box of questions where no question would be repeated. I'm talking about questions per instance which is a box of questions for each instance. I'm guessing that isn't making any sense to you. If we had a single box of questions then we could have one sentence of "Does the cow have spots?"

So, we start with a simple problem. John owns a Holstein. Holsteins are cows with spots. Does the cow have spots?

This does not have an answer with pattern matching unless the question is self referential. Such as, "Does the spotted cow have spots?" The problem with trying to answer this question is that we cannot create a reference to a single instance with pattern matching alone. We could answer this question if it was more general such as, "Do cows have spots?"

We can do better with set theory because we can create a set for a single instance. The information above is adequate to create a set that will give us an answer. But there is actually more than that. We could handle a question such as, "Does John's cow have spots?" This question is again not answerable with pattern matching.

I have a hard time trying to figure out what I have to explain to get basic concepts across. If we were only talking about a set of questions as a string of symbols then it would be countable and each question could have a reasonable answer. However, as soon as we instantiate any topic, the questions become uncountable and reasonable answers are not possible. If we move up to set theory then we can answer a larger number of questions. In other words, using set theory we can reduce some classes of questions from uncountable to countable.

Why don't you just list your basic concepts for us and describe exactly what you mean by each of them. Once these are resolved progress can progress.

 

[W.D.Clinger]

However, what is decidedly discouraging is that you think I'm not aware of this.

The reason I think you're not aware that the set of questions that can be phrased using the Chinese language is countable is that you have said (in three separate posts) that the set of questions is uncountable.

This does not have an answer with pattern matching unless the question is self referential.

...snip...

"Does John's cow have spots?" This question is again not answerable with pattern matching.

Part of the problem here is that you haven't said what you mean by "pattern matching".

In the absence of any specific definition, I interpret "pattern matching" to include the operation of type 0 grammars, which are Turing-complete.

So the claims you've made about the weakness of "pattern matching" just look wrong to me. If you define "pattern matching" more narrowly, however, your claims might be right.

We won't be able to tell what you're saying until you actually say it. Using vague and/or ambiguous terminology doesn't help. You need to explain exactly what you mean by "pattern matching" (and what you mean by a number of other words and phrases you've been using).

I have a hard time trying to figure out what I have to explain to get basic concepts across. If we were only talking about a set of questions as a string of symbols then it would be countable and each question could have a reasonable answer. However, as soon as we instantiate any topic, the questions become uncountable and reasonable answers are not possible. If we move up to set theory then we can answer a larger number of questions. In other words, using set theory we can reduce some classes of questions from uncountable to countable.

I'm sorry, but what you wrote in that paragraph is just nonsense.

You started out by talking about the questions that could be phrased in Chinese. That set of questions is countable.

That's true of any language, including the language of set theory, unless you are using the words "question" or "language" to mean something rather different from what those words mean in the theory of computation (and in set theory). If you are using your own idiosyncratic meanings for those words instead of their standard meanings, then that's part of the reason you aren't making yourself clear.

 

[Reality Check]

You specified that the language consisted of a bounded set of questions.

Which is an extremely simple language.

1. Start with the same premises except using a different simpler language.
2. Make the same argument.
3. Come to the same conclusion as the Chinese room.
4. Therefore conclude that this functionally equivalent version of the Chinese room makes your assertions in the OP wrong.

You seem to have missed how the Chinese room test works. It is not a infinite series of questions every one of which has to be answered correctly. It is a finite series of questions whose answers are coherent enough such that the questioner thinks that the person in the room speaks that language. "I do not know", "I do not understand the question", etc. are valid answers. A factually wrong answer is a valid answer. Thus the room does not have to contain an infinite set of answers. The questioner might conclude that the person in the room is an idiot or a genius but that is irrelevant to whether the person speaks the language or not.

 

[Reality Check]

N+1 is not possible as a construct with either pattern matching or set theory.

What sinks in now is that this is a strawman thread, barehl. The OP is not about the actual philosophical Chinese room thought experiment which is not about pattern matching or set theory. However as I pointed out there can be a "Chinese" room test using a language so simple that just pattern matching will work.
I was taking about the actual philosophical Chinese room thought experiment where any program can be used such as neural networks.

 

[barehl]

You seem to have missed how the Chinese room test works.

