Probability, uncertainty and unpredictability

This is topic 1 on our philosophy topics list.

1. Likely/unlikely as a primitive concept

What are the key differences between human intelligence and animal intelligence? This may never have a definitive answer, but "conscious and not infrequent planning for the future" is surely one key difference. Wondering in what contexts humans first made conscious plans can only be speculation, though "where to search for food today" comes naturally to mind. If a creature were not aware that whether it would catch a prey animal or find plentiful edible fruit today was uncertain, we would be reluctant to classify that creature as human. And planning in the face of uncertainty requires some notion of what is likely or unlikely to happen. From this argument one may assume that, built in to the common sense that all humans share, must be some intuitive notion related to likelihood.

Let me make an analogy with weight. Long before any civilization could measure weight quantitatively, humans surely had a common sense notion of weight of an object, on a qualitative light/heavy scale, derived from how easy it was to pick up and carry. Similarly, a primitive human's idea of where one was likely or unlikely to find food was surely derived from memory of where it had been found more frequently or less frequently in the past (i.e. were "frequentists". Imagining that primitive humans would consciously interpret likelihood as "degree of belief in a proposition" is frankly absurd. How our unconscious minds work is a different matter.)

A qualitative sense of likelihood, for instance a conscious recognition of some future events as likely and some as unlikely, is part of the common sense that the human species is endowed with.

2. Framing a question

Whenever we think about something being "likely" or "unlikely", we are consciously recognizing unpredictability or uncertainty. But not every situation where we consciously recognize unpredictability or uncertainty is a situation where we habitually think in terms of probabilities. So we can ask On this page I am thinking qualitatively about probabilities. We can rephrase the empirical issue as follows. What questions might we answer using words such as likely or unlikely that imply we are thinking in terms of chances -- some rough position on the qualitative probability spectrum -- and what questions might we instead answer with words such as I don't know, uncertain, maybe which don't refer to chances. (Digression: of course one might have a probability assessment but want to conceal it, as in the old "difference between a diplomat and a lady" joke, but here I am assuming people say what they are thinking).

Now ideally (for my purpose) there would be some established body of data relevant to the empirical question which one could use as a starting point for discussing the second question. But I don't know any authoritative data (though our blog examples illustrate one particular type of data one might study) So the rest of this page is just hypothetical discussion, with only a very tentative conclusion at the end.

There is a briefer discussion at this Understanding Uncertainty page.

3. A first hypothetical example

What kind of answers might you get to the question (asked in June) are you going away on vacation over Christmas? You might get an answer like providing an explicit or implicit yes or no. You might get an answer like which expresses uncertainty without referring to chance. Or you might get an answer like which does explicitly refer to chance.

To me there's a practical distinction between (2 or 3) and (1), between perceived uncertainty and perceived certainty. But there's much less distinction between (2) and (3) -- the words one says without much deliberation might indicate uncertainty without implication of likely or unlikely, or with such an implication, but different casual choices of words might not reflect different mental states. So

One could do many hypothetical examples (a few appear below in ".... opposite of") but let me first jump to something more serious.

4. A real-world context where the issue matters

(xxx identical copy here -- should delete one).

The Intergovernmental Panel on Climate Change (IPCC) issues periodic reports, widely regarded as the most authoritative analysis of scientific understanding of climate change caused by human activity. Future predictions involve uncertainty, and they want their many authors to be consistent in how they write about uncertainty, so provide a technical document Guidance Notes for Lead Authors of the IPCC Fourth Assessment Report on Addressing Uncertainties from which I have extracted the table below, there labelled "A simple typology of uncertainties".

Type Indicative examples of sources Typical approaches or considerations
Unpredictability Projections of human behaviour not easily amenable to prediction (e.g. evolution of political systems). Chaotic components of complex systems. Use of scenarios spanning a plausible range, clearly stating assumptions, limits considered, and subjective judgments. Ranges from ensembles of model runs.
Structural uncertainty Inadequate models, incomplete or competing conceptual frameworks, lack of agreement on model structure, ambiguous system boundaries or definitions, significant processes or relationships wrongly specified or not considered. Specify assumptions and system definitions clearly, compare models with observations for a range of conditions, assess maturity of the underlying science and degree to which understanding is based on fundamental concepts tested in other areas.
Value uncertainty Missing, inaccurate or non-representative data, inappropriate spatial or temporal resolution, poorly known or changing model parameters. Analysis of statistical properties of sets of values (observations, model ensemble results, etc); bootstrap and hierarchical statistical tests; comparison of models with observations.

This table is addressing the issue of uncertainty and mathematical modeling. It makes the point that, within a complex setting (such as future climate change), any asserted numerical probability is (at best) an output from some complicated model in which all these different kinds of uncertainty are present. This point is obvious once you think about it; but it's just different from what's said in textbooks on the mathematics or philosophy of probability.

5. Chance is the opposite of ........... ?

I started by asserting that "chance" is related to "unpredictability" or "uncertainty". As the uns imply, we often think of "chance" as the opposite of something. Here are some possible opposites, with trite hypothetical examples.

Is there a bottom line?

The topics of the 3 sections above are rather haphazard, and one could go on for ever discussing different aspects of the uncertainty - probability relationship. Let me just say my own views, without claiming to have justified them.