You invited us on DarkBuzz to comment on this, Roger, so, ...

Your statement that "The nature of positivism is to emphasize what can be known for sure, and to avoid speculation about other matters" seems to disregard the necessity to make predictions, which I take in mathematical terms to be interpolations or extrapolations from what is, so to speak, known for sure. Someone else could...

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You invited us on DarkBuzz to comment on this, Roger, so, ...

Your statement that "The nature of positivism is to emphasize what can be known for sure, and to avoid speculation about other matters" seems to disregard the necessity to make predictions, which I take in mathematical terms to be interpolations or extrapolations from what is, so to speak, known for sure. Someone else could reasonably enough say that all such predictions are speculations.

For any given collection of experimental raw data (which different people might or might not accept as "known for sure"), we can imagine arbitrarily many possible ways to interpolate or extrapolate to what the experimental raw data would be if we performed a new, different experiment. A particular theory gives a particular scheme for constructing predictions, which we subsequently discover are more or less accurate and, hence, more or less useful. A particular theoretical system of interpolations and extrapolations gives a particular account of what the regularities are.

After a theory has been useful in a science lab for a while, engineers start wondering what they can build using the theory, then after a while we start to think of successful theories as rather more than speculations. Different people will think it's more or less speculative to extrapolate the theory to arbitrarily small scales or to arbitrarily great precision, say, but it's always reasonable to suppose that at least some extrapolations are reasonable, until it turns out that they are not.

I wonder whether you would agree with something like that discussion? I think I detect in your usual writings a mixture of realism and pragmatism as well as of positivism, which perhaps can be balanced rather than advocating only for positivism. FWIW, that's what I have tried to do above. Is it possible that you advocate positivism for a similar reason to mine: as a way to reign in my tendency to want a realist interpretation.

Your comments on QM are very brief, so I will pass over them except to say that I think you are a little too pessimistic insofar as QM is perhaps not a perfect scheme for constructing interpolations and extrapolations from insufficient experimental raw data, but with experience it can be made to work pretty well.

Having said all that, FWIW I agree with much of your essay. My own feeling is that I doubt positivism will find much favor with the voters here, but I could easily be wrong about that, so Good Luck.

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