Twenty years ago, Marr (1969) and Albus (1971) suggested that the circuitry of thecerebellum resembles the learning machine known as the "perceptron." A perceptron learns howto assign an appropriate output to each input by obeying the suggestions of its "teacher". Theteacher provides encouragement when the perceptron is successful, and discouragementotherwise. Marr and Albus proposed…
If the Principle of Indifference tells us what probabilities to assign given no backgroundknowledge, what is the corresponding principle for the case when one does have somebackground knowledge? Seeking to answer this question, E.T. Jaynes studied the writings of J.Willard Gibbs and drew therefrom a rule called the maximum entropy principle. Like thePrinciple of…
The branch of mathematics known as probability theory provides one way of makinginferences regarding uncertain propositions. But it is not a priori clear that it is the onlyreasonable way to go about making such inferences. This is important for psychology because itwould be nice to assume, as a working hypothesis, that the mind uses…
In accordance with the philosophy outlined in Chapter 5, I define perception as patternrecognition. Pattern recognition is, of course, an extremely difficult optimization problem. Infact, the task of recognizing all the patterns in an arbitrary entity is so hard that no algorithm cansolve it exactly — this is implied by Chaitin’s (1987) algorithmic-information-theoretic proof…
When deduction is formulated in the abstract, in terms of assumptions and transformation, it isimmediately apparent that deductive reasoning is incapable of standing on its own. In isolation, itis useless. For why would there be intrinsic value in determining which x lie in D(I,T)? Whocares? The usefulness of deduction presupposes several things, none of…
Contemporary mathematical logic is not the only conceivable deductive system. In fact, Isuggest that any deductive system which relies centrally upon Boolean algebra, withoutsignificant external constraints, is not even qualified for the purpose of general mentaldeduction. Boolean algebra is very useful for many purposes, such as mathematical deduction. Iagree that it probably plays an…
In mathematical logic, deduction is analyzed as a thing in itself, as an entity entirelyindependent from other mental processes. This point of view has led to dozens of beautiful ideas:Godel’s Incompleteness Theorem, the theory of logical types, model theory, and so on. But itslimitations are too often overlooked. Over the last century, mathematical logic…
In Section 7.2 I explained the structurally associative memory by analogy to Quilliannetworks. But, as hinted there, the Quillian network has several undesirable properties not sharedby the STRAM. Some of these are relatively technical, such the fact that the Quillian networkhas no connection with the details of analogical reasoning. But there are also more…