Table Of ContentGRUEi
THE NEW RIDDLE OF INDUCTION
EDITED BY
DOUGLAS STALKER
OPEN* COURT
Chicago and La Salle, Illinois
Dedicated to the Memory of
*
Henry B. Tingey
OPEN COURT and the above logo are registered in the U.S. Patent
and Trademark Office.
© 1994 by Open Court Publishing Company
First printing 1994
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any
means, electronic, mechanical, photocopying, recording, or
otherwise, without the prior written permission of the publisher,
Open Court Publishing Company, POB 599, Peru, Illinois 61354.
Printed and bound in the United States of America.
Library of Congress Cataloging-in-Publication Data
Grue! : the new riddle of induction / [compiled by] Douglas
Stalker.
p. cm.
Includes bibliographical references and index.
ISBN 0-8126-9218-7 (cloth).-ISBN 0-8126-9219-5 (paper)
1. Induction (Logic) I. Stalker, Douglas Frank, l 947-
BC91.G78 1994
161- dc20 94-11203
CIP
Contents
Introduction 1
l. Inductive Inference: A New Approach 19
Israel Scheffler
2. Luck, License, and Lingo 31
Joseph Ullian
3. Natural Kinds 41
W.V. Quine
4. Concerning a Fiction about How Facts Are Forecast 57
Andrzej Zab/udowski
5. Grue 79
Frank ] ackson
6. Concepts of Projectibility and the Problems of Induction 97
John Earman
7. Induction, Conceptual Spaces, and AI 117
Peter Giirdenfors
8. The Projectibility Constraint 135
John L. Pollock
9. Simplicity as a Pragmatic Criterion for Deciding What
Hypotheses to Take Seriously 153
Gilbert Harman
10. A Grue Thought in a Bleen Shade: 'Grue' as a
Disjunctive Predicate 173
David H. Sanford
11. Entrenchment 193
Ian Hacking
12. No Model, No Inference: A Bayesian Primer on the
Grue Problem 225
Elliott Sober
13. Bayesian Projectibility 241
Brian Skyrms
vui
Contents
14. Learning and Projectibility INTRODUCTION
Patrick Suppes 263
15. Selecting Variables and Getting to the Truth
Clark Glymour and Peter Spirtes 273
Annotated Bibliography
281
Index The grue debate has been going on for almost fifty years. It started
459 eight years before the word "grue" appeared in print in philosophy.
(The word "gruebleen" appeared in print in 1939, on page 23 of
James Joyce's novel Finnegan)s Wake.) In 1946 Nelson Goodman
published a short paper entitled "A Query on Confirmation," and
as.,,
this paper introduces the grue-like predicate This predicate
appears in an example about drawing marbles from a certain bowl.
Goodman asks us to suppose that we have been drawing one marble
per day from this bowl for ninety-nine days-indeed, the
ninety-nine days up to and including Victory in Europe Day, May
8, 1945. He also asks us to suppose that each marble has been red
so far. If we draw a marble on the next day, the hundredth day, we
might expect that it will be red as well. After all, the first marble
was red, the second was red, and so on through the ninety-ninth
marble: they were all drawn from the bowl and they were all red.
The evidence plainly supports our prediction about the next marble
we draw: it will be red. Or so it seems. Goodman introduces us to
as/)
the predicate which means "is drawn by Victory in Europe
Day and is red, or is drawn later and is nonred." This predicate
applies to the ninety-nine marbles that we have drawn from the
bowl so far. They were all drawn by Victory in Europe Day, and
they were all red-so they were all S. This evidence seems to
support a different prediction about the next marble we draw: it
will not be red. Of course we do not expect the next marble we
draw from the bowl, the one we draw after Victory in Europe Day,
to be nonred. It doesn't matter that the first marble was S, the
second was S, and so on through the ninety-ninth marble. This
doesn't support a prediction about the next marble being nonred.
