Second solution to the paradox of "believing (and disbelieving) all things"

I like the "alternating solution" to the paradox of "believing (and disbelieving) all things." It seems to capture reality. One's belief can and does waver, alternating over time. But, while I like it, it strikes me as legerdemain insofar as a way to avoid the stronger paradox of believing and disbelieving at the same time—an adroit maneuver to reframe the problem so as to escape.

The stronger paradox resembles a mirror. You look into a mirror and see the right side of your face as the left side of the image looking back at you. But the image looking back at you is you. The right side of your face is on the right at the same time it is also on the left.

My second solution to the paradox begins with the fact that when we know that something is so, its probability value is 1; when we know something is not so, its probability value is 0. One and 0 represent certainty. When we only believe that something is so or that something is not so, the probability value lies somewhere between 0 and 1. Beliefs and disbeliefs have values less than 1 but more than 0.

When a man predicts the weather—for example, whether it will rain in Cleveland—he gives the chance of rain as a percentage between 0 and 1. "There's a 60% chance of rain." Note that if he assigns a probability of 50%, he indicates that he has no more reason to believe that it will rain than he has to believe that it won't. "Fifty-fifty" represents maximum uncertainty.

In the stronger version of the paradox (in which we believe and disbelieve the same thing at the same time) the quantity that is less than 1 and greater than 0 is divided between the two. If it is divided equally, that would indicate that we are maximally uncertain as to which might be true. When belief alternately becomes stronger than disbelief, its quantity is more than one-half, disbelief's less.

The philosophy of "believing (and disbelieving) all things" seems, though, to call on us to be even-handed (or "open-minded") in how we regard things that we don't know, to treat believing and disbelieving equally; that is, as a "fifty-fifty" proposition. Even if maximal uncertainty ensures that we won't become fanatical, it's an untenable (unrealistic) position to maintain. Not even dispassionate, rational scientists can maintain it. We've got scientists, for example, whose belief that God exists approaches a probability of 1, while atheistic scientists' belief in God approaches zero.

Solution two rejects the notion that the philosophy of believing all things requires us as a logical necessity both to believe and to disbelieve everything that we don't know to be true.

Why was that not a logical necessity, after all? Well, look again into the mirror. Your head is atop your body both in reality and in the mirror, and your feet (assuming you have them) are below in both cases. But the right side of your face is also on the right in the mirror, and the left side on the left! No different from the reflection of your head and your feet. The mirror paradox works (or seems to work) because a switch in point of view is subtly introduced. You have to turn 180 degrees to assume the position of the image in the mirror. But the image in the mirror is not you. Its left and right hands are wrong.