“I OBJECT. DON'T FORGET BLEEN!” (NELSON GOODMAN)

All of this is subject to what seems like a devastating objection. In charac­terizing a disjunctive property such as grue as one satisfying condition (1) or, more generally, (2), I indicated that the properties Q₁ and Q₂ must not be disjunctive properties satisfying (1) and (2).

Definition: x is bleen at time t if and only if t is prior to A.D. 2500 and x is blue at t or t is A.D. 2500 or later and x is green at t.

Now, thinking of grue and bleen as our basic properties, we can characterize the properties green and blue in a way that satisfies conditions (1) and (2):

(3) x is green at t if and only if t is prior to A.D. 2500 and x is grue at t or t is A.D. 2500 or later and x is bleen at t.

(4) x is blue at t if and only if t is prior to A.D. 2500 and x is bleen at t or t is A.D. 2500 or later and x is grue at t.

Looking at the properties green and blue this way and treating grue and bleen as our basic nondisjunctive properties, green and blue become dis­junctive properties satisfying conditions (1) and (2). Accordingly, to pro­ject green with respect to emeralds we need to examine emeralds both before and after 2500. We must use selection procedure SP₁ and not SP₂. This directly contradicts what was said earlier.

So where do we stand? Can the property grue be projected with re­spect to emeralds by examining only emeralds before 2500? In gathering information that will warrant the hypothesis that all emeralds are grue can we use SP₂ and select emeralds to observe at times that are only be­fore 2500? Similarly, can the property green be projected with respect to emeralds only by examining emeralds both before and after 2500, that is, by following only SP₁?

My answer is that for us, that is, for normal human beings, green and blue are not disjunctive properties of types (1) and (2) subject to a tempo­ral condition, while grue and bleen are.

(a) For us, the properties green and blue are not defined in the disjunctive way given above. Our dictionaries do not define the terms “green” and “blue” in terms of “grue” and “bleen” and a specific time. Nor do dictionaries in other languages with words for the properties blue and green. Indeed, the dictionaries I own do not even contain the words “grue” and “bleen.”

(b) When we attempt to ascertain whether something we are examining is green (or blue) at a certain time t we do not, and do not need to, ascertain whether it is grue at t and t is before 2500 or whether it is bleen at t and t is 2500 or later. For example, if it is within five minutes of midnight, one way or the other, December 31, 2499, but we do not know which, and we are presented with a colored object, we could examine it and determine whether it is then green (or blue) without knowing whether midnight has passed.

By contrast,

(c) For us, the properties grue and bleen are defined disjunctively in the manner of (1) and (2) and are subject to a temporal condition. We understand these properties only by reference to such definitions.

(d) When we attempt to ascertain whether something is grue (or bleen) at a certain time t we need to ascertain whether it is green at t and t is before 2500 or whether it is blue at t and t is 2500 or later. For example, if it is within five minutes of midnight, one way or the other, December 31, 2499, but we do not know which, and we are presented with a colored object, by examining it we could not determine whether it

is then grue (or bleen) without knowing whether midnight has passed.

We might, however, imagine some extraordinary group of individuals very different from us in the following respects:

(a') For members of this group the properties grue and bleen are not defined disjunctively in the manner of (1) and (2). Their dictionaries do not define “grue” and “bleen” in terms of “green” and “blue” and a specific time.

(b') When members of this extraordinary group attempt to ascertain whether something they are examining is grue (or bleen) at a certain time t, they do not, and do not need to, ascertain whether it is green at t and t is before 2500 or whether it is blue at t and t is 2500 or later. For example, if it is five minutes before or after midnight, December 31, 2499, but they do not know which, if they are presented with a colored object they could determine whether it is then grue (or bleen) without knowing whether midnight has passed.

(c') For them, the properties green and blue are defined in the manner of (3) and (4). They understand these properties only by reference to such definitions.

(d') When they attempt to ascertain whether something is green (or blue) at a certain time t they need to ascertain whether it is grue at t and t is before 2500 or whether it is bleen at t and t is 2500 or later. If it is five minutes before or after midnight, December 31, 2499, but they do not know which, and they are presented with a colored object, by examining it they could not determine whether it is then green (or blue) without knowing whether midnight has passed.

It may be useful to draw an analogy with a different sort of case involving a disjunction that is nontemporal but is different from ones that can spawn Goodman's paradox. Suppose there is an extraordinary group of persons who have a word in their language for male robins and a different word for female robins, but no word for robins. (Perhaps they regard male robins and female ones as belonging to different species.) Using their words for “male robin” and “female robin” we can then define our word “robin” for them, as follows:

x is a robin if and only if x is a male robin or a female robin.

This is how they will understand the word “robin,” which is new for them. Moreover, when members of this group attempt to ascertain whether something is a robin they will determine whether it is a male robin, and if it is not, whether it is a female robin.

In the case of grue, what we are imagining is that for members of the extraordinary group the properties green and blue are disjunctive ones subject to a temporal condition, while grue and bleen are not. We have no idea how they do what they do, in particular how they determine whether something is grue at a certain time t without knowing whether t is before 2500 or later. Nor do we have any idea why, in order to deter­mine whether something is green at a certain time t they need to know whether t is before or after 2500. We are imagining simply that these things are so.

My claim is that if there were (or could be) such extraordinary people, they would be justified in projecting the property grue with respect to emeralds after examining emeralds before 2500; they would not need to wait until 2500 to examine emeralds then as well. They would be justi­fied in using selection procedure SP₂. And if there were such extraordi­nary people they would be justified in projecting the property green with respect to emeralds only by examining emeralds both before and after 2500, that is, by using SP₁.

However, the claim is not that there are people such as the extraor­dinary ones being imagined. Nor is it that there could be, in some robust sense of “could be.” It may not be physically possible. The claim is only that it is logically possible.^[30] There is no contradiction (or at least I have not found one) in imagining the existence of extraordinary persons satisfying conditions (a')-(d'). Accordingly, there is no contradiction in supposing the existence of extraordinary persons who are justified in projecting the property grue with respect to emeralds after examining only emeralds before 2500. However, we are not such extraordinary people and there is no reason to believe that any such people exist or, physically speaking, could exist.

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