But why not? Why do the marbles add up to confirmation in one
case, but not the other?
In 1954 Goodman published a small book entitled Fact, Fiction
and Forecast. The word "grue" appears in Chapter III, Section 4,
which is entitled "The New Riddle of Induction." Goodman asks
us to consider emeralds that have been examined before time t, and
to suppose that all of them have been green. Thus, by time t, these
observations support the hypothesis that all emeralds are green, and
the prediction that if we happen to examine the next emerald after
3
Introduction
2 Introduction
former student, Israel Scheffler, was a lecturer at Harvard. In
time t, it will be green as well. As before, Goodman introduces a
"Inductive Inference: A New Approach," Scheffler attempts to
new predicate to show that things aren't as simple as they might
inform scientific readers about Goodman's (then) recent work on
seem. Something is grue, he tells us, if it is examined before time t
induction. He develops the new riddle in connection with Hume's
and determined to be green, or it is not examined before time t and
challenge and the generalization formula, and he explains the basic
it is blue. It should be plain how this applies to the emeralds
ideas in Goodman's entrenchment solution. Scheffler sees Hume's
examined before time t, and all of which we have found to be
challenge as a question about how to tell reasonable (rational,
green. They are all grue. Thus, by time t, we have a good deal of
justified) inductive inferences from unreasonable ones, and he
support for the hypothesis that all emeralds are grue, and the
introduces the generalization formula as a popular answer to this
prediction that if we happen to examine the next emerald after time
question. Scheffler uses the generalization formula with a pair of
t, it will be grue as well-that is, it will be blue. Indeed, we seem
to have just as much support for the green hypothesis as the grue opposing next-case predictions, such as "The next F will be c>> and
hypothesis. Each emerald has been green, and each has been grue. "The next F will not be G. >> The former prediction agrees with the
universal generalization "All F are G,)) and the latter prediction
Be that as it may, we know that the green emeralds (or, to be
agrees with the universal generalization "No Fare G.)) If the
precise, the evidence statements describing the green emeralds)
evidence to date uniformly supports the generalization "All F are
support the green hypothesis and that the grue emeralds (or, to be
G)) and thereby disconfirms the contrary generalization "No F are
precise, the evidence statements describing the grue emeralds) don't
G,)) then the reasonable prediction is "The next F will be G.))
support the grue hypothesis. Why, as before, do we have
Scheffler thinks that Goodman's new riddle of induction refutes the
confirmation in one case but not the other?
generalization formula, and he extends Goodman's copper example
The new riddle of induction has become a well-known topic in
to show how it does. Consider the predictions "The next specimen
contemporary analytic philosophy-so well-known that only a
of copper will conduct electricity" and "The next specimen of
philosophical hermit wouldn't recognize the word "grue." Fact,
copper will not conduct electricity." The first prediction agrees with
Fiction and Forecast is in a fourth edition, and the best journals
the generalization "All specimens of copper conduct electricity"
contain articles on the puzzle year in and year out. There are now
and the second agrees with the generalization "No specimens of
something like twenty different approaches to the problem, or
copper conduct electricity." If the evidence to date uniformly
kinds of solutions, in the literature: the entrenchment solution the
supports the hypothesis that copper conducts electricity and thereby
positional-qualitative solution, the simplicity solution, the natu'ral
disconfirms its contrary, then it is reasonable to predict that the
kind solution, the coherence solution, the incoherence dissolutions,
next specimen of copper will conduct electricity, and unreasonable
the falsificationist response, the evolutionary approach, the real
to predict that it will not. Or that is how it seems until we
property approach, the counterfactual approach, the various
introduce a grue-like hypothesis about copper: viz., "All specimens
Bayesian approaches, and so on. None of them has become the
of copper have either been examined before t and conduct
majority opinion, received answer, or textbook solution to the
electricity or have not been examined before t and do not conduct
problem. There hasn't even been complete agreement on what the
electricity." The evidence to date uniformly supports this grue-like
proble~ really a~ounts to. In short, the grue debate is still going
hypothesis and thereby disconfirms its contrary as well. If the next
on. This volume is the first collection of essays devoted to that
debate, and it includes selections from the 1950s to the present. specimen of copper will not be examined before time t> then it is
reasonable to predict that the next specimen of copper will not
The selections are in chronological order. Seven of them have been
conduct electricity because this prediction agrees with the grue-like
published before, and eight are appearing for the first time. The
hypothesis. The generalization formula, then, has not picked out
collection ends with a 316-entry, annotated bibliography. The
the reasonable prediction here. Indeed, it can't even select one
annotations range in length from one line to several hundred lines.
