The Beginning of Infinity: Explanations That Transform the World Read Online Free PDF Page A

instance, I could not tell from the rule of thumb whether it would be possible to perform the trick with lighted candles instead of balls. If I had an explanation of how the trick worked, I could tell.
    Explanations are also essential for arriving at a rule of thumb in the first place: I could not have guessed those predictions about conjuring tricks without having a great deal of explanatory information in mind – even before any specific explanation of how the trick works. For instance, it is only in the light of explanations that I could have abstracted the concept of
cups
and
balls
from my experience of the trick, rather than, say,
red
and
blue
, even if it so happened that the cups were red and the balls blue in every instance of the trick that I had witnessed.
    The essence of experimental testing is that there are at least two apparently viable theories known about the issue in question, making conflicting predictions that can be distinguished by the experiment. Just as conflicting predictions are the occasion for experiment andobservation, so
conflicting ideas
in a broader sense are the occasion for all rational thought and inquiry. For example, if we are simply curious about something, it means that we believe that our existing ideas do not adequately capture or explain it. So, we have some
criterion
that our best existing explanation fails to meet. The criterion and the existing explanation are conflicting ideas. I shall call a situation in which we experience conflicting ideas a
problem
.
    The example of a conjuring trick illustrates how observations provide problems for science – dependent, as always, on prior explanatory theories. For a conjuring trick is a trick only if it makes us think that
something happened
that
cannot happen
. Both halves of that proposition depend on our bringing quite a rich set of explanatory theories to the experience. That is why a trick that mystifies an adult may be uninteresting to a young child who has not yet learned to have the expectations on which the trick relies. Even those members of the audience who are incurious about how the trick works can detect that it
is
a trick only because of the explanatory theories that they brought with them into the auditorium.
Solving
a problem means creating an explanation that does not have the conflict.
    Similarly, no one would have wondered what stars are if there had not been existing expectations – explanations – that unsupported things fall, and that lights need fuel, which runs out, and so on, which conflicted with interpretations (which are also explanations) of what was seen, such as that the stars shine constantly and do not fall. In this case it was those interpretations that were false: stars are indeed in free fall and do need fuel. But it took a great deal of conjecture, criticism and testing to discover how that can be.
    A problem can also arise purely theoretically, without any observations. For instance, there is a problem when a theory makes a prediction that we did not expect. Expectations are theories too. Similarly, it is a problem when the way things
are
(according to our best explanation) is not the way they
should be
– that is, according to our current criterion of how they should be. This covers the whole range of ordinary meanings of the word ‘problem’, from unpleasant, as when the Apollo 13 mission reported, ‘Houston, we’ve had a problem here,’ to pleasant, as when Popper wrote:
    I think that there is only one way to science – or to philosophy, for that matter: to meet a problem, to see its beauty and fall in love with it; to get married to it and to live with it happily, till death do ye part – unless you should meet another and even more fascinating problem or unless, indeed, you should obtain a solution. But even if you do obtain a solution, you may then discover, to your delight, the existence of a whole family of enchanting, though perhaps difficult, problem children . . .
    Realism and the