Hard to Vary or Hardly Usable?
Showing only those parts of the discussion that lead to #3863.
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With an account, you can revise, criticize, and comment on ideas.Deutsch’s stance in my own words:
The distinguishing characteristic between rationality and irrationality is that rationality is the search for good explanations. All progress comes from the search for good explanations. So the distinction between good vs bad explanations is epistemologically fundamental.
A good explanation is hard to vary “while still accounting for what it purports to account for.” (BoI chapter 1 glossary.) A bad explanation is easy to vary.
For example, the Persephone myth as an explanation of the seasons is easy to change without impacting its ability to explain the seasons. You could arbitrarily replace Persephone and other characters and the explanation would still ‘work’. The axis-tilt explanation of the earth, on the other hand, is hard to change without breaking it. You can’t just replace the axis with something else, say.
The quality of a theory is a matter of degrees. The harder it is to change a theory, the better that theory is. When deciding which explanation to adopt, we should “choose between [explanations] according to how good they are…: how hard to vary.” (BoI chapter 9; see similar remark in chapter 8.)
Deutsch contradicts his yardstick for understanding a computational task. He says that you haven’t understood a computational task if you can’t program it. His method of decision-making based on finding good explanations is a computational task. He can’t program it, so he hasn’t understood it.
@dirk-meulenbelt suggested in a space (at 21:30) that a bunch of epistemology is underspecified. There are many epistemological concepts (like criterion of democracy, falsifiability, etc.) that we don’t know enough about to express in code.
Deutsch’s yardstick applies to computational tasks. It’s not meant for other things. It’s not clear to me that the criterion of democracy is a computational task.
Yes, the criterion for democracy is not a computational task, but an abstraction that constrains computational tasks. In the same way: the criterion for HTV is also not a computational task, it constrains the possible computational tasks that attempt to quantify HTV.
We understand computational tasks by being able to program them (as per Deutsch' criterion). But we understand criteria/ principles/ axioms/ theories ... (non computational tasks) in another way: by varying them and eliminating the variants that do not solve the problem the principle purported to solve.
For example:
a+b=b+a (in arithmetic) is a principle/ axiom that we understand by elimination of possible variants (a+b =/= a ... a+b =/=b ... etc)
but 3+5=5+3 is a specific transformation that should be understood via a computational task: adding 5 to 3 and then 3 to 5 and comparing both outcomes, via a program.
So my criticism is that the HTV criterion is not a computational task (but a principle, universal statement) and Deutsch's criterion of understanding (you need a program) only applies to computational tasks.
With principle/ universal statement/ theory, I mean for example: for all masses, there is a force proportional to the inverse square of their distances/ for all integers, addition is commutative/ for all species, their evolution is governed by variation and selection, for all interpretations of moral actions, these are moral relativistic one/ ....
- Principles/ universal statements/ theories are not computable because they speak about sets of (possible) transformations (not 1 in particular which would be a computation) and they offer a constraining criterion to those transformations in the set.
- Whereas a computer program is an abstraction capable of causing 1 particular transformation (between sets of inputs and sets of outputs)
There may be a way to quantify HTV, and thus deal with specific evaluations of how HTV of one theory is higher than another. That would be a computational task. But that is different from the criterion for HTV (which is by definition not computable). And having no program for that computational task does not imply that the criterion for HTV is irrelevant or not usable, or even fluff.
Compare for example to the theory of evolution: the theory of "variation and selection" is the criterion for a set of allowable transformations (of species), but not having a specific program (e.g. for how a particular species can evolve in some particular niche) does not imply that the criterion is useless or fluff.
I think the usefulness of the HTV criterion becomes clear when you link it to Constructor Theory, then one can argue that HTV criterion adds more than criticisms alone can do. But that's a whole other story we could get into.