prediction-reasonable or otherwise-from our pair of opposing
They cover articles from more than forty different journals and
next-case predictions.
chapters from more than eighty books.
Scheffler describes how Goodman's approach distinguishes the
The first selection originally appeared in Science in 1958.
confirmable "All copper conducts electricity" from its
Goodman was teaching at the University of Pennsylvania, and his
4
Introduction
Introduction 5
nonconfirmable counterpart by looking at historical information
have ended up with classes which are actually .valuab'.e to us. Insofar
about the predicates in each hypothesis. Their biographies differ in
there is an explanation for this state of affairs, Ulhan suggests
an important way. The predicate "conducts electricity" has been as · d d h'
that it will be along evolutionary lines. In a postscnpt ad e to ts
used longer and more often in formulating predictive hypotheses
original paper, Ullian discusses the current status of Goodman's
on the basis of positive, albeit partial, evidence. In Goodman's
theory of projectibility. .
terminology, the predicate "conducts electricity" is better
The third selection is by Goodman's longtune colleague at
entrenched than the predicate "has either been examined before t
Harvard, W.V. Quine. He originally wrote his essay "Natural
and conducts electricity, or has not been examined before t and
Kinds" for a 1970 festschrift for the philosopher of science Carl
does not conduct electricity." Since the grue-like hypothesis
Hempel. Quine describes both the new riddle and Hempel's raven
conflicts with a hypothesis whose predicate is plainly better
paradox in terms of projectibl.e predicates. Wi~h ~empel's paradox,
entrenched, the grue-like hypothesis is nonconfirmable or, as
a white shoe ends up confirmmg the hypothesis All ravens are
Goodman puts it, unprojectible. Likewise, since "All emeralds are
black" because a white shoe confirms the logically equivalent
grue" conflicts with "All emeralds are green," and the predicate
hypothesis "All nonblack things are n?nrave~1s." Wh~le "raven" and
"green" is plainly better entrenched than the predicate "grue," the
"black" are projectible predicates, Qume believes their complements
grue hypothesis is unprojectible.
are not projectible. Thus a white shoe does not confirm "All
As Scheffler notes, some critics believe that Goodman's
nonblack things are nonravens" any more than a green emerald
entrenchment solution is inadequate because Goodman does not
confirms the hypothesis "All emeralds are grue." Quine maintains
say enough about entrenchment itself. Joseph Ullian discusses this
that projectible predicates are true of.things ~f ~ ki.nd, and th~t the
point in the second selection, "Luck, License, & Lingo," which he
notion of a kind is related to the not10n of s11111lanty at least 111 the
prepared for a symposium on justification and originally published
sense of covariation: e.g., if we first think object a is more similar
in The Journal of Philosophy in 1961. Ullian presents the new riddle
to object b than to object c and later think object a is less similar to
and the entrenchment solution in connection with Goodman's view
object b than to object c, then we will likewise ch~n~e h.ow we
of justification. Goodman takes justifying to be a matter of
assign these objects to kinds. In short, the more s1milanty .between
describing, defining, and codifying. On this view, we justify a
objects, the more reason to count them as members of a kmd. .
