Robert R. Wadholm

W.V. Quine’s “Natural Kinds”: The Dubiousness of Similarity & Kind and the Induction of Grue Non-RavensRobert R. Wadholm, Missouri UniversitySeptember 11, 2012

Is the notion of kinds and similarities a dubious concept? Are the natural kinds ultimately reducible and

superfluous? Can we inductively arrive at grue non-ravens (and what in the world is a grue or a non-

raven)? In this paper, I wish to critique W.V. Quine’s argument regarding the puzzles about non-black

non-ravens and grue emeralds put forth in his essay “Natural Kinds”.

Non-black non-ravens

Hempel’s puzzle of non-black non-ravens suggests that “each black raven tends to confirm the law that

all ravens are black,” and further that “each green leaf, being a non-black non-raven, should tend to

confirm the law that all non-black things are non-ravens, that is, again, that all ravens are black.” This is

said by Quine to be “paradoxical”. Quine posits a solution to this puzzle by stating that the “complement

of a projectible predicate need not be projectible”. So a green leaf counts toward “All leaves are green”,

but not toward “All non-black things are non-ravens”. Quine’s argument for rejecting the projectibility of

complements of a projectible predicate seems to be based on a distaste for the idea that looking at one

kind (or non-kind) can help us confirm projections about another kind (because for him, kinds are too

messy). However, if we take Hempel’s puzzle at face value, there is not much of a puzzle, and no

paradox, and our notion of kind/similarities does not seem to be put into doubt.

If there are one million ravens in the world, and I have examined 800,000 of them, and every one

of them has been black, we can use induction to predict that the next raven I examine will be black, and

further that it is likely that all ravens are black. When I examine raven number 800,001 and it is black, I

get closer to confirming this prediction based on induction. Let us say, for the sake of argument, that there

are 1082 other objects in the universe (other than ravens). If I examine a green leaf (which is both a non-

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raven and non-black), I show that one of those many other objects in the universe that is non-black is also

a non-raven. While we don’t usually do things this way, we can see that it is just a question of statistics. 1

in 1082 is very small, and thus is not much of a confirmation of our hypothesis that all non-black things

are non-ravens (and thus that all ravens are black). However, 1 in 1 million is statistically larger, and thus

is more of a confirmation of our hypothesis that all ravens are black. As long as there are more things that

are non-ravens than there are that are ravens, it is exceedingly more easy (and intuitive) to confirm that all

ravens are black on the basis of seeing ravens than on the basis of seeing non-ravens. That’s not a

paradox, that’s just statistics. And it doesn’t seem to be much of a puzzle. There is a puzzle, however,

involving induction from kinds related to this: If we only had an idea of a raven, and no one had ever

examined a raven’s color, could we examine every non-black non-raven in the universe and confirm that

ravens are always black (or say anything about what ravens are, based on what other things are not)? Or

does the notion of kinds (like black things or ravens) require at least one example (and not merely non-

examples) to uncover the nature of the kind?

Grue emeralds

Quine asks us to picture Goodman’s “grue” emerald puzzle as an example of the “dubious scientific

standing of a general notion of similarity, or of kind.” So what is the puzzle? Goodman creates a universe

in which emeralds are being examined to see what color they are. As we examine each emerald, we notice

that all the emeralds we have examined thus far are green. So far so good. We would use induction to

predict that any emerald we examine tomorrow will likely be green (they have all been green so far, so

that would be a good hypothesis about the state of things, unless we know that the emeralds will change

color overnight, or we have examined emeralds that are not green, which is not the case).

However, Goodman proposes a new idea in the form of a proposition: “Call anything grue that is

examined today or earlier and found to be green or is not examined before tomorrow and is blue.” Let’s

think a little about Goodman’s proposition. He is asking us to create a new naming convention whereby

we name emeralds based on color and examined date (green and examined today or earlier, blue and not

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examined before tomorrow). So any emeralds before this specific date in time are green, because they are

green, correct? They are also grue, because they are green and were examined today and earlier. So this

state of affairs seems to imply that inductively we should hypothesize that an emerald examined

tomorrow will have the same likelihood of being green as it does of being grue. Or that induction based

on kinds of things is dubious, because the notion of kinds and similarities is dubious. That seems to be the

way that Quine deals with the puzzle, but let’s take a closer look.

I have a daughter named Emily that turned 10 on July 15, 2012. On July 14, I could have said “9

is the age of Emily Wadholm today or 10 is the age of Emily Wadholm tomorrow.” But in this case,

Emily is in fact 9 today and 10 tomorrow (because it is her birthday tomorrow). Emily was 9 every other

day of the year before July 15, so we should predict that she will still be 9 years old on July 15 and after.

Unless something happens. Something did happen—she changed from 9 to 10 because July 15 was her

birthday. Let’s propose, then, to call nen any Emily Wadholm that is 9 on July 14 and earlier or is 10 on

July 15 and after. I’m okay with that. We can predict on July 14 that Emily will be 9 on July 15 based on

her being 9 years old for so many days previously, but we’d be wrong (she’s going to change ages). If we

knew anything about aging and birthdays, we would be able to use inductive reasoning to say that Emily

would be 10 on July 15. Good thing we have the number nen. We can instead predict that Emily is nen

years old, and we’ll be right! Emily is nen: she is 9 on July 14 and earlier or 10 on July 15 and after. But

wait, if we’re correct, that means that we have misdefined nen; nen should be “9 on July 14 and earlier

and 10 on July 15 and after.” If our prediction about nen is correct, we are forced to get rid of the “or”

and replace it with an “and”. If nen is correct, nen needs redefined (as both statements are true, and no

disjunctive is needed). If Emily is nen tomorrow, she is 9 today and earlier and 10 tomorrow.

