Re: Can Computers Have Incomputable Concepts?

On Jun 24, 5:28 pm, Chris Smith <cdsm...@xxxxxxx> wrote:
LauLuna <laureanol...@xxxxxxxx> wrote:
Unless you define what it means "computer has a concept", everything
what you write is just a nonsense jumble-mumble.
That is exactly why I'm asking for help. I don't know what it means
for a computer to have a concept.

This isn't a satisfactory answer.

The problem is that you've juxtaposed a few words together -- "has a
concept" -- in a way that doesn't intrinsically mean anything.
Obviously you have some idea of what it means; otherwise, you wouldn't
be saying those words in that order. While I understand that you may
not be able to easily express what you mean, no one else in this
newsgroup is better equipped to do so. The question is about what is in
your mind, and you are the only person who can answer that.

What do you not like about the following trivial argument (as a program
in Java) that a computer can "have" any concept you want:

class HaltingProblem { }
HaltingProblem hp = new HaltingProblem();
// now the computer "has" the halting problem, which in undecidable

--
Chris Smith

It appears I don't make myself understood.

Perhaps the expression 'have a concept' is unfortunate; I could have
said 'understand a concept' instead, but I wished to avoid the flavor
of consciousness the word 'understand' conveys.

What I mean is that 'understanding the concept of arithmetical truth'
can hardly be tested by means of observed behavior. Suppose we have
two 12 years old boys, John and Peter. We teach John just the
definition of arithmetical truth so that he can reproduce it if asked,
even though he does not understand it. We teach Peter what the formal
language of arithmetic is and its standard interpretation; then we
teach him that an arithmetical truth is any sentence of that language
that so interpreted is true.

Peter understands what arithmetical truth is and can define it. But
John, who doesn't understand it, can define it as well. We can go on
testing and ask John and Peter to decide the truth value of some
arithmetical sentences. Since there is no algorithm for this, Peter
could fail as much as John. Let's suppose he does.

Now assume John and Peter are both computers. We cannot find out who
of them understands the concept of arithmetical truth by observing
their outputs, so to say. Could we do it by looking inside their
machinery?

Is there any internal configuration of a computer that can show us the
computer understands the concept of arithmetical truth as Peter does
or Tarski did when he proved that it is not an arithmetical predicate?
Remember we are supposing that configuration has no observable
behavioral consequences!

There are most probably some theories about neural encoding of
concepts. Is there any theory about the relation between mental
representation of concepts and internal configuration of computer
machinery?

I hope this clarifies.

Regards


.

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