particular inductive inference by showing that it agrees with a valid
Quine argues that we must have an innate standard of comparative
rule of inductive inference, and we justify a rule of inductive
similarity in order to form any habits and expectations at all, and
inference by showing that it agrees with the inductive inferences we
that this innate subjective standard makes for successful everyday
make and accept. If Goodman's general rule accurately codifies the
inductive inferences because it is the result of Darwinian natural
particular cases by taking into account the entrenchment of
selection. Quine also emphasizes the development and change of
predicates, then it is justified on this view and solves the new
standards of similarity and systems of kinds, notably from our
riddle. However, some critics want more than accurate description.
subjective standard and intuitive kinds to scient.ifically obje~t~ve
In particular, they want to know why the right predicates have
standards and theoretical kinds, such as marsupials and pos1t1vely
become well entrenched while the spurious ones have not. Is it
charged particles. Moreover, he believes that wh~n a bra~ch. of.
simply a matter of luck that the well-entrenched predicates show up
science matures, we can analyze the relevant not10ns of sumlanty
in the confirmable hypotheses? Ullian believes that the real question
and kind in special terms from that branch of science and from.
here is about predicates in general, not just the well-entrenched or
logic. For example, we can analyze object a being,. from. a chemical
projectible ones. It is, he argues, a question about the utility of
point of view, more similar to object b than to object c 111 terms of
predicates or general terms. Ullian considers it remarkable that we
the ratios of matching to unmatching pairs of molecules. We can
have any use-inductive or otherwise-for our general terms. As
then use this analysis of comparative similarity to analyze chemical
he points out, if general terms mark off classes and there are
kinds in terms of a paradigm and a foil. A paradigm is an example
indefinitely many classes, with each class just as good as the other
of the central norm for a kind, and a foil is an example of
from a logical point of view, then it seems extraordinary that we
something that is not a member of the kind because it differs a
6 Introduction
Introduction 7
little too much from the paradigm. A kind is then a set of objects
entrenched predicates at present. In a postscript, Zabludowski
such that the paradigm is more similar to the members of this set
considers an attempt to modify Goodman's entrenchment theory,
than it is similar to the foil.
and an attempt to solve the new riddle by appealing to a distinction
The fourth selection is a revised version of Andrzej
between genuine and pseudo properties.
Zabludowski's "Concerning a Fiction about How Facts Are
The new riddle of induction is typically seen as a problem about
Forecast." This paper was originally published in 1974 in the
projectible and nonprojectibl~ predica:es or prop~r:ies or
Journal of Philosophy, and it started an eight-year exchange between
hypotheses, and typical. so~ut1ons consist o.f expla111111g .the
Zabludowski and proponents (notably Goodman and Ullian) of the
difference between pro1ect1ble and nonpro1ect1ble predicates or
entrenchment approach to projectibility. Zabludowski maintains
properties or hypotheses. The fifth selection presents a different
that Goodman's theory has a number of absurd consequences, not
view of the problem and its solution. In his essay "Grue," which
the least of which is that no hypothesis is projectible. Zabludowski
was originally published in the Journal of Philosophy in 1975, Frank
believes this consequence obtains because, for any supported,
Jackson maintains that all consistent predicates (or properties or
unviolated, and unexhausted generalization h, we can devise
hypotheses) are projectible. He believes .t~at we c~~ avoid the new
another generalization that is supported, unviolated, and
riddle by paying attention to a defeasab1hty cond1t1on on most of
unexhausted-and that conflicts with h. Moreover, this rival
our everyday inductive reasoning. When this condition is satisfied,
generalization will have predicates that are at least as well
the fact that certain Fs-which are H-are G does not support the
