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
unpredictability or uncertainty. But not every situation where we consciously
unpredictability or uncertainty is a situation where we habitually think in terms of
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).
- [empirical question]:
describe the distinction between the situations of unpredictability or uncertainty
in which people do habitually think in terms of chance or probabilities, and the
situations where they don't
- [philosophical question]: where does this distinction fall, on the spectrum
"arbitrary artifact of contemporary human culture" to "objective feature of the
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
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
explicit or implicit yes or no. You might get an answer like
"I'm going to Hawaii" or "I prefer to stay home over Christmas"
which expresses uncertainty without referring to chance.
Or you might get an answer like
"maybe -- I haven't decided yet" or "it depends on the end of year workload"
which does explicitly refer to chance.
(3) "probably -- we'll try to arrange a ski trip if our friends are free" or
"not so likely -- we're saving for college tuition for the twins"
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.
In many everyday settings, whether one identifies uncertainty with chance
is a rather arbitrary and unimportant choice.
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).
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
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
||Indicative examples of sources
||Typical approaches or considerations
||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.
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
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
Missing, inaccurate or non-representative
data, inappropriate spatial or temporal
poorly known or changing model
Analysis of statistical properties of sets of
values (observations, model ensemble
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.
- Chance as the opposite of physical determinism.
A pendulum, or the orbits of planets, are icons for physical determinism;
a die roll or the weather
in Denver on Valentine's Day next year may in principle be results of deterministic physical forces
but are in practice only statistically predictable.
- Chance as the opposite of usual experience.
Finding my car tire flat one morning
is an event I would attribute to chance.
- Chance as the opposite of individual human volition.
If I encounter a friend in a cafe by chance, the meaning of "by chance" is as
opposed to making an appointment to meet. If I say there's a 50-50 chance I'll go on vacation
because I haven't made up my mind, the "chance" just means "non-decision".
- Chance as the opposite of skill.
Saying a team was lucky to win a sports match is implying they were
less skillful than their opponents.
- Chance as the opposite of collective human planning.
Seeing the start of a construction project, to build a 7-storey building in 18 months, you might say
"I bet it takes 2 years" but you wouldn't say "I bet it has 8 storeys".
Here you are recogizing practical unpredictability in some aspects of
(and identifying it with chance) in contrast to practical predictability of other aspects.
- Chance as the opposite of superstition.
Your friend walks under a ladder, trips over a black cat and breaks his ankle.
Superstitious effect or just chance?
- Chance as the opposite of divine volition.
Chance or Purpose? Creation, Evolution and a Rational Faith
the author, Cardinal Schoenborn, uses "chance" precisely as the opposite of "divine volition",
unless I completely misunderstand him.
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.
There is no very sharp distinction in actual usage.
That is, in some settings of uncertainty most people (in our culture)
would think in terms of chances, in other settings most people would not, and
in other settings they would be inconsistent about whether to invoke chance or not.
So I believe there is no sharp philosophical distinction, either.
Whenever we think about chance, we are consciously recognizing unpredictability or uncertainty.
But not conversely. There are many settings where we recognize unpredictability but do not naturally
think in terms of chance.
- Recall the original issue: in what
situations of unpredictability or uncertainty do (or should)
we think in terms of chance?
My own best attempt at a single criterion is
when we are interested in
comparing the given situation with other (perhaps quite dissimilar) situations.
This is what I would call the
probability as a medium of exchange viewpoint.
(xxx not yet written).
As repeated often, I am skeptical about general claims about Probability illustrated by
hypothetical examples; readers should habitually
check general claims against some reference list of examples such as ours.