Thank you so much for your thoughtful and thought-provoking commentary.

It was absolutely not my intention to dismiss attempts to refute theories, only that we shouldn't (and don't) *only* try to refute theories, that confirmation - and other criteria - can have a place in an open contest between rival theories, but also that refutation is harder than we might think.

I left Kuhn out, because the article was already long enough, but Kuhn is clearly essential in all this. I'd argue, though, that Kuhn, like Popper, is most persuasive in his rejection of the positivist view that science ought and does proceed from theory-free observation and in his insistence on pre-existing paradigms that inform our selection and interpretation of data - much like Popper's conjectures.

This is the main point of my last two articles. Data don't speak. We always have theoretical, hypothetical, conjectural notions, however weak or well-hidden; we always seek, select and make sense of data informed by these notions (an idea that goes back to Kant). The only way, then, to ensure impartial and objective development is to put conjecture into overdrive and generate multiple hypotheses that compete in an adjudicated arena of competitive discourse.

So far, I think, we are completely agreed.

I don't think, though, that Kuhn is as persuasive about the role of anomalies and crisis. He chooses his examples carefully. The development of Quantum Mechanics works well for him, but the Copernican "revolution" is much messier than he makes out, as is atomism and the early modern development of chemistry, Einstein himself was dismissive of the role of anomalies in the development of General Relativity and the discovery of DNA is a triumph of puzzle-solving and normal science.

None of these go against the essentially Kantian view of the necessity of an interpretive paradigm for the act of observation. But they speak to a richer discourse in the contest and ultimate choice of victor between rival paradigms than that empirical shortcomings of the old simply usher in a revolution to the new.

I think Duhem makes a very strong point. If refutation is the only permitted prosecutorial device in the court of conjecture, it's hard to know - at least in cases of interest - whether the theory itself or one of its auxiliary assumptions is being refuted. What's worse, theories can often be protected by claiming their refutations go to auxiliary assumptions and not the theory itself (though I don't think Quine was right in saying you can always do this. At some point the weight of refutation gets too much.) This situation its substantially worsened where inherent irreducible uncertainty enters the picture and empirical adequacy then has the additional burden of statistical whimsy.

So I would argue for a richer set of tools. I would allow for a broader set of criteria by which to adjudicate between conjectures, including simplicity, explanatory power and fruitfulness.

And I would also permit contingent, preferably probabilistic confirmation by data, preferably by data conjectures were not constructed to accommodate, and only by comparison with the extent the same data are consistent with other hypotheses.

Your prospecting example is really interesting, but I think it rather supports my points. First, sadly, my experience is that exploration teams tend rather to seek confirmation for the successful models they postulate. They look for confirmation and look away from what is hostile. They ought not, but the observation rather supports the descriptive myth. We do not exclusively seek falsification. We should much more, but not exclusively.

Prospecting is exactly the arena where we should be making multiple conjectures and searching for data that *distinguish between them* (possibly even generating new conjectures) rather than trying to knock them off one by one. We should look at how the data align with all the theories in play. We should allow for confirmation where data are likely in one conjecture and unlikely in others, for partial refutation in the converse case, and for accepting the indifference of data where they are equally likely (or unlikely) in all conjectures.

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Mathematical modelling for business and the business of mathematical modelling. See stochastic.dk/articles for a categorized list of all my articles on medium.

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