entrenched as the predicates in h. On Goodman's approach, this
conclusion that certain other Fs-which are not H-are G. For
means that h is not projectible. For example, we can let h be the
example, if all the lobsters you have observed have been red, and all
hypothesis "All emeralds are green" when we have examined some
of them have been cooked, and you know that cooking makes
emeralds, found them all to be green, and still have more emeralds
lobsters red, then you will not take your observations as support for
to examine. Zabludowski claims that the predicates "stone,"
the prediction that the next uncooked lobster you observe will be
" roun d , " an d "ha rd " are among t h e b est entrenched predicates at
red. In other words, you know that if these lobsters (the ones you
this time. He also claims that we know all three predicates apply to
have observed to date) had not been cooked, they would not have
some objects at this time, and that we know "stone" applies to
been red. More generally, you know that if the Fs-which are
some green emeralds but "round" does not apply to them. Lastly,
H-had not been H, they would not have been G. Jackson refers
Zabludowski believes that the information we accept at this time
to this as the counterfactual condition. He believes this condition
does not prohibit the hypothesis "All stones are hard" from being
resolves the new riddle because it shows why a series of examined
true and conflicting with "All emeralds are green." Given all of
(by time t) emeralds being green supports a next-case prediction
this, Zabludowski introduces the following generalization as a
about an unexamined (by time t) emerald being green, while the
supp~rted, unviolated, and unexhausted rival to the hypothesis in
series being grue does not support a next-case prediction about an
question: (x)(Sx ~ ((Rx & -Kx) v (Hx & Kx))), where <<sx,>>
unexamined (by time t) emerald being grue. With respect to the
<<Rx,)) and aHx)) stand for ax is a stone," ax is round," and ax is
series of examined green emeralds, if they had not been examined
hard." The predicate <<JG:)) means ax is such that the hypothesis
by time t, they would still have been green. However, with respect
'All stones are hard' conflicts with the hypothesis 'All emeralds are
to the series of examined grue emeralds, if they had not been
green.'" Or, in other words, <<Kx)) stands for <'X is such that some
examined by time t, they would not have been grue because they
emeralds are either green but not hard or hard but not green."
would have been green and unexamined by time t.
Zabludowski argues that this generalization is both incompatible
The grue debate is filled with claims and counterclaims about
with and conflicts with "All emeralds are green," and its predicates
projectible hypotheses, projectible predicates, and theories of
are at least as well entrenched as "emerald" and "green"-that is,
projectibility. In the sixth selection, "Concepts of Projectibility and
t1:e ante~edent predicate "stone" and the disjunctive consequent.
the Problems of Induction," John Earman attempts to raise the
Smee this consequent predicate is coextensive with either "round"
level of discussion about projectible hypotheses and predicates. His
or "hard" and Goodman maintains that entrenchment is really
essay, which originally appeared in Nous in 1985, presents eleven
about the extension of a predicate, it is also among the best
definitions for different senses of projectibility along with necessary
Introduction 9
8 Introduction
the field of artificial intelligence. Peter Gardcnfors maintains that AI
and/or sufficient conditions for each sense. Earman takes a
practitioners will have to find a way to identify projcctible
quantitative, Bayesian approach to the projectibility of universal
generalizations in connection with instance or particular induction predicates in order to pr~duce c?mputer models of how we ma~~
inductive inferences. In Induct10n, Conceptual Spaces, and AI,
and general or hypothesis induction. He distinguishes between
which originally appeared in Philosophy of Science in 1990,
hypotheses (or predicates) being strongly projectible or weakly
Gardcnfors takes projectible predicates to be predicates that
projectible, and he also distinguishes between them being
designate natural properties, and he introduces his theory of
projectible in the future-moving sense or the past-reaching sense.
