All Hope Of Logic Becoming Useful (Was Lost In Translation)

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

John,

My concern is whether our logical calculi, formalisms,
and languages will ever begin to serve the actual work
of reasoning on significant practical questions in any
meaningful way.  As a matter of course, that will take
their efficient computational implementation.  However,
there are some preliminary questions about what logic is,
what it's supposed to be good for, and what it will take
to design a computational calculus that is good for that.

We have a hundred years of mostly wrong answers to these questions.
You can tell they are wrong because nobody actually uses them for
any significant practical purpose in everyday real-world research
on real hard questions in any field.

Our best models of significant phenomena in any field of serious
research remain in the form of quantitative mathematical models.
Our best therorem provers remain the guys and gals who learned
the art of theorem proving in the process of actually doing
mathematics, and what that's about remains as untouched
as it ever was by the recipes of the logic textbooks.

So the moribund condition of formal logic is already clear,
I am merely trying to diagnose the causes of its morbidity.

It is a sad fact of history that I have to go back to Peirce
to find anybody who shows the least signs of recognizing the
problem of scientific inquiry as something that isn't hacked
already, but it's a fact, nonetheless.

One of the causes of this sad condition, and its persistence,
seems to be the detachment of our current excuse for logic
from the realities of "experience and logical reflexion".

By "experience" is meant experience of an object world.
By "reflexion" is meant the ability to observe and to
critique the actual process of inquiry that occurs.

Can we design computational calculi that will actually help with these tasks?
Perhaps.  But it will take waking up to the near total inutility of current
systems, along with the near-sighted philosophies of logic that went into
producing them, before we can even begin.

So I will continue to say that current notions of lingusitic order and
popular misconceptions about metalanguage as "language about language"
are simply inadequate to transmit what logic is meant to be good for.

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

John F. Sowa wrote:
>
> Jon,
>
> Your note addresses an important distinction that is often confused:
> The difference between higher-order logic and metalanguage.  In his
> development of logic, Peirce explored both of these notions, but it
> is not clear whether he himself clearly distinguished them.
>
> Following is the ending of the passage you quoted
> from Peirce:
>
> CSP>  By 'logical' reflexion, I mean the observation
>  > of thoughts n their expressions.  Aquinas remarked
>  > that this sort of reflexion is requisite to furnish
>  > us with those ideas which, from lack of contrast,
>  > ordinary external experience fails to bring into
>  > prominence.  He called such ideas 'second intentions'.
>  >
>  > It is by means of 'relatives of second intention'
>  > that the general method of logical representation
>  > is to find completion.
>  >
>  > C.S. Peirce, 'Collected Papers', CP 3.488-490,
>  > "The Logic of Relatives", 'The Monist', vol. 7,
>  > pp. 161-217, 1897.
>
> In this passage, it seems that Aquinas and Peirce are
> using the term "second intention" for language about
> language, which is now called metalanguage.  But
> in his paper of 1885, "On the Algebra of Logic II",
> Peirce used the term "first-intentional logic" for
> quantifcation over individuals, which is now called
> first-order logic.  In that same paper, he used the
> term "second-intentional logic" for quantification
> over relations, and he gave some formulas that are
> clear examples of second-order logic.
>
> JA> Another way of stating my concern is to say that something
>  > has evidently been lost in the translation from classical
>  > discussions about higher intentional logic to epi-Fregean
>  > ramblings about the orders of logical formalism.  I begin
>  > to suspect that the current fuss about "order" is similar
>  > to those pre-Hausdorff confusions about dimensionality.
>
> There certainly is a lot of confusion about these two notions,
> and it is important to realize that they are orthogonal:
>
>   1. You can use pure first-order logic as a metalanguage to
>      talk about statements in FOL.  (Tarski did a lot of
>      work on this topic in connection with model theory.)
>
>   2. You can use higher-order logic to quantify over
>      relations without using metalanguage.
>
> Many people use the term "higher-order" when they are
> actually using metalanguage.  And it is possible to get
> an enormous increase in expressive power by using
> metalanguage without using higher-order logic.
>
> For more about metalanguage and its use in supporting
> versions of modal, temporal, and intentional logics,
> see the following paper and the references cited there:
>
>     http://www.jfsowa.com/pubs/laws.htm
>     Laws, Facts, and Contexts
>
> John Sowa

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
inquiry e-lab: http://stderr.org/pipermail/inquiry/
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o