An epistemology of APL
Authors: Benkard J. Philip 
Published: January 2007

Epistemology is the study of what we know and how we know it. In
every day life this usually means trying to understand how we build
a mental model which seems to correspond to the reality of the
world around us. From the dot matrix of our retinas, with their
million or so pixels, our brains recognize as units such objects as
straight lines, curves, and human faces. From vibrations of nearby
air molecules we hear conversations and C major triads. Ordinary
people simply consider what we know about our surroundings, as
interpreted by our senses, to be what we can know about the
world.
Humans do not have ways of knowing possessed by other creatures
in the world. Dogs hear sound frequencies beyond the range of human
ears. Some insects can directly sense ultra-violet light. These and
other animals with various modalities of perception experience
worlds that may be quite different from the one that humans know.
UV sensitive insects use their eyes to find the flowers they need
from which to grab pollen. Conversely, the flowers are pollinated.
One can wonder who is using whom.
Philosophers like to muse about such things. What do we really
know? How do we create symbolic constructs in our brains? Iris
Murdoch [ref 1] puts it this way:

The idea of a self-contained unity or limited whole is a
fundamental instinctive concept. We see parts of things, we intuit
whole things. We seem to know a great deal on the basis of very
little. Oblivious of philosophical problems and paucity of evidence
we grasp ourselves as unities, continuous bodies and continuous
minds. We assume the continuity of space and time. This intuitive
extension of our claim to knowledge has inspired the reflections of
many philosophers & The urge to prove that where we intuit
unity there really is unity is a deep emotional motive to
philosophy, to art, to thinking itself.
Intellect naturally
one-making.
[emphasis added]

Murdoch has distinguished two levels of understanding, calling
one of them intuitive. The other one we shall call logical. Within
the ellipsis in the quotation above, Murdoch suggests Hume and Kant
as spokesmen respectively for two views:
[Hume said that] if a fiction is necessary enough, it is not a
lie.
[Kant said that] we could not infer reality from experience when
the possibility of experience itself needed to be explained.
The division is between laws and customs, between logic and
intuition, between analysis and synthesis, between rules and
judgment, between the engineer and the poet. One might describe
philosophy as the art of logical analysis of the intuitive.

Epistemology is not static. The ways in which we view the world
change as our perceptions change. For hundreds of thousands of
years our five senses were the only windows of perception.
Gradually, mental models became more important. Who has ever seen,
smelled, or touched a positron or a black hole? These and even more
mysterious phenomena --- from the cosmological construct on the
large scale to quarks on the small --- are not only the primary
studies of physics: they also appear regularly in the
New York
Times Science Times.

The physical universe became a different place with the
Copernican revolution. It wasn't much of a revolution
scientifically; it was little more than a change of origin. It did,
however, shake up the religious establishment a bit. As the
heliocentric view took hold it diminished the long assumed
centrality of humanity, but, curiously, enough it also made
possible not only seeing the earth as a minor bit of the solar
system but also seeing the solar system as a trivial item in an
ordinary galaxy, and the galaxy as part of a galactic group, and so
on to higher levels of cosmic organization.
The sky today is generally believed to be full of neutrinos,
entangled quantum states, and dark matter. This newly cluttered
cosmos has led to wonderful new structures in our brains,
particularly in the brains of cosmologists, of course, but also ---
and more important --- to readers of the daily news. Perception is
translation from sensory inputs to what Pinker [ref 2] calls
mentalese.
APL epistemology has its own history. Since its beginnings APL
has extended the perceptual field which characterized many early
linear languages. In succeeding section several stages of this
development will be discussed.