Epistemological Adequacy often Requires Approximate Partial Theories

(McCarthy and Hayes 1969) introduces the notion of epistemological adequacy of a formalism. The idea is that the formalism used by an AI system must be adequate to represent the information that a person or program with given opportunities to observe can actually obtain. Often an epistemologically adequate formalism for some phenomenon cannot take the form of a classical scientific theory. I suspect that some people's demand for a classical scientific theory of certain phenomena leads them to despair about formalization. Consider a theory of a dynamic phenomenon, i.e. one that changes in time. A classical scientific theory represents the state of the phenomenon in some way and describes how it evolves with time, most classically by differential equations.

What can be known about common-sense phenomena usually doesn't permit such complete theories. Only certain states permit prediction of the future. The phenomenon arises in science and engineering theories also, but I suspect that philosophy of science sweeps these cases under the rug. Here are some examples.

1. The theory of linear electrical circuits is complete within its model of the phenomena. The theory gives the response of the circuit to any time varying voltage. Of course, the theory may not describe the actual physics, e.g. the current may overheat the resistors. However, the theory of sequential digital circuits is incomplete from the beginning. Consider a circuit built from NAND-gates and D flipflops and timed synchronously by an appropriate clock. The behavior of a D flipflop is defined by the theory when one of its inputs is 0 and the other is 1 when the inputs are appropriately clocked. However, the behavior is not defined by the theory when both inputs are 0 or both are 1. Moreover, one can easily make circuits in such a way that both inputs of some flipflop get 0 at some time.
   
   This lack of definition is not an oversight. The actual signals in a digital circuit are not ideal square waves but have finite rise times and often overshoot their nominal values. However, the circuit will behave as though the signals were ideal provided the design rules are obeyed. Making both inputs to a flipflop nominally 0 creates a situation in which no digital theory can describe what happens, because the behavior then depends on the actual time-varying signals and on manufacturing variations in the flipflops.
   
   
2. Thermodynamics is also a partial theory. It tells about equilibria and it tells which directions reactions go, but it says nothing about how fast they go.
   
   
3. The common-sense database needs a theory of the behavior of clerks in stores. This theory should cover what a clerk will do in response to bringing items to the counter and in response to a certain class of inquiries. How he will respond to other behaviors is not defined by the theory.
   
   
4. (McCarthy 1979a) refers to a theory of skiing that might be used by ski instructors. This theory regards the skier as a stick figure with movable joints. It gives the consequences of moving the joints as it interacts with the shape of the ski slope, but it says nothing about what causes the joints to be moved in a particular way. Its partial character corresponds to what experience teaches ski instructors. It often assigns truth values to counterfactual conditional assertions like, "If he had bent his knees more, he wouldn't have fallen".

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