EVIDENCE
So far I have talked about generalizing from examined cases of green or grue to all cases (projecting these properties). Goodman, Carnap, and others who write about the grue paradox are concerned with the question of what counts as confirming evidence for a hypothesis.
So, finally, on my solutions, is the fact that(e) All emeralds examined so far are green
evidence that
(h) All emeralds are always green?
To answer, we need to distinguish several concepts of evidence used in the sciences. In The Book of Evidence (hereafter, BE), I distinguish four such concepts, which I call (1) subjective, (2) ES (epistemic situation),
(3) potential, and (4) veridical. Very briefly, (1) e is some person's (or group's) subjective evidence that h if the person (or group) believes that e is evidence that h, and if that person's reason for believing h true or probable is that e is true. That 24 hours ago Ann ate a pound of arsenic is my subjective evidence that she is now dead. It is what I take to be evidence; and my reason for believing she is dead is that she ate the arsenic. (2) e is ES-evidence that h, relative to a type of epistemic situation (a situation in which one knows or believes certain things), if anyone in that epistemic situation would be justified in believing that e is evidence that h. Relative to an epistemic situation containing the knowledge that arsenic is lethal, the fact that Ann ate the arsenic is ES-evidence that she is dead. (3) e is potential evidence that h if e provides a good reason to believe h, irrespective of epistemic situations. No matter what is assumed known or believed, the fact that Ann ate the arsenic is a good reason to believe she is dead, since arsenic is lethal. (4) e is veridical evidence that h if e is potential evidence that h, and h is true.[31]
Only the first concept is subjective: whether e is (subjective) evidence that h depends upon what some person or group in fact believes about e, h, and their relationship.
The other types are objective. ES-evidence is relativized to a type of epistemic situation, not to the specific one of some individual or group; no one need be in an epistemic situation of that type. Finally, like the concepts of “sign” and “symptom,” at least on one standard use of these, potential and veridical evidence are not relativized to any actual or potential epistemic situation.In BE, as well as in chapter 1 in the present volume, I provide definitions for each of these concepts (which need not be given here). I argue that although potential evidence is the most basic concept (the others can be defined by reference to it), veridical evidence is what scientists seek. In the characterization of subjective evidence as what one believes to be evidence, the evidence one believes it to be is veridical; an analogous claim can be made for ES-evidence.
Our question, then, is whether information e above (concerning examined emeralds) is evidence that h (all emeralds are always green). Consider the simplest case first, subjective evidence. We green speakers (the normal folks who satisfy (a)-(d) of section 3 with respect to green and grue) believe that e is (veridical) evidence that h and that h is true; our reason for believing that h is true is that e is. In short, the fact that e is true is our subjective evidence that h is true. Similarly, if grue speakers existed (extraordinary but imaginary beings who satisfy (a')-(d')), the fact that all the emeralds examined so far are green (and hence grue) would be their subjective evidence that all emeralds are always grue.
In section 3 I claimed that a grue speaker is justified in projecting the property grue, while a green speaker is justified in projecting the property green. This is a case of ES-evidence, where the epistemic situation is understood as including a speaker's knowledge of definitions and of how to ascertain whether something is grue or green. A grue speaker's ES- evidence that all emeralds are always grue would be that all emeralds so far examined are grue.
A green speaker's ES-evidence that all emeralds are always green is that all emeralds so far examined are green.Is e potential evidence that h? Whether it is depends on the selection procedure used. I have characterized a selection procedure as a rule for determining how to test, or obtain evidence for or against, a hypothesis. In the case of our hypothesis h a selection procedure might include a rule for selecting emeralds to observe. If, for example, such a rule called for selecting emeralds only from a box containing green objects, then e would not be potential evidence that h. But a selection procedure for our hypothesis h may also include a rule for how to determine whether an emerald is green at a given time t.[32] Many such rules are possible, but let me concentrate on two.
SP(green)1: Determine whether an emerald is green at a time t simply by looking at it at t, in good light, at a distance at which it can be seen clearly (etc.), and ascertaining whether it looks green.
SP(green)2: Determine whether an emerald is green at t by looking at it at t and ascertaining whether it looks grue at t (the way our imagined grue speaker does) and t is prior to 2500 or whether it looks bleen at t and t is 2500
or later.
