A central concern of scientists [some would say the central
concern] is to formulate generalizations. An example of such a
If you heat water to 212 degrees Fahrenheit, it will boil.
(1) concerns the past and present. If (1) is true, water heated to 212
in the past has always boiled, and water heated to that temperature
now is boiling. But (1) also concerns the future. Water heated to
212 in the future will boil. So, if we know that (1) is true, we know
something about the future.
Quite apart from science we have a great interest in acquiring
knowledge of the future. If we could acquire no knowledge, or, at
least, justified belief, in the future, our lives, it seems, would come
to a speedy end. So, how can we know about the future?
David Hume’s answer to this last question is that we can
know about the future only if we can know generalizations like (1)
to be true. For example, I am planning, let us say, to meet my friend
at the airport. I call the airline, and hear that the flight has been
delayed two hours. I travel to the airport two hours later than I
intended to. Why do I do that? Hume would answer, because I rely
on the generalization: if the airline is announces a flight is delayed
then that flight is delayed.
If Hume is right, our knowledge of the future depends upon
our knowledge of generalizations like (1). So, how can we have
knowledge of such generalizations? An obvious answer goes like
this. Suppose, we had only once ever observed water to be heated to
212, and subsequently boiling. On the basis of a single such
observation could we know that (1) is true? Surely not. We need to
observe water being heated to 212, and then boiling, a great many
times to know it will boil in the future when heated to 212.
Suppose, we have observed on a large number of occasions