Can There Be A Knowledge-First Ethics of Belief? - Western ...

For any person s, world w and time t: (s should believe p at t in
w) iff (s knows p at t in w)
I will consider numerous views in this paper, and it would be cumbersome
to state each of them so explicitly. Thus I will often leave implicit the
quantifiers over people, worlds, and times, as well as leaving implicit the
point that the biconditionals are material.
As for the narrow scope identity theory, it is clearly mistaken. Knowledge
entails belief; hence it follows from the narrow scope identity theory that
whenever we should believe we do believe. This is tantamount to the claim
that we cannot fail to believe what we should, which is absurd. It will help to
have a name for this particular absurd result. We’ll say that a theory entails
“compulsory completeness with respect to what we should believe”, or in
short, “compulsory completeness”, when it entails that we always believe
everything we should.
This terminology is borrowed in the obvious way from logic. Just as a logical
system is complete with respect to a given property x iff every formula
having x is a theorem, one’s belief corpus is complete with respect to a
given property x iff every proposition having x is something one believes.
From an epistemic point of view, it is good for one’s belief corpus to be
complete with respect to what one should believe. Of course, it is possible
for our belief corpuses to not be complete with respect to what we should
believe. Theories denying this possibility have the problem of compulsory
completeness.
The narrow scope identity theory is false because it has this very problem.
Of course, there is an easy fix. We can just widen the scope of the “should”
(as Sutton does by putting the colon after his “must”, and as Williamson
means to do with his own principle). This gives us
Wide Scope Identity Theory
You should (believe p iff you know p)
Or, to put it completely explicitly,
For any person s, world w and time t: s should not be such that
he believes p at t in w without knowing it, or such that he knows
p at t in w without believing it.
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