Let us assume for the moment that intelligence is a single thing that can be precisely described by a single number.
Now imagine nobody has invented a way of measuring that number yet, so you set out to create an IQ test. You put together a number of tests and tasks, and assign various weights to each question and score. You administer the test to a bunch of people and the results seem reasonable.
Here's the question: how do you know you are actually measuring intelligence, and not something else that approximately correlates with it?
Alfred Binet, when faced with this problem, validated his test by correlating it with school achievement. This, at least, ensured that the test was at least somewhat useful in predicting school achievement. But it should be obvious that different kinds of people thrive in different kinds of schools, so at best tests calibrated this way are imprecise. We've all known underachievers and overachievers in school.
At their very best, IQ tests tell us what we expect to hear. That's actually more useful than it sounds, as long as we remember that we've calibrated the test to do just that. Test results must be *contrived* to correlate with things we're interested in. That mightinclude stuff like algebra and geometry, and arguing as in a legal brief, which are all valuable mental tasks. But it might not correlate to stuff like finding food in a forest during an unseasonable drought, or negotiating with a neighboring group, or evaluating the motives of strangers, all of which are tasks requiring mental acuity, and at which people differ in talent.