Your statement would be accurate if I were Searle and I were talking about my own example. But, I'm not Searle and the actual example in this thread was not limited to Searle. This was clear in my very first post in this thread. So, could you please post something relevant to the thread instead of needlessly telling me that I'm not precisely matching Searle's example?

 

[barehl]

The OP is not about the actual philosophical Chinese room thought experiment which is not about pattern matching or set theory.

I thought this was clear. Are you caught up now?

 

[Reality Check]

So, could you please post something relevant to the thread instead of needlessly telling me that I'm not precisely matching Searle's example?

Ok: In the OP you start describing the actual philosophical Chinese room thought experiment. Then you basically ignore it!
Then you go wrong by assuming your conclusion, i.e. that pattern matching and a real language is being used.

Questions are entered but as they become more complex the data will not have matches. So, we add more data. This works for a little while however we then realize that it will be impossible to have all permutations of reality. The number of questions is uncountable in the same way that real numbers are uncountable. Therefore there isn't enough information available on the internet and in the Library of Congress to answer these questions and there would never be no matter how large we made the data store.

This has nothing to do with the foundations of Cognitive Theory (the title of the thread) unless this is your personal "cognitive theory" or another actual Cognitive Theory.

Replacing the actual test that the person is the room can be recognized as a speaker of the language with "must be able to answer any question (correctly?)" is leads to a fatal flaw that a program that answers every question with "I do not know" (in Chinese if you want) passes your test!
A simple pattern match of 'any question maps to a single answer' debunks the OP assertions.

Keeping the actual test requirement means that the program can work with a finite set of answers (Chinese equivalent to Encyclopedia Britannica rather than Library of Congress) and produce answers are correct, wrong, answer not known, question cannot be understood. These would reflect the finite knowledge of a human Chinese speaker.

 

[barehl]

The reason I think you're not aware that the set of questions that can be phrased using the Chinese language is countable is that you have said (in three separate posts) that the set of questions is uncountable.

Actually, that is the opposite of what I said. A set of symbol patterns from any alphabet (and therefore any language) is countable. And, as I've already said, there is no reason to limit this to Chinese. In English this would give use many nonsense patterns such as: "aaxxx", "wgnt", "aaaeee", etc.
However, even if we count the nonsense patterns the set is still countable.

Part of the problem here is that you haven't said what you mean by "pattern matching".

You have a set of symbol patterns associated with answers (which are also symbol patterns). A match occurs when the symbol pattern of a question is the same as a symbol pattern in your set. For example:

I have a set of symbol patterns:
{"nxm", "vht", "rpx"}

I also have an associated set of answers:
{"a1a", "b2b", "c3c"}

If the first question has the symbol pattern, "qcp", there is no match. We could however have a default answer for all non-matches. If the next question has a symbol pattern of "vht" then we have a match and we would return the associated answer pattern of "b2b". So, let's try this with actual text:

We put in "John owns a Holstein."
We get back the default answer, "I don't understand."
We put in "Holsteins are cows with spots."
A: "I don't understand."
We put in "Does the cow have spots?"
A: "I don't understand."

A simple pattern matcher has no way of storing information so it doesn't include our initial statements. If it could create sets then we could derive an answer.

In the absence of any specific definition, I interpret "pattern matching" to include the operation of, Type O Grammars, which are Turing-complete.

That would be an amazing point except for the fact that you don't have a Turing Machine. All you have is a simple pattern matcher.

We won't be able to tell what you're saying until you actually say it. Using vague and/or ambiguous terminology doesn't help. You need to explain exactly what you mean by "pattern matching" (and what you mean by a number of other words and phrases you've been using).

Did you ever play Old Maid or Go Fish?

 

[barehl]

Ok: In the OP you start describing the actual philosophical Chinese room thought experiment. Then you basically ignore it!

Actually I didn't ignore it; I used it as the basis of a thought experiment because I figured most people would have heard of it and could easily understand it.

This has nothing to do with the foundations of Cognitive Theory (the title of the thread) unless this is your personal "cognitive theory" or another actual Cognitive Theory.

It might help if you used the right link. https://en.wikipedia.org/wiki/Cognitive_science

Cognitive science consists of multiple research disciplines, including psychology, artificial intelligence, philosophy, neuroscience, linguistics, and anthropology. It spans many levels of analysis, from low-level learning and decision mechanisms to high-level logic and planning; from neural circuitry to modular brain organization. The fundamental concept of cognitive science is that "thinking can best be understood in terms of representational structures in the mind and computational procedures that operate on those structures."

