on a few Protagorean themes...

Allegedly, Protagoras held that

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.