John F. Sowa
Copyright ©2002, John F. Sowa
A talk presented at the Conference on Knowledge and Logic, 15 June 2002, at the Technische Universität Darmstadt.
- The contents of the human mind are inconsistent, loosely organized, and in perpetual flux.
- The mind is not a highly organized knowledge base.
- And it is not a large fuzzy peach.
- A better term is knowledge soup: Fluid, lumpy, with chunks that float in and out of awareness.
- Herbart: "Ideenkomplexe sinken und heben in Bewußtsein."
Aspects of the Soup
- Overgeneralizations: Birds fly.But what about penguins? A day-old chick? A bird with a broken wing? A stuffed bird? A sleeping bird? A bird in a cage?
- Abnormal conditions: If you have a car, you can drive from New York to Boston.But what if the battery is dead? Your license has expired? There is a major snowstorm?
- Incomplete definitions: An oil well is a hole drilled in the ground that produces oil.But what about a dry hole? A hole that has been capped? A hole that used to produce oil? Are three holes linked to a single pipe one oil well or three?
- Conflicting defaults: Quakers are pacifists, and Republicans are not.But what about Richard Nixon, who was both a Quaker and a Republican? Was he or was he not a pacifist?
- Unanticipated applications: The parts of the human body are described in anatomy books.But is hair a part of the body? Hair implants? A wig? A wig made from a person's own hair? A hair in a braid that has broken off from its root? Fingernails? Plastic fingernail extender? A skin graft? Artificial skin used for emergency patches? A band-aid? A bone implant? An artificial implant in a bone? A heart transplant? An artificial heart? An artificial leg? Teeth? Fillings in the teeth? A porcelain crown? False teeth? Braces? A corneal transplant? Contact lenses? Eyeglasses? A tattoo? Make-up? Clothes?
- Why isn't the mind better organized?
- Is the complexity the result of ordinary language?
- Is it the result of the complexity of the world?
- If people can reason with such complexity, why can't computers?
- Can we represent the complexity in logic?
How can we extract a crystalline theory from a soupy mess?
Comments by two logicians and a poet.
Some Views of the Problem
- Alfred North Whitehead:Human knowledge is a process of approximation. In the focus of experience, there is comparative clarity. But the discrimination of this clarity leads into the penumbral background. There are always questions left over. The problem is to discriminate exactly what we know vaguely.
- Robert Frost:I've often said that every poem solves something for me in life. I go so far as to say that every poem is a momentary stay against the confusion of the world.... We rise out of disorder into order. And the poems I make are little bits of order.
- Charles Sanders Peirce:Get rid, thoughtful Reader, of the Okhamistic prejudice of political partisanship that in thought, in being, and in development the indefinite is due to a degeneration from a primal state of perfect definiteness. The truth is rather on the side of the Scholastic realists that the unsettled is the primal state, and that definiteness and determinateness, the two poles of settledness, are, in the large, approximations, developmentally, epistemologically, and metaphysically.
Point of agreement: We make order out of disorder.
Models and Reality
George Box: "All models are wrong, but some are useful."
Truth is an Indexical
- Truth is not fuzzy — it is context dependent.
- It is a relation between a theory and a model of some aspect of the world for some purpose.
- Examples:Is the earth spherical?
Is a ball bearing spherical?
Is a meatball spherical?
- The answer is yes or no, depending on your purpose.
Induction, Deduction, and Abduction
Peirce's three categories of reasoning:
- Induction or learning:
- Start with observations.
- Look for commonalities.
- Derive a theory that summarizes the data.
- Deduction or inference:
- Start with a theory.
- Observe some new data.
- Use the theory to deduce the implications.
- Abduction or guessing:
- Start with disconnected observations.
- Guess (hypothesize) a theory that relates them.
- Test the hypothesis by induction and deduction.
The Knowledge Cycle
A summary of Peirce's theory of pragmatism
Problems of Communication
People with different background, views, theories, and purposes
- Different people have different background, views, theories, purposes, and vocabulary.
- Every application of logic assumes a fixed model, a fixed vocabulary, and no implicit purpose or background knowledge.
- Peirce, Wittgenstein, and Austin: Every utterance in every natural language has three components, (s,p,b):
- Speech act s, which states the purpose.
- Proposition p, which states the content.
- Background knowledge b, which is unstated, but assumed.
- For communicating with computers, John McCarthy proposed the Elephant language with the same three components, (s,p,b).
The talk presented on 15 June 2002 contained a brief overview of a method called Task-Oriented Semantic Interpretation, which implements a technique for dealing with the knowledge soup.
The slides on the TOSI method have been deleted from this section. For more detail on TOSI, seehttp://www.jfsowa.com/talks/tosi.htm
The framework of knowledge soup can span the gap between natural language semantics and formal systems of logic.
Natural languages must do everything:
- Express the full range of everything that people do, think, want, need, hope, and fear.
- Serve as a medium of communication between people with totally different views of what to do, think, want, need, hope, and fear.
- Enable people to negotiate their differences and reach compromises on specific tasks where they have common interests.
Formal logics have been designed to do one thing at a time:
- Express clearly delimited propositions about one aspect of one problem for one purpose.
- Serve as a medium of communication between people or computers that are in complete agreement about the topic, the vocabulary, and the purpose.
- Support deep reasoning about that narrow topic.
Bridging the gap requires a framework that accommodates both:
- Support the full richness of natural languages.
- Represent the precise, narrow theories of formal logic.
- Enable the enormous scope of natural language to be mapped to appropriate logical theories as needed.