Hard to Vary or Hardly Usable?
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With an account, you can revise, criticize, and comment on ideas.My critique of David Deutsch’s The Beginning of Infinity as a programmer. In short, his ‘hard to vary’ criterion at the core of his epistemology is fatally underspecified and impossible to apply.
Deutsch says that one should adopt explanations based on how hard they are to change without impacting their ability to explain what they claim to explain. The hardest-to-change explanation is the best and should be adopted. But he doesn’t say how to figure out which is hardest to change.
A decision-making method is a computational task. He says you haven’t understood a computational task if you can’t program it. He can’t program the steps for finding out how ‘hard to vary’ an explanation is, if only because those steps are underspecified. There are too many open questions.
So by his own yardstick, he hasn’t understood his epistemology.
You will find that and many more criticisms here: https://blog.dennishackethal.com/posts/hard-to-vary-or-hardly-usable
Have some thoughts, which might be way off. But interested in your response. It seems to me that "hard-to-vary" is itself the criterion that a theory should be as programmable as possible. As you note, the goal of a theory should be to make it as explicit as possible, and a program is explicitness in its most complete form. Any theory with ambiguous components automatically has a breaking point that is changeable without detection. A programmable theory has strict causal relations all the way from the axioms to the prediction, which makes any change to the components detectable. In other words: a theory is hard to vary to the extent that its components and the couplings between them can be specified as a program. If a theory is vague, you cannot tell when it has been varied.
This gives a concrete operationalization. A breaking point is any place in the formalization where the chain stops being programmable: a primitive with no implementable type, a coupling between components that cannot be specified, or a step that requires implicit theories to fill the explanatory gaps. A mathematical theory with no remaining gaps has zero breaking points and is maximally hard to vary. A theory in natural language is already worse, because words carry ambiguity and vary from mind to mind. This does not rule out better and worse theories in natural language, since we can use more or less ambiguous words and relations. But it does create a hierarchy of hard-to-vary explanations, where the share of the explanation that is programmable, or at least unambiguous, forms the basis for the criterion.
This is probably too crude a formalization. But evaluating the two theories of Demeter's emotions and axial tilt as explanations, you could check how much of each is programmable. Detecting seasons is programmable in both cases through temperature and changes in weather. Demeter's emotions and the causal link from them to the weather, which is the entire explanation, are not programmable. In the axial tilt theory, every component is. So on this measure Demeter scores 25% and axial tilt scores 100%.
If we normalize a theory into the parts that can be put on a computer, the types it uses, the nodes (specific values) it commits to, and the functions between them, we can score the theory by how many of those parts run.
The program goes through each item in a theory, counts how many are marked True, and divides by the total. That fraction is the score of how hard the theory is to vary.
An item is True if it can be put on a computer, either by reusing an existing type (Float, Int) or by defining a new one that compiles. It is False if no working type system can express it. The user fills in the labels; the program just counts.
Demeter: 2 of 8 items program (Latitude and Temperature). Demeter, her emotions, and the functions linking them to weather can't. So the score is 25%.
Axial tilt: 9 of 9 items program. Standard types, measured constants, and functions from standard physics. So the score is 100%.