BACKGROUND INFORMATION

Two views about the role of background information are possible. One is that probability statements should be relativized to the background information to which any appeal is made.

(1) e is potential evidence that h, given b, if and only if (a) e and b are true, (b) e does not entail h, (c) p(h/e&b) > k, (d) p(there is an explanatory connection between h and e/h&e&b) > k

(2) e is veridical evidence that h, given b, if and only if e is potential evidence that h, given b; h is true; and there is an explanatory connection between the truth of h and e.

In what follows I will discuss that version of the relativization view given by (1) and (2). According to it the fact that Alan has yellow skin can be shown to be potential evidence that he has an i.c.b., given the doctor's background information on Monday (which includes the fact that people with that kind of skin usually have an i.c.b. and usually have that kind of skin because they have an i.c.b.). However, the fact that Alan has yellow skin is not potential evidence that he has an i.c.b., given the doctor's background information on Friday (which includes the results of tests).

By contrast to the relativization view, one might claim that background information need not be construed as a part of the probability statement itself, but only as information to which one appeals in defending or justi­fying that statement.

(3) The probability that Alan has an i.c.b., given that he has yellow skin, is high

might be defended by appeal to the empirical fact that

(4) In most cases people with (that kind of) yellow skin have an i.c.b.

But on this view the fact that (3) is defensible by appeal to the empir­ical fact that (4) is true shows that (3) itself is an empirical statement. It does not show that (3) is an incomplete version of the (perhaps) a priori statement that

The probability that Alan has an i.c.b., given that he has yellow skin and that in most cases people with (that kind of) yellow skin have an i.c.b., is high.

On Monday the doctor defends (3) by appeal to (4). On Friday he has accumulated new information, which includes the results of tests, and he then defends the negation of (3) by appeal to this new information. By contrast, the relativist must say that on Monday the doctor is asserting a probability statement of the form “p(h/e&b₁) > k,” while Friday he is as­serting one of the form “p(h/e&b₂) < k.” And these are not incompatible statements.

Returning to evidence, a non-relativist with regard to background in­formation can accept the definitions of evidence as these are given in section 4, and need not relativize them to the background information by writing either “e&b is evidence that h” or “e is evidence that h, given b.” He can consider statements of the form

(5) The fact that Alan has yellow skin is potential evidence that he has an i.c.b.

to be complete, even though appeals to background information will be made in defending (5) or its denial. On Monday, on the basis of the in­formation available to him, the doctor affirms (5); on Friday, on the basis of the new information, he denies (5). The relativist, on the other hand, regards (5) as incomplete. If (5) if relativized to the background informa­tion on Monday it is true, and if relativized to the background information on Friday it is false.

I shall not here try to arbitrate between these views. Perhaps each re­flects different tendencies in the way we speak about probability and evi­dence. Perhaps one is more dominant than the other in linguistic practice or is more advantageous for other reasons. But which of these views about background information we employ will affect what claims about poten­tial and veridical evidence we are prepared to make.

Thus, in section 1 it was asked whether there is a concept of potential evidence according to which

(6) Alan's yellow skin was evidence of an i.c.b. (on Monday) and still is (on Friday)

is true, despite the fact that on Friday the doctor's tests prove negative. Using (1), a background-relative concept of potential evidence, (6) might be understood by reference to

(7) The fact that Alan has yellow skin is potential evidence that he has an i.c.b., given the background information of the doctor on Monday.

And (7) is as true on Friday as it is on Monday, since it is true timelessly. Of course if (6) is relativized to the information of the doctor on Friday then it is false timelessly. But the relativist who wants to explain the sense in which (6) is true can use definition (1) and relativize his evidence state­ment to the doctor's information on Monday.

The non-relativist will not be able to regard (6) as true, if construed as it has been so far. He will say that whereas on Monday he believed (5) to be true, on Friday he realizes that it is false; but he cannot as­sert that (5) was true on Monday and remains true on Friday, as (6) suggests.

Nevertheless, the non-relativist can resurrect (6) by claiming that it is true if it is construed as making a general claim rather than a particular one, namely,

(8) Having the kind of yellow skin which Alan has is (timelessly) evidence of (having) an i.c.b.

And he can provide the following set of necessary and sufficient condi­tions for statements of this type, using as a guide the previous definition of potential evidence:

(9) Having F is potential evidence of having G (for A’s) if and only if (a) “X is F” does not entail “X is G”; (b) the probability of something’s (an A's) having G, given that it has F, is high; (c) the probability that there is an explanatory connection between something’s (an A’s) having F and its having G, given that it has both, is high.

Using (9) the non-relativist can argue that (8) is true and therefore that a sense of potential evidence can be provided which sanctions (6). There is then a certain analogy between the relativist’s and the non-relativist’s response to (6), since according to both (6) has different interpretations. The relativist argues that (6) is true if construed as (7) but false if con­strued as

The fact that Alan has yellow skin is potential evidence that he has an i.c.b., given the background information of the doctor on Friday.

The non-relativist argues that (6) is false if construed as (5) but true if construed as (8).

6.