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Why? The best explanation I have heard is advanced by the physicist John H Marburger, who is currently science advisor to US President George Bush. By 1930, Marburger points out, physicists had found a perfectly adequate way of representing classical concepts within the quantum framework using Hilbert (infinite-dimensional) space. Quantum systems, he says, “live” in Hilbert space, and the concepts of position and momentum, for instance, are associated with different sets of coordinate axes that do not line up with each other, thereby resulting in the situation captured in ordinary-language terms by complementarity.“It’s a clear, logical and consistent way of framing the complementarity issue,” Marburger explained to me. “It clarifies how quantum phenomena are represented in alternative classical ‘pictures’, and it fits in beautifully with the rest of physics. The clarity of this scheme removes much of the mysticism surrounding complementarity. What happened was like a gestalt-switch, from a struggle to view microscopic nature from a classical point of view to an acceptance of the Hilbert-space picture, from which classical concepts emerged naturally. Bohr brokered that transition.”

In his book Niels Bohr’s Times, the physicist Abraham Pais captures a paradox in his subject’s legacy by quoting three conflicting assessments. Pais cites Max Born, of the first generation of quantum physics, and Werner Heisenberg, of the second, as saying that Bohr had a greater influence on physics and physicists than any other scientist. Yet Pais also reports a distinguished younger colleague asking with puzzlement and scepticism “What did Bohr really do?”.

Professor Nisbet is a social scientist who studies strategic communication in policy debates and public affairs. His current work focuses on scientific and environmental controversies, examining the interactions between experts, journalists, and various publics. In this research, Nisbet examines how news coverage reflects and shapes policy, how strategists try to mold public opinion, and how citizens make sense of controversies.

The first way to think about probability is as a measure of the frequency of an event: if I say that the probability of a coin to land heads up is 50% I may mean that, if I flip the coin say 100 times, on average I will get heads 50 times. This is not going to get us out of Hume’s problem, because probabilities interpreted as frequencies of events are, again, a form of induction

Secondly, we can think of probabilities as reflecting subjective judgment. If I say that it is probable that the coin will land heads up, I might simply be trying to express my feeling that this will be the case. You might have a different feeling, and respond that you don’t think it's probable that the coin will lend heads up. This is certainly not a viable solution to the problem of induction, because subjective probabilities are, well, subjective, and hence reflect opinions, not degrees of truth.

Lastly, one can adopt what Okasha calls the logical interpretation of probabilities, according to which there is a probability X that an event will occur means that we have objective reasons to believe (or not) that X will occur (for instance, because we understand the physics of the solar system, the mechanics of cars, or the physics of coin flipping). This doesn’t mean that we will always be correct, but it does offer a promising way out of Hume’s dilemma, since it seems to ground our judgments on a more solid foundation. Indeed, this is the option adopted by many philosophers, and would be the one probably preferred by scientists, if they ever gave this sort of thing a moment’s thought.