Understanding Science 5. The Burden of Proof © Colin Frayn,

Introduction New claims –Too many to investigate them all –Many (the majority?) are false Psychic powers –Are they real? –Prof. Brian Josephson thinks so –Should we believe him? How to proportion research funds? Is it reasonable to be “closed minded”? © Colin Frayn,

Proof – A Recap The Spectrum of Certainty –Science rarely talks in absolutes –Science moves hypotheses along the spectrum by… Gathering evidence Building models Making (and testing) predictions Applying Bayes’ Theorem © Colin Frayn, Certainly True Certainly False Neutral

Sufficient Evidence When does a theory become fact? –In theory, never –In practice, when it’s close enough –Probability of falsehood is “zeroid” We need to know –Quantity of evidence in support –Quantity of evidence against –Evidential support of alternative hypotheses © Colin Frayn, Certainly True Certainly False Neutral Probably False Probably True

Closed-Mindedness Science doesn’t dictate truths –…it assigns probabilities What does “Open minded” mean? –Willing to accept any truth… Regardless of provenance Regardless of implications Regardless of our prior beliefs …but not regardless of plausibility Open minded != gullible –Skepticism is the middle ground © Colin Frayn,

Scientific Approach to Claims Using Bayes’ theorem Prior plausibility –Compatible with existing science? Theoretical plausibility –Can we build a model that explains this? –Do we need “special pleading”? Empirical plausibility –What evidence do we have? –How strong is the evidence? © Colin Frayn,

Hume on Miracles David Hume ( ) –An Enquiry Concerning Human Understanding (1748) –Classic text in empirical epistemology –Section 10 : “Of Miracles” Miracles are transgressions of a law of nature –Generally with little evidence Laws of nature are established by repeated experience –Exceptions do not exist Anecdote is insufficiently strong evidence –“…no testimony is sufficient to establish a miracle, unless the testimony be of such a kind that its falsehood would be more miraculous than the fact which it endeavours to establish.” © Colin Frayn,

The Burden of Proof Remember Bayes’ Theorem... If the Prior is low, and the posterior needs to be high, then the support needs to be very high –Extraordinary claims (low prior, high posterior) –Extraordinary evidence (very high support) P(E) ~ P(H) © Colin Frayn, P (H | E) = P (E | H) * P (H) P (E) Posterior Support Prior

Summary What does “open minded” mean? Can we be truly open minded? –Without being gullible How to decide what to investigate? –Filtering on plausibility Rely on Bayes’ theorem –Require sufficient evidence Accepting that we can never be certain © Colin Frayn,