Of all things the measure is man, of the things that are, that
they are, and of things that are not, that they are not.

We’ll call
this thesis *the thesis attributed to Protagoras *or tap. Many understand tap to mean something like the following:

tapi If a person believes that p is true,
then p is true. And ditto if a person believes that p is false.

I have some
comments on tapi. Suppose that tapi is true and Sam believes that the moon is made of
cheese. It follows that the moon
is made of cheese. Suppose further
that Max believes that the moon is not made of cheese. It follows that the moon
is not made of cheese. If Sam and
Max were to believe as they do at the same time, it follows that one and the
same object is both made of cheese and not made of cheese at the same
time. *That sh cra’y*.

I suppose,
though, that one can hold on to tapi
without accepting such craziness by insisting that every time persons disagree
about something, they are both right because they live in two different
worlds. So both Sam and Max
are right because Sam’s moon is cheesy and Max’s moon is not. But *that sh cra’y*, too.

Suppose tapi is true and that Sam believes p is
false, and the p he believes to be false is TAPi. I’m pretty sure that this would mean that tapi is both true and false. *That sh cra’y*.

But suppose we
understand tap a different way,
like, say

tapii Persons believe things. Some persons may believe p is true. Some persons may believe p is false, and
maybe still others are not sure whether p is true or false.

tapii seems
utterly unproblematic, if utterly boring.

Suppose we
understand tap as

tapiii If a person S is noetically perfect, and S believes p is
true,

then
p is true.

I
think tapiii is
true. Here’s an argument for tapiii. If S were noetically perfect and
believed p were true, but p is false, then S would not be noetically perfect,
now would she? Therefore, tapiii.

Considering tapiii may also help
us distinguish *logical sufficiency*
from *ontological dependence*. Since tapiii is true, suppose that it is. Suppose further that S believes p is
true and that S is noetically perfect. It follows that p is true. But it would be a mistake to think what
makes p true is the truth of tapiii
and S’s believing p to be true and S’s being noetically perfect. The
conjunction of the last three conditions are *logically sufficient* for p’s being true, but surely they don’t make p
true. On the contrary, p’s being
true is what would make a noetically perfect person believe p to be true.