Stephen Mumford
With Rani Lill Anjum, unpublished, 2015

Powers can ground the facts of probability: as a tendency towards a distribution, e.g. a 50/50 propensity is a tendency towards a 50:50 distribution. However, because tendencies can come in degrees, it might be tempting to think that we should explain powers in terms of probabilities, i.e. that each power is a probability of a certain effect. This would suggest that the dispositional modality was reducible to the facts of probability. The possibility of overdisposing shows, however, that there is a difference between having a power to some degree and the probability of the power’s manifestation occurring. The mathematisation of chance has given us probabilties on a bounded scale between 0 and 1 whereas the strength of a power has to be unbounded. No matter how strong a power is, there can always be another that is stronger. This is an in-principle problem, then, of converting propensities to probabilities. Previous attempts, in terms of frequencies, ratios or degrees of belief, have not overcome this. Overdisposing means there can be more than enough for the production of an effect and yet the dispositional modality tells us that the probability of a natural event will always be less than 1.