Justifiably Believing That Something Is True Doesn’t Mean You Know It

by John Allen Paulos

I’ve always liked stories that depended on mistaken identity, a very old theme in general. Having a degree in mathematical logic, I was also drawn to the subject on a more theoretical level, on which lies Gettier’s Paradox.

Since Plato and the ancient Greeks, knowledge has been taken by many philosophers of science to be justified true belief. A subject S is said to know a proposition P if P is true, S believes that P is true, and S is justified in believing that P is true. The philosopher Edmund L. Gettier showed in 1963 that these three ancient conditions are not sufficient to ensure knowledge of P. His counterexamples to a straightforward understanding of knowledge are paradoxical and seem particularly prevalent in politics. For me, this is part of their appeal since politics and mathematical logic occupy such different realms of cognitive space.

To provide a topical one consider the 2016 election. Trump and Clinton in October before the 2016 election were certainly evaluating their chances to win the election. Trump had strong evidence for the following compound proposition:

Proposition (1): Clinton is the person who will be elected, and there was a little clock that might help her out mounted in her lectern during the final debate. Trump’s evidence for (1) might be that the polls were showing Clinton was going to win the election and President Obama and the Democratic establishment were strongly supporting her. He also noticed the clock as he hovered around Clinton’s lectern during the debate.

If (1) is true, it implies

Proposition (2): the person who will get elected had a lectern with a little clock mounted in it. Trump saw that (1) implied (2) and thus accepted (2) on the basis of (1), for which he had strong evidence. Clearly Trump was justified in believing that (2) was true.

So far, so good. But unknown to Trump at that time, was that he, not Clinton, would be elected.

Also unknown to him was that his lectern also had a small clock mounted in it that he hadn’t noticed. Proposition (2), the winner of the election had a little clock in the lectern, was thus true even though (1) from which it was inferred was false. Now all the following are true: (2) was true; Trump believed (2) was true; and Trump was justified in believing (2) was true. But, of course, it is quite clear that Trump didn’t really know that (2) was true since (2) was true in virtue of the fact that his lectern had an unnoticed clock mounted in it. Thus justified true belief does not constitute knowledge.

Speaking of clocks, I should mention Bertrand Russell’s stopped clock as a somewhat trivial example. The clock might be stopped at 8:11 and thus indicate that it was 8:11 when you glanced at it as you passed by. If the time happened to be 8:11, your belief that it was 8:11 would be justified and true, but it couldn’t very well be said that you knew it was 8:11.

Clocks are, of course, not the issue. More generally we all believe true statements with good justifications, but in many cases we can’t characterize what we believe as real knowledge. Consider a different, but common sort of example. You see a dog that is groomed or disguised to look like a sheep standing out in a hilly field. It might be the case that in the field on the other side of a hill stands a real sheep that you can’t see. You would believe there was a sheep in the field, the belief would be justified, and the belief would be true. Still, you could not be said to know there was a sheep in the field. For sheep in disguise, you can substitute a Republican elephant or a Democratic donkey to induce people to believe they know something they don’t. (Compare Judge Kavanaugh’s claim in his defense that there was a doppelganger who was Blasey Ford’s real assailant.)

In any case, if justified true belief does not constitute knowledge, the question remains: what does? One answer, due to the philosophers Fred Dretske (with whom I took several courses at the University of Wisconsin) and Robert Nozick, involves the notion of subjunctive or counterfactual conditionals. But this is perhaps getting too deep into the philosophical weeds.

Suffice it to say that given all the varieties of fake news (and true news), epistemology and politics should not be such strangers. Abstract and visceral though they respectively may be, they do dance together more often than many realize.

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John Allen Paulos is a mathematics professor at Temple University and the author of many books, including Innumeracy, A Mathematician Reads the Newspaper, and, most recently, A Numerate Life.

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