modlin at concentric.net writes:
>In <6hqseq$q8n at ux.cs.niu.edu>, rickert at cs.niu.edu (Neil Rickert) writes:
>[modlin] What is your definition of computation?
>>A computation is a set of causal operation which take place in the
>>world, and which have a certain kind of mathematical description.
>[modlin] Under your rules, is a Turing machine capable of computation?
>>No. It is capable of formal computation, but not of computation,
>>where formal computation is a mathematical idealization of
>>computation.
>Interesting. Your conflation of "computation" with notions of
>physically realized causality is something I've not encountered
>before... none of the classic works on computability uses it that way,
>and indeed I can't think of a single author who would balk at saying
>that a Turing machine computes.
I don't think I am conflating anything. Many big corporations have
been purchasing expensive computers for decades, because of the causal
operations that they perform.
I would use 'computability' in the same way as the works you refer
to. You have to remember that mathematics ain't real life.
Mathematicians work with idealized models of real life. The Turing
machine is an idealized model of computation. The mathematical
theory of computation is a theory of this idealized model, just as
the mathematics of the real numbers is about an idealization of the
decimal measurements we make.
In a context of talking about the mathematical theory of computation,
I would also have no problem with saying that a Turing machine
computes. But in that case the context reminds us that we are
actually talking about a mathematical idealization of computation.
> Computation is an abstraction,
>inherently distinct from the engineering practicalities of a device
>which might instantiate it.
Well if that is right, then there is something terribly wrong with
the idea that cognition is computation. To make that claim, you
would either have to say:
there is a little man inside having abstract thoughts, and doing
abstract computation, and that is what creates human cognition;
or
God is having abstract computational thoughts, and that creates
human cognition.
In the first case, you haven't explained anything, for you had to
hyupothesize the little man inside. In the second case you have a
severe case of substance dualism.
>I think I'll just stop talking to you about this... it would be too
>annoyingly clumsy to adopt your idiosyncratic usage just for that
>purpose. Unfortunate.
>Bill Modlin
