SUO: RE: Re: Logic & Programming Languages
This is certainly a thought-provoking thread. While not finding fault with
John's arguments, there are one or two points where I have trouble reaching
a clear resolution in my own mind.
If we reason about the cat and the mat, we are treating these as atomic
entities, and this calls for an ability to differentiate between the two. If
we only see these through our sonar as a single furry blob on the floor,
then our reasoning ability becomes limited to say the least. In effect, the
truth value of the situation is context-sensitive (through the eye of the
beholder). This obviously doesn't suggest that God's RFC on FOL is no longer
valid, but does cause problems in the mapping of the language of humans to
that of bats - is the SUO of bats likely to have much in common with that of
humans?
I have another quandary with the logic/physics divide - deduction, induction
and abduction are abstract techniques, but seem quite intimately linked with
the kind of physics we experience. Might it be that if time worked
differently, we would have a completely different set of logical tools? Or
would the argument be that we'd simply be using a different subset of FOL?
From another angle - if we lose the ability to absolutely distinguish one
entity from another (drop the integers but keep the reals?) is it possible
to build a reasoning system with FOL?
Incidentally, I've argued elsewhere that it would be quite possible for
there to be aliens nearby in the universe, and for us to be completely
unaware of their attempts to communicate with us, citing the human
relationship with other animals. (I doubt very much whether there are aliens
nearby, BTW). Perhaps a copy of John's KRep book would make a better
introduction to ET than the silly etching they sent up with that space
probe...
Cheers,
Danny.
>There is no combinatorial explosion. On the contrary, any
>intelligent being from any planet of any species that seeks
>forms of inference that preserve truth must converge on one
>particular logical form, which we happen to call classical
>first-order logic.
>
>Aristotle converged on one subset, Boole converged on a
>different subset, Peirce and Frege converged on exactly the
>same superset of Aristotle and Boole, even though they used
>very different notations and came from very different starting
>points. Any intelligent insect or dolphin on any planet
>in the universe that wanted a notation for doing reasoning
>that would preserve truth would inevitably coverge on some
>notation equivalent to some subset or superset of FOL.
>
>Bottom line: FOL does not require standardization by ANSI,
>ISO, or W3C, since it was long ago standardized by a higher
>authority -- namely God.
>
>Bottom line #2: If you want to demonstrate that your notation
>is adequate for doing reasoning, the first thing to verify
>is what subset or superset of FOL it represents.
>
>Bottom line #3: The simplest way to verify bottom line #2 is
>to define a two-way formal mapping of your notation to some
>other notation whose expressive power has already been defined
>as some subset or superset of FOL.
>
>John Sowa
>