Suppose that all the emeralds selected for observation so far (before 2500) have been determined to be green. Is that fact potential evidence that all emeralds are always green? That depends not only on which selection procedure was used to select emeralds for observation but on which one was used to determine whether an emerald is green. Suppose that SP(green)2 was used (e.g., by genuine grue speakers, who could not use SP(green)j). Someone following SP(green)2 and examining only emeralds before the year 2500 to determine whether they look grue and hence are green would need to wait until 2500 to examine emeralds to determine whether they look bleen after 2500 and hence are green. Such a person would need to do this in order to “vary the instances” to obtain genuine potential evidence that all emeralds are always green.
If SP(green)2 is really the selection procedure that was used for determining whether an emerald is green, then e is not potential evidence that h. By contrast, someone following SP(green)1 and examining only emeralds before 2500 would not need to wait until 2500 to examine emeralds to determine whether they look bleen after 2500 and hence are green. The date 2500 plays no role in following SP(green)1 the way it does in following SP(green)2. If e were obtained by following SP(green)p e would be potential evidence that h.Now, as Goodman loves to do, let us compare the situation with respect to the grue hypothesis. The question is whether
e': All emeralds examined so far are determined to be grue
is potential evidence that
h': All emeralds are always grue.
We need to say what selection procedure is being used. By analogy with the previous ones for green emeralds we have
SP(grue)1: Determine whether an emerald is grue at t simply by looking at it at t in good light (etc.) and ascertaining whether it looks grue.
SP(grue)2: Determine whether an emerald is grue at t by looking at it at t and ascertaining whether it looks green at t, where t is prior to 2500, or whether it looks blue at t and t is 2500 or later.
If SP(grue)2 is used in obtaining the result e', then e' is not potential evidence that h'. Someone (such as us) following this selection procedure and examining only emeralds before 2500 to determine whether they look green and hence are grue would need to wait until 2500 to examine emeralds to determine whether they look blue and hence are grue. Such a person would need to do this in order to “vary the instances” to obtain genuine potential evidence that all emeralds are always grue. Using SP(grue)2, examining emeralds only before 2500 would not suffice.
By contrast, a genuine grue speaker following SP(grue)1 and examining emeralds only before 2500 would not need to wait until 2500 to examine emeralds to determine whether they look blue and hence are grue.
Using SP(grue)1, examining emeralds only before 2500 and determining that all of them are grue would allow e' to be potential evidence that h'.In short, (e) the fact that all emeralds observed so far are green is potential evidence that (h) all emeralds are always green, if selection procedure SP(green)1 is used, but not SP(green)2. And (e') the fact that all emeralds observed so far are grue is potential evidence that (h') all emeralds are always grue, if selection procedure SP(grue)1 is used, but not SP(grue)2. It should be emphasized that this is not to relativize the concept of potential evidence to a particular person or to a type of epistemic situation. If SP(green)1 is used e is potential evidence that h, and if SP(grue)1 is used e' is potential evidence that h', independently of who believes what. Nor are e and e' just potential evidence for persons in epistemic situations of certain types.
Now, as a matter of fact, there are no grue speakers, that is, extraordinary persons who satisfy conditions (a')-(d') of section 3 for defining and identifying grue and green properties. There are just ordinary, everyday people like us, who satisfy conditions (a)-(d). So, even if it is logically possible that a selection procedure such as SP(grue)1 is followed in determining whether an emerald is grue, and that a selection procedure such as SP(green)2 is followed in determining whether an emerald is green, this will never happen (we confidently believe). In any real-life situation in which selection procedures involve actual observations of emeralds, SP(green)1 and SP(grue)2 will be followed, in which case the fact that all observed emeralds are determined to be green will be potential evidence that all emeralds are always green, and the fact that all observed emeralds are determined to be grue will not be potential evidence that all emeralds are always grue. If (as we also confidently believe) the green hypothesis is true, then the fact that all observed emeralds are determined to be green is veridical evidence for this hypothesis. If the hypothesis turns out to be false, then the fact about the observed emeralds is not veridical evidence that all emeralds are green.