 

[Reality Check]

It might help if you used the right link. https://en.wikipedia.org/wiki/Cognitive_science

It would have helped if you has spelt Science correctly in the thread title !
However thank you for confirming that this rather vague thought experiment has nothing to do with the foundations of Cognitive Science since no one who founded Cognitive Science would have heard of it decades ago.

P.S. You did not address A simple pattern match of 'any question maps to a single answer' debunks the OP assertions.

 

[W.D.Clinger]

In the absence of any specific definition, I interpret "pattern matching" to include the operation of, which are Turing-complete.

That would be an amazing point except for the fact that you don't have a Turing Machine. All you have is a simple pattern matcher.

You misquoted me by omitting the three words I wrote following the highlighted word.

Are you denying the fact that type 0 grammars are Turing-complete? Are you unaware that type 0 grammars operate via a kind of pattern matching?

I can accept that type 0 grammars are ruled out by whatever you mean by "simple" when you say "simple pattern matcher", and you did write "simple pattern matcher" in your OP. We've had to guess what you meant by "simple", however, and I still don't know exactly what you mean.

As usual, I doubt whether it's important.

 

[barehl]

It would have helped if you has spelt Science correctly in the thread title !
However thank you for confirming that this rather vague thought experiment has nothing to do with the foundations of Cognitive Science since no one who founded Cognitive Science would have heard of it decades ago.

Cognitive science is a large field. I'm only working in one specific area, namely how the human mind works and how to duplicate it. Cognitive theory seems the best description of this. Do you have another suggestion?

P.S. You did not address A simple pattern match of 'any question maps to a single answer' debunks the OP assertions.

Let me see if I'm understanding you. You are claiming that returning one answer to any question demonstrates something? That isn't a pattern matcher; that's what most people call a sign hanging on the wall. For example, you've accurately described a pop machine with an "Out of Order" sign.

 

[Reality Check]

Let You are claiming that returning one answer to any question demonstrates something?

It demonstrates a very trivial pattern matcher (maybe the simplest). But I will make the pattern matching even more explicit for you.

• There is a database. It is empty.
• There is a pattern matcher. It takes any input, splits it into symbols and looks each symbol up in the database.
• The pattern matcher will return "I do not know" if the pattern cannot be resolved.
• All patterns input to this pattern matcher will not be able to be resolved.
• This pattern matcher returns "I do not know" to all inputs.

Using your example of a pattern matcher:
There is a "language" X comprised of a set of symbol patterns.
I have a set of symbol patterns: {"nxm", "vht", "rpx"}
I have an associated set of answers: {"a1a", "b2b", "c3c"}
If the first question has the symbol pattern, "qcp", there is no match. We could however have a default answer for all non-matches, e.g. "I do not know".
We put in "John owns a Holstein." We get back the default answer.
We put in "Holsteins are cows with spots.". We get back the default answer.
We put in "nxm". We get back the answer "a1a'.
We put in "Does the cow have spots?". We get back the default answer.
etc. etc.
A questioner could conclude say that the person in the Chinese room is speaking "language" X.

 

[barehl]

You misquoted me by omitting the three words I wrote following the highlighted word.

Right, I apparently deleted it by mistake when I removed the link. I fixed it.

Are you denying the fact that type 0 grammars are Turing-complete?

No, I'm denying that you have a Turing Machine to interpret the grammar.

Are you unaware that type 0 grammars operate via a kind of pattern matching?

Aren't you getting a bit ahead of yourself? Try showing how a pattern matcher could parse a Finite State Grammar first.

We've had to guess what you meant by "simple", however, and I still don't know exactly what you mean.

I explained in detail with examples. Should I switch to crayons and hand puppets?

 

[barehl]

It demonstrates a very trivial pattern matcher (maybe the simplest).

To be the simplest pattern matcher it would have to be capable of matching at least one pattern. A fixed response is less than this. The phrase "Blindingly Obvious" comes to mind.

But I will make the pattern matching even more explicit for you. <snip waste of time>

What is it about a pattern matcher that you are not comprehending? A vending machine does this when it determines what coins you put in. However...please pay attention: a real vending machine accumulates the value of coins up to a certain amount. A pattern matcher does not.