Paper: Minds, substrate, measure and value

Part 3: The problem of arbitrariness of interpretation

By Paul Almond

In previous articles I argued that probability in some thought experiments in which you are unsure about your status is based on the substrates on which algorithms are running and that the nature of the substrate is statistically relevant to the measure with which an algorithm runs and affects the measure of any minds associated with such algorithms. In this article I provide a deeper explanation for this by discussing the real problem, which is arbitrariness of interpretation.

Previously called "multiple realizability" by John Searle, this is the problem caused by the need to apply an interpretation to a physical system to say that it is running an algorithm and the possibility of applying any interpretation to obtain any algorithm, leading to an apparent observer subjectivity in the algorithms that a physical system is running. The idea of interpretation is formalized with a hypothetical machine, an algorithm detector, which uses a detection program to make interpretations, and other, similar, devices. It will be shown that the problem of arbitrariness of interpretation is really one of arbitrariness about selection of an appropriate detection program to use in an algorithm detector.

Searle argues that multiple realizability makes the strong AI hypothesis incoherent. This conclusion is unnecessary, although the strong AI hypothesis needs some clarification. Any observer subjectivity can be removed by admitting all interpretations as corresponding to algorithms that are running. This does not mean that all algorithms are equal. Some algorithms, and algorithms of some types, will occur with greater measure than others, due to a larger proportion of all interpretations "finding" them. The set of all interpretations is infinite, so absolute numbers of interpretations cannot be counted. Instead, the measure of an algorithm, or a type of algorithm, relative to that of another algorithm, or type of algorithm, is defined as being the number of all interpretations that produce that algorithm, or type of algorithm, as a proportion of the number of interpretations that produce the other algorithm or type of algorithm, as the length of the detection program tends to (but does not reach) infinity.

This provides the real explanation for the "weak substrate dependence" or statistical substrate dependence which I argued to be necessary in the previous two articles. It was suggested that "redundancy" or "inefficient use of matter" tends to increase the measure with which a particular algorithm may be running in a physical system. The reason for this is that redundancy is likely to allow more ways in which different interpretations can produce algorithms. As an example, if we imagine increasing the thickness of the wires in a computer then this allows more (speaking informally) ways for detection programs in an algorithm detector to make interpretations and find algorithms in that system, which will have an effect on the probability of being of being in various situations in thought experiments like those in the previous articles.

Admitting all interpretations like this removes observer subjectivity, making Searle's "multiple realizability" argument against the strong AI hypothesis invalid.

Read full paper here.