Re: Computability and logic

Peter_Smith wrote:
Tom wrote:
Just how the very comparison is effected(!), where the result of the
first comparison is returned, i.e. how the subsequent stages of
comparison (and substitution) communicate with each other, and how the
process knows which are the first two and the subsequent two and
further and further symbols /i.e. primitive strings/ to be compared -
remains a mistery to me when I attempt to give a mathematically
plausible exposition of an automaton that performs this. ..
....
All I am asking is a reading suggestion that treats these matters in an
honest and transparent way, i.e. mathematically.

Well I confess I don't really see what you are after.

Mathematical truth. /Now and always/.

You gave, so to speak, a low-level software description (compare the contents of two
memory registers, if they're the same, do this, if they're not do that,
etc, etc,), and you now ask "how the very comparison is effected" which
looks like an engineering problem, how to get some hardware to execute
that kind of program step.
*That* doesn't look like a mathematical problem at all.

Yes, Peter. Still, IMHO, comparison and substitution is a mathematical
problem entirely (as are all engineering problems, again, IMHO).

But I'm sure I'm missing your point, so I'll stop.

I am very sorry to have mispronounced my intentions. I though I did
express a need for an entirely /mathematical and _abstract treatment of
comparison and substitution/, and a mathematical treatment of a way to
concatenate these arbitrarily. I think you understood me perfectly,
still, I myself seem to be missing something important here.

Thank you very much indeed for writing.
Tom

.

Relevant Pages

  • Re: Computability and logic
    ... comparison (and substitution) communicate with each other, ... It sounds like a proof that Post systems are equivalent to Turing ...
    (sci.logic)
  • Re: Computability and logic
    ... comparison (and substitution) communicate with each other, ... It sounds like a proof that Post systems are equivalent to Turing ...
    (sci.logic)
  • Re: Computability and logic
    ... comparison communicate with each other, ... looks like an engineering problem, how to get some hardware to execute ...
    (sci.logic)
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