[Martin Taylor 2009.01.14.15.38]

We have been talking around each other in a non-communicative fashion about subjective and objective probabilities, so I'm trying a different tack, to ask what is meant by "probability" in the first place.

First, what is it not. It is not an observation (a set of data). Observations are perceptions, and as such are assured. They have happened, and no probability can be assigned to them. They are the basic data. From the observations (including all ancilliary available evidence) we must discover whatever probability interests us.

Probability necessarily relates to future possible observations. If a probability is assigned, it is always assigned to an observation not yet made. Some possible values of a possible future observation are more likely than others. Where does this "more likely" comparison exist? Does it exist in the world that is observed? Does it exist in the entity that will do the observing? Where? The probability exists, but the observation does not, as yet. So where is the probability to be found? My answer is that it is in a mind. It is "subjective".

What is "objective" probability? Is it the "true" likelihood of the future observation? It can't be in the already taken observations, because they are fixed and their values are not in question. So where is it? To what can it be applied? If it is factually true, but unknown to anyone, that there are a million swans in the world (of which you have seen 10), and in all the world there are 16 black swans, all in Togoland, what does it mean to ask what the probability is that the next swan you see will be white? Is it (1,000,000 - 16)/1,000,000? Or is it 1, because all the black swans are where you won't ever see them? Or is it much less, because your observations have encountered only 10 swans? What is the probability that a random swan of all swans in the world is white? How could you know? Surely there must be ONE "objective probability" for this -- or must there?

To what can "objective probability" be applied? Can it be to the probability that a fair die will come up "4"? Surely not. To determine the value 1/6 (which we presumably agree is the "correct" value) for that depends on a mental model of what it means to have a fair die, and mental models are subjective. Oh, that's no problem. The die is real and is really fair, really and truly, out there in the "objective" world. So that's an "objective probability". Or is it? Why do we think it is? Is it because we each postulate the same mechanisms, and that mechanism (model) results in the value 1/6? If so, how is it an "objective" (true in the real world that we assume to exist) probability?

I heard a noise. It sounded like a bump or a muffled bang. Is someone knocking at the door? Did something fall? Is someone working on the roof next door? I think it was more probably someone knocking at the door than either of the others. "I think" but what is the true "objective" probability of each possibility? How would I find out? Am I perceiving a probability? If not, just what is it that feels as though I am perceiving a probability comparison? My feeling about the probability I think I perceive changes when I go to the door and find nobody there? What "objective probability" changed? My perception is that my probabilities for the three possibilities changed, but that's not objective, is it? What is the objective probability that someone was there but went away before I got to the door?

The concept of "objective probability" seems fraught with so many problems, starting with the fact that it is always about something in the future, and cannot ever be measured or observed, that I am bewildered by the apparent fact that other people believe it to be a useful scientific concept.

Martin