Let’s look back at grue and imagine, for the sake of testing the argument, that Goodman and

Quine are right in suggesting that it seems to be equally plausible (inductively) that an emerald we

examine tomorrow will be green and that it will be grue. (For Quine, an intuitive notion of similarity

between green emeralds makes them more likely intuitively, though not necessarily inductively). After

all, all of the other emeralds were green in the past, leading us to make a prediction that all emeralds are

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green (even the emeralds we have not yet examined). And as we examine more emeralds, we may find

ourselves closer to being statistically able to predict that all emeralds are green (as the unexamined

emeralds near 0) as we did with ravens earlier. However, we also find that all the previously examined

emeralds seem to point to a prediction of a grue emerald tomorrow, despite the fact that a grue emerald is

nonsensical and smelling of philosophical trickery. So how do we choose between green and grue? On the

basis of the intuitiveness of similarity/kind, as Quine seems to suggest? If we allow ourselves to be drawn

into the puzzle, we may have to admit the equal likelihood of either green or grue, or like Quine, to

speculate about projectible predicates and question the scientific standing of the idea of similarities and

kind. But let’s not give up yet. Maybe Emily being nen is a clue to emeralds not being grue. Let’s look

ahead to tomorrow when our predictions about the color of previously unexamined emeralds will be

tested, and see what the results are, then use a time machine and come back to today to make our decision

about the color of emeralds that will be examined tomorrow (we’ll be testing the nature, value and

validity of a proposition based on its results).

Let’s take the simple choice first: we say that emeralds examined tomorrow will be green based

on inductive reasoning that seems to suggest that as we experience more green-only emeralds we are

more likely to experience green-only emeralds in the future. If an emerald we examine tomorrow is green,

we were right about our prediction (for the time being). If an emerald we examine tomorrow is red, we

were wrong. But we based our hypothesis on past empirical data, so we were right to hypothesize that

based on our previous research, all emeralds are green. It is just a matter of an incorrect hypothesis. We

merely need to adjust our hypothesis about the future to account for our experiences in the past.

Tomorrow we will adjust our hypotheses if need be. That’s how science works.

Now let’s take the more difficult choice: we say, based on the grue proposal, that emeralds

examined tomorrow will be grue (and thus blue). If an emerald we examine tomorrow is green (or red, or

purple, etc.) we were wrong. If an emerald we examine tomorrow is grue (and thus blue), we were right.

Unfortunately, if we were right, grue is not what we thought it was. Grue was supposed to mean any

emerald that is “examined today or earlier and found to be green or is not examined before tomorrow and

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is blue.” But we find that if an unexamined emerald is blue tomorrow after examination (and thus, grue

according to our proposed prediction), then grue actually means any emerald that is “examined today or

earlier and found to be green and is not examined before tomorrow and is blue.” If the prediction about

grue is true, grue is not a disjunctive proposition. True grue as it was proposed satisfies both sides of the

disjunction, meaning that there is no disjunction (and we may infer no intended disjunction). May we

infer from this that the nature of grue is nonsense (and mere philosophical gobble-dee-gook) or that it has

been miscommunicated? If it is nonsense (which I think it is), let’s get rid of it as a proposition. If it has

merely been miscommunicated, then let’s be more clear about what grue means (“and”, not “or”). So if

we will be right about grue tomorrow, then grue is a bad (non-inductive) option. Without the disjunction,

grue is a green emerald examined today or earlier and is predictive of a blue emerald tomorrow. But

based on inductive reasoning, we have already stated that it is most likely that an emerald examined

tomorrow will be green—after all, all of the earlier examined emeralds were green. We have no good

reason to choose grue (there is no evidence for unexamined emeralds to be blue), and subsequently no

puzzle over kinds or similarities. Grue is not equal to B or C, it is equal to B & C, and thus not a good

choice (unless, like nen, we know beforehand something about the rest of the emeralds or about a change

that will take place in the unexamined emeralds overnight, but if that is so, we should have entered that

into the proposal concerning grue). Inductively we should hypothesize today that tomorrow’s examination

of emeralds will yield similar results to what we have observed thus far, and they will be green, not blue

or grue. Further, if we find that all non-green things are also non-emeralds, and we have at least one

example of an emerald and it is green, we could hypothesize that all emeralds are green. Consequently,

we could also say that all ravens are non-grue (but could we say that all non-non-grue things are non-

ravens?).

Can we infer from the non-raven and grue puzzles that the notion of similarities or kinds is

dubious in its scientific standing? I think the reasoning behind this inference has been dissipated. The

kinds seem to have stood their ground. Even if science advances and posits reduction of kinds into

superfluity (as Quine asserts at the end of his argument), still humans and animals seem to make use of

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kinds and similarities at every point in their lives, causing recognitions of kinds and similarities to

proliferate. They are now richer kinds, but they are nevertheless persistent and useful (and made use of by

even the scientists and philosophers who wish to deny them validity). Another question might be “Does a

study of kinds belong to ontology, or to epistemology?” An answer to that, I fear, could be full of

unending puzzles, though perhaps not of the grue non-raven variety.

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