The Washington Paradox

The absurdly great musical Hamilton includes the following line from President Washington’s farewell address:

Though, in reviewing the incidents of my administration, I am unconscious of intentional error, I am nevertheless too sensible of my defects not to think it probable that I may have committed many errors.

This seems like an admirably humble thing to say, but one of the philosophically interesting things about it is that it also seems like a reasonable thing to say. That is, Washington does not seem to be describing an unreasonable or irrational attitude about his decisions as president. It is often the case that when examining our actions or beliefs, no one of them seems to be a mistake, and yet we know that we are fallible beings who have likely made at least some mistakes.

The trouble is that certain ways of expressing this general idea lead to puzzling conclusions. Suppose Washington had said something slightly different:

Having carefully reviewed each decision I made as President, I believe of each one that it was not a mistake. Nevertheless, I know that I am not perfect, and so I believe that I must have made some mistakes as President.

This also seems like a reasonable thing to say. Having evaluated all of the consequences, obligations, and whatever other relevant factors, Washington might reasonably believe, for example, that appointing Jefferson as Secretary of State was not a mistake. He might then do the same for each other decision that he made until, for each decision he made, he reasonably believed that it was not a mistake. To see the puzzle more clearly, let’s assign a name to each of Washington’s decisions. We’ll call the first decision ‘D1’, the second ‘D2’, and so on. So, we can represent Washington’s beliefs about his decisions like this:

D1 was not a mistake.
D2 was not a mistake.
D3 was not a mistake.
…
Dn was not a mistake.

Given that Washington’s careful examination of each decision has left him with good reasons to think that it was not a mistake, it seems reasonable for him to believe each proposition on the list. However, it also seems reasonable for Washington, aware of his own imperfections, to believe that some of D1-Dn were mistakes.

But these beliefs cannot all be true. If the beliefs on the list are all true, then none of D1-Dn were mistakes, and so the belief that some of them were mistakes is false. On the other hand, if some of D1-Dn really were mistakes, then some of the beliefs on the list must be false. More than that, with a little reflection, it should be obvious to Washington that these beliefs cannot all be true, and as a result it does not seem reasonable for Washington to believe all of them. So, now we have a puzzle, a version of the Preface Paradox. Each of Washington’s beliefs seems reasonable, and yet it seems unreasonable to hold all of them together.

And Washington is not alone here. You’re very likely in the same boat. Consider all of your beliefs about some topic—Biology, for example. Supposing you’re a good epistemic agent, each of those is a belief in a proposition that you have carefully considered the evidence for and concluded is true. So, each of those beliefs is reasonable. However, you know that you are imperfect. Sometimes, even after careful consideration, you misread the evidence and accidentally believe something false. So, you have good reason to believe that at least one of your many beliefs about Biology is false. And now you have obviously inconsistent beliefs, all of which seem reasonable. So, what should you do?

I think that you and Washington should keep all of your beliefs, even though you know that they are inconsistent. The trick is to explain why it is reasonable to maintain these particular inconsistent beliefs, even though it is generally unreasonable to have inconsistent beliefs. If I have just checked the color of a dozen swans, for example, and come to believe of each one that it is white, it would be unreasonable for me to believe that some of them were not white. So, what is it about Washington’s situation that makes it different from this swan case?

One interesting difference is that it is reasonable for me to think that if one of the swans had not been white, I would have some sign or evidence of that—if some of them were black, for example, I would have noticed. Washington, on the other hand, not only has good reason to think that he has made some mistakes, but also has good reason to think that he might not have noticed some mistakes in his evaluation of hundreds of complex decisions. But this fact does not seem to prevent him from believing that he would have noticed if, for example, Jefferson’s appointment had been a mistake. He might think, for example:

If appointing Jefferson had been a mistake, he would have been a poor Secretary of State, which is something I would notice. So, if it were a mistake, I would have noticed.

Given his careful inspection of all of his evidence about each decision, Washington could give a similar good reason for believing of each decision that he would have noticed if it were a mistake. In fact, the point of carefully inspecting the evidence about each decision seems to be that, in doing so, Washington would notice if it were a mistake.

So, even though, for any decision we pick, Washington has good reason to think he would have noticed if it were a mistake, he still has a good reason to think that he might not have noticed if some of his decisions were mistakes. Perhaps this is what makes it reasonable for him to believe that each particular decision was not a mistake while still believing that some of them were mistakes.

Brandon Carey
Department of Philosophy
Sacramento State