FAITH AND REASON 353least a pound; I weigh at least a pound; so I weigh a billion pounds.
Confirmationism, then, has to be stated carefully enough to make it
clear that committing this fallacy is not part of confirmationism; it
encourages no such absurdities.
Second, “entails” here must bear a specific meaning; it must mean
“non-vacuously entails” where this term is defined as follows:
Definition 7: P non-vacuously entails Q if and only if (i) it is
logically impossible that P is true and Q is false, (ii) P
is not a necessarily false proposition, and (iii) Q is not
a necessarily true proposition.
Otherwise, each logically contingent proposition C will entail all of the
necessary truths and so will be confirmed by them – by an infinite
number of truths that would be true even were C false. Thus if C is a
logically contingent proposition, both C and not-C would be
“confirmed” by an infinite number of truths. Reading “entails” as “non-
vacuously entails” avoids these absurdities.
Third, consider this unhappy argument: Either (a) the moon is a
prime number or the Packers have a winning record; (b) the moon is not
a prime number; so (c) the Packers have a winning record. Since (a) and
(b) entail (c), (c) confirms ((a) and (b)). But this is obviously false.
Similarly, (c) entails (c); but (c) does not confirm (c). So we need
something like this: P’s entailing Q and Q’s being true does not confirm
P if either Q is identical to P or Q is a component of P.^9 Then that (a)
and (b) entails (c) does not by itself explain (c)’s being true. All this is
implicit in confirmationism.
Perhaps, then, we can more carefully put confirmationism along these
lines: If P entails Q, and P is a scientific or a personal explanation of Q,
then if Q is true, its truth confirms P. Q confirms P means something
like Q’s truth supports P’s truth or That Q is true is evidence that P is
true or the like; it does not mean Q’s truth shows or guarantees that P
is true. Suppose that Q is entailed by all of P1, P2, P3,... P100. Then if
Q is true, and if confirmationism is true (assuming that P1... P100
satisfy the conditions stated above) Q’s truth confirms each of P1
through P100.
Typically, data underdetermines theory in the sense that any fact or
set of facts can be explained by various theories; nonetheless, it is often
not easy to think of explanations that both satisfy the conditions stated
above and are not known or reasonably believed to be false.
Confirmationism claims that a theory that explains a little is confirmed
a little and a theory that explains a lot is confirmed a lot, even if neither
“little” nor “lot” can be quantified.