A NEW PROPOSAL

Although neither the probability nor explanation definitions are ade­quate, if these are combined in a certain way the outcome may be more successful. Here are my proposals:

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

(2) e is veridical evidence that h if and only if e is potential evidence that h, h is true, and there is an explanatory connection between the truth of h and e. (This is simply (1) of section 1.)

For e to be potential evidence that h we require, in addition to e's being true and not entailing h, the satisfaction of two probability conditions. One is that the probability of h given e be high. The other is that the probability that there is an explanatory connection between h and e, given that h and e are both true, be high; that is, that it be probable, given h and e, that h is true because e is, or conversely, or that some hypothesis correctly explains both. Veridical evidence requires, in addition to this, that h be true and that there be an explanatory connection between the truth of h and e.

In section 1 the following features of potential evidence were cited: (i) e can be potential evidence that h even if h is false; (ii) potential evi­dence is objective, that is, whether e is potential evidence that h does not depend on whether anyone believes e or h or anything about their relationship; (iii) e is potential evidence that h only if e is true; (iv) e is potential evidence that h only if e does not entail h. Features (i), (iii), and (iv) are obviously satisfied by (1) above, as is feature (ii) provided that the concept of probability used in conditions (1c) and (1d) is construed as an objective one.

To assess these definitions let us reconsider the counterexamples to the previous probability and explanation definitions.

The lottery case. The fact that all the lottery tickets except those of John and Bill have been destroyed, that of the original 1,000 tickets John has 100 and Bill has 1, and that one ticket will be drawn at random, does not make it probable that Bill will win. Hence by condition (1c) this fact is not potential (and therefore not veridical) evidence that Bill will win. On the contrary, as previously indicated, it ought to be poten­tial evidence that John will win. And indeed it is on definition (1), since given the fact in question it is probable that John will win (1c); and given the same fact and the fact that John will win it is probable that a correct explanation of why John will win is that all the 1,000 lottery tickets except those of John and Bill have been destroyed, that of the 101 remaining tickets John has 100 and Bill 1, and that one ticket will be chosen at random (1d). Definition (1) above gives us a reasonable analysis of this case in a way that the probability definition (1) of section 2 does not.

The paradox of ideal evidence. The fact that (e) the roulette ball has landed on numbers other than 3 approximately 35/36ths of the time during the second 5,000 spins ought to be potential evidence that (h) it will land on a number other than 3 on the 10,001st spin, even if the probability of this hypothesis has not increased over its prior probability. Definition (1) gives us what we want, since the probability of h on e is high. And given that h and e are both true it is probable that both h and e are correctly explained by the hypothesis that on the roulette wheel there are 36 places of equal size for the ball to land, 35 of which show numbers other than 3.

The Wheaties case. The fact that (e) this man eats Wheaties should not be (potential or veridical) evidence that (h) this man will not be­come pregnant, even though the probability of h given e is high. And it is not evidence on definition (1) since condition (d) is violated. Given that h and e are both true it is not probable that there is an explanatory connection between h and e; it is not probable that this man will not become pregnant because he eats Wheaties, or that he eats Wheaties because he will not become pregnant, or that there is some hypothesis that correctly explains both his eating Wheaties and his not becoming pregnant. His eating Wheaties and his not becoming pregnant are not only probabilistically independent, they are (probably) explanatorily independent.

However, we might alter the example as follows. Let e' be the infor­mation that this man who wants to become pregnant believes that he never will and as a consequence becomes anxious and eats Wheaties to reduce his anxiety. In this case, it might be urged, given both h and e' it is probable that h does correctly explain e': it is probable that this man believes what he does, becomes anxious and eats Wheaties because in fact he will not become pregnant. Then by definition (1) e' is potential evi­dence that h. Assuming that h is true and that there is such an explanatory connection between e' and h, then e' is also veridical evidence that h, by definition (2). Is this reasonable?

A claim that it is not might be made on the ground that we do, after all, have extremely good evidence for h, namely, that this man is indeed a man, not a woman. And this is both potential and veridical evidence that there will be no pregnancy. However, the fact that there is other evidence whose support for h is stronger than that given by e' does not by itself mean that e' is not evidence that h. Here it is important to recall the distinction between something’s being evidence that h and its being someone’s evidence that h. In our earlier example at the end of section 1, the fact that Alan is receiving treatment T might be (potential or verid­ical) evidence that he has an i.c.b. without its being the doctors evidence. (The fact that Alan is receiving this treatment may not be the doctor’s reason for believing that he has an i.c.b.) Similarly, the fact that this man, who wants to become pregnant, is anxious because he believes he never will and eats Wheaties to reduce his anxiety can be evidence that he will not become pregnant without its being anyone’s evidence for this. No one who believes that this man will not become pregnant may do so for the reason just given.

The case of the stalled car. The fact that (e) my car won't start this morning is not potential evidence that (h) at precisely 2.07 last night 5 boys and 2 girls removed the 18.9 gallons of gas remaining in my tank and substituted water.

The proposed definition of potential evidence thus avoids the counter­examples to previous definitions. Will it sanction evidence statements that we are usually prepared to make? Is the fact that all the observed crows have been black potential evidence that all crows are black? Is the fact that hydrogen and oxygen combine in a simple ratio by volume potential evidence that nitrogen and oxygen do too (as Gay-Lussac thought)? Is the fact that electrons produce tracks in cloud chambers potential evidence that they carry a charge? Is the fact that Alan has yellow skin potential evidence that he has an i.c.b.? Whether these claims can be made depends on whether certain probability statements can be asserted. The fact that Alan has yellow skin is potential evidence that he has an i.c.b. only if it is probable that he has an i.c.b., given that he has yellow skin, and it is prob­able that there is an explanatory connection between his having yellow skin and his having an i.c.b., given that he has both. And whether these probability claims can be made depends on what background information is being assumed, and on the general relationship between probability statements and background information. What view we take of this rela­tionship will determine what evidence statements we can assert, as will be shown next.

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