392 NOTES5 Exactly what else besides true belief is required for knowledge is highly controversial.
Roughly, one party to the contemporary disputes requires only that the beliefs have
been formed in the right way (with different accounts of what that is). Their opponents
require that the believer be in possession of the right sort of recognized evidence
(with different accounts of what that is). It will not be necessary for us to decide that
matter here.
6 Indeed, it is logically impossible that delicate knowledge be a variety of unbreakable
knowledge. For any person S and proposition P, if P is a necessary truth or it is true
that S believes that P entails P is true, then it is necessarily true that P is a necessary
truth or that S believes that P entails P is true. Unbreakable knowledge consists in
comprehending belief that necessarily true or belief-entailed truths are true. Kim’s
holding a delicate belief is a matter of Kim’s accepting a proposition that is not a
necessary truth and is not such that her accepting it entails its being true. Kim’s
having delicate knowledge is a matter of her accepting a true proposition of the
indicated sort. So for any person S and proposition P, it is logically impossible that
P be the object of both S’s unbreakable and S’s delicate belief or knowledge.
7 One reason for this is that Kim needs salvation entails Kim exists and that proposition
is not a necessary truth. That Kim exists is a belief-entailed proposition relative to
Kim if Kim believes it, but its truth does not entail that Kim needs salvation.
8 This idea is often thought of as part of Reformed Epistemology. It is an essential
plank in that program, but it is also a perfectly detachable plank that was known
long before, and independent of, any commitment to Reformed Epistemology.
9 Truth-functional.
10 Consider two scenarios. One: a universe U1 exists in which there are a trillion distinct
numbered places, one item X that fills exactly one place, and it is not in place 407; if
Rita believes that X is in place 500, the fact that X is not in place 407 increases the
odds in favor of one’s belief – the chances of Rita’s belief being true is, not one in a
trillion, but one is a trillion-minus-one. Tw o: a universe U2 exists in which there are
three places, one item Y that fills exactly one place, and it is not in place 3; if Rita
believes that Y is in place 1, the fact that Y is not in place 3 increases the odds that
Rita’s belief is true – rather than the chances of her belief being true being 1 in 3, it
is now 1 in 2. This much is common ground between our disputants. The
confirmationist, who likely will begin with Tw o, claims that Y not being in place 3 is
evidence that Y is in place 1 – and equally evidence that Y is in place 2. The
falsificationist denies this. The confirmationist, of course, is also in all consistency
committed to holding that X’s not being in place 407 is evidence that it is in place
500, although it is also equally evidence that it is in place 1, place 2, and so on for a
trillion places minus two (since 407 and 500 are already mentioned). The
falsificationist, who likely will begin with One, denies that X’s not being in 500 is
any evidence whatever for X’s being in place 407; she also denies that it is evidence
that X is in any of the other places in U1. (Strictly, it is not X’s not being in place 407
or Y’s not being in place 3 that is evidence, but knowledge that these things obtain.)
The confirmationist assumes, and the falsificationist denies, that A increases the
probability of P’s truth entails A is evidence for P’s truth. This is a nice example of
what Everett Hall, in his genuinely brilliant but neglected Philosophical Systems
(Chicago: University of Chicago Press, 1960) calls a categorial dispute.
11 One could make the notion of competing theories less restrictive, allowing competition
to include cases of only partially overlapping data explained, and in other ways. But
doing so is not necessary to the argument here.