[Inquiry] Re: Really Useful Logic

[Jon Awbrey]

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

RUL.  Discussion Note 9

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

JA = Jon Awbrey
PC = Party of Citizens

PC: In other words, what if you were the world's first logician?
    What would the 'elements' of your logistic system be?  Would
    you say that all of arithmetic, logic, and mathematics consists
    of "truth-functions"?  Are there some basic components of those
    truth-functions which apply to or account for, every elaboration,
    no matter how sophisticated?  By analogy, consider than an amazing
    complexity of business transactions are accounted for fully by just
    two 'elements', debits and credits, and seven transaction types to
    which those debits and credits are applied.

PC: Why the focus on fundamentals?  Because I think that could give us
    a better understanding of how we think, given that thinking is logic.
    Isn't that what Boole was getting at when he wrote in "Mathematical
    Analysis of Logic" (1847, p. 7), "The mathematic we have to construct
    are the mathematics of the human intellect"?

Well, let's not confuse the aims of the mathematician and the logician
with the aims of the logicist or the psychologist.  It's not my aim,
here or elsewhere, to reduce mathematics to logic, or to reduce
either of them to psychology.

It seems to be one of the principal rationales of our work in this group
that a lot of our hard-won knowledge about the real world is stored up
in these things that we call "ontologies", and that it would therefore
be a good thing to go about constructing these ontologies in a more
critical, a more deliberate, and a more organized fashion than we
may have done in the past.  Then there is the secondary notion
that better organization would naturally lead to sorting the
components of these ontologies into their more general and
their more specialized components, and we have picked the
task of focusing on the more general aspects of things.

Logic comes into this in at least two ways:

1.  The obvious utility of logical analysis in all of the above tasks.
2.  The idea that an "ontology" is itself some type of logical system.

For my part, I think that a lot of our hardest-won knowledge
about the real world, to the extent that we have been able to
formalize it at all, is stored up in various mathematical and
statistical models of natural systems.  I do not have the sense
that the properties of these models can be fully captured by any
overly restrictive logical system, say, ZOL, or FOL, or even SOL,
but it's always to our advantage to know if any approximation to
our best working models can be represented, at least partially,
in a simpler or more intuitive way.

Still, just as it's been a standard slogan in software engineering for
about as long as I can remember to consider the whole life-cycle of the
whole software system in its natural application environment, I believe
that it is wise to reflect on our Snapshottily Upheld Ontologies in much
the same light, and this means that we ought to take them with the whole
tide that washes them in and washes them out, and the name of that tide
is "Inquiry".  But there is no reason to think that an approximation
to the process of inquiry can be captured by purely deductive rules
of inference, or reduced to solely syntactic methods of procedure.

Then again, none of this does not mean that it would not do us
a lot of good to improve the effectiveness and the efficiency
of what automatable methods we have.  So it seems to me that
a person can pretty much pick any one of several fronts on
which to work.

As far as Boole's supposed psychologism, consider
the following statement, where he is setting up
his discussion of "selective operations" and
their corresponding "selective symbols":

| The operation which we really perform is one of 'selection according to
| a prescribed principle or idea'.  To what faculties of the mind such an
| operation would be referred, according to the received classification of
| its powers, it is not important to inquire, but I suppose that it would be
| considered as dependent upon the two faculties of Conception or Imagination,
| and Attention.  To the one of these faculties might be referred the formation
| of the general conception;  to the other the fixing of the mental regard upon
| those individuals within the prescribed universe of discourse which answer to
| the conception.  If, however, as seems not improbable, the power of Attention
| is nothing more than the power of continuing the exercise of any other faculty
| of the mind, we might properly regard the whole of the mental process above
| described as referrible to the mental faculty of Imagination or Conception,
| the first step of the process being the conception of the Universe itself,
| and each succeeding step limiting in a definite manner the conception
| thus formed.  Adopting this view, I shall describe each such step,
| or any definite combination of such steps, as a 'definite act
| of conception'.
|
| Boole, 'Laws of Thought', p. 43.
|
| George Boole,
|'An Investigation of the Laws of Thought,
| On Which are Founded the Mathematical
| Theories of Logic and Probabilities',
| Reprinted, Dover, New York, NY, 1958.
| Originally published, Macmillan, 1854.

Now, a person who says "To what faculties of the mind such an operation
would be referred, according to the received classification of its powers,
it is not important to inquire ...", that person is not really taking the
psychological point of view on logic, no matter what sop he tosses to the
intellectual fashion of his times.

Jon Awbrey

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