SUO: Re: Logic & Programming Languages
Seth,
I didn't mean any arbitrary form. What I meant was a form
that would be used to preserve truth when populated with
some content -- any content that represents something about
what any agent perceives in terms of its own sensory organs
about its own environment.
>From: "John F. Sowa" <sowa@bestweb.net>
>
>> The basic point I would make is that the logical forms used by
>> intelligent insects, apes, dolphins, and humans would necessarily
>> be equivalent --
>
>I think the combinatorial explosion of form alone makes it useless to model
>reality.
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