An epistemology of APL

Abstract

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 theNew 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.