conceptual spaces as a nonlinguistic and nonlogical way to represent
With instance induction for the hypothesis "All emeralds are
green," we are concerned with the probability that emerald n + 1 information about the properties of individual objects. A
will be green (or emeralds n + m will be green) given that n conceptual space is a set of quality dimensions such as color,
length, weight, temperature, and time. Each quality dimension has
emeralds have been green and our background knowledge. If we are
concerned with the probability that emerald n + 1 will be green, a topological or metrical structure. With respect to color, there are
we are concerned with our hypothesis being weakly projectible. If three dimensions: hue, brightness, and saturation. The hue
we are concerned with the probability that emeralds n + m will be dimension has the topology of a circle (the color circle), while the
brightness dimension (white to black) and the saturation (color
green, we are concerned with our hypothesis being strongly
projectible. Earman explains the distinction between future-moving intensity) each have a linear structure, with the saturation
dimension isomorphic to an interval on the real number line. The
and past-reaching in terms of two ways of taking the limit of the
hue dimension is circular instead of linear because Gardenfors's
probability as the number n of instances approaches infinity. For
quality dimensions are psychological dimensions as opposed to
example, if "All emeralds are green" is weakly projectible in the
future-moving sense, then the probability that emerald n + 1 is scientific or theoretical ones. The hue dimension is based on
green, given that n emeralds have been green and our background psychophysics and stimulus magnitudes instead of phy~ics .and
knowledge, is equal to 1 as n approaches infinity. The next instance wavelengths. Gardenfors represents a property as a region 111 a
n + 1 is in the direction in which this limit is being taken. If this conceptual space. If the region represents a natural property, then it
must be convex in the following sense: if a pair of points are in the
hypothesis is weakly projectible in the past-reaching sense, then the
probability that emerald n + 1 is green, given that n - j emeralds region, then all points between them are also in the region. On this
have been green and our background knowledge, is equal to 1 as j analysis, the predicate "green" differs from the predicate "gruc"
approaches infinity. Here the next instance n + 1 is not in the because the former predicate designates a property that we can
represent with a convex region, while the latter predicate designates
direction in which the limit is being taken. With general induction
a property that we cannot represent by a convex region because it
for the hypothesis "All emeralds are green," we are concerned with
involves both the color dimensions and the time dimension.
the probability of our hypothesis given that n emeralds have been
Gardenfors notes that his analysis makes a property natural relative
green and our background knowledge. If we are concerned with the
to a conceptual space, and so it appears that "grue" could designate
probability of our hypothesis per se, we are concerned with it being
a natural property and "green" could designate a nonnatural
strongly projectible, and it can be strongly projectible in either the
property relative to some nonstandard conceptual space. He argues
future-moving or past-reaching sense depending on how we take
that relativism is not a problem with respect to innate quality
the limit as the number of positive instances approaches infinity. If
we are concerned with whether its probability after n + 1 green dimensions, such as the color dimensions. If some form of
emeralds is greater than after n green emeralds, then we are psychological relativism can occur here, it will occur only with
concerned with our hypothesis being weakly projectiblc. In a new standard quality dimensions that depend on learning and
postscript to his essay, Earman discusses some alleged and real acculturation.
The remaining selections were written especially for this
morals of Goodman's gruc problem and examines some of the early
volume. Some are by philosophers who have previously written
correspondence between Goodman, Carnap, and Hempel on the
about the new riddle, while others are by philosophers who work in
topic.
the area of inductive logic and confirmation theory-but who,
The seventh selection presents the new riddle as a problem 111
10 Introductwn Introductwn 11
until now, haven't really entered the grue debate. John L. Pollock is relationship between two variables P and C based on four data
one of the former. He has written about projectibility and points. He introduces two hypotheses that fit the dat~ points but
principles of induction since 1972, and he reports his current views that make different predictions for other values of vanable P. One
in the eighth selection, "The Projectibility Constraint." Pollock hypothesis is C = 2 x P and the other hypothesis is C = 2 x P +
emphasizes two points. First, he stresses that most concepts arc not (P - 1) x (P - 3) x (P - 4) x (P-:- 8) ..H arman believes that a
projectible. He claims this is implied by the closure conditions for scientist would take the first hypothesis senously but not the second
projectibility. These conditions tell us that if some concepts are one. Moreover, he believes that a scientist would decide this on the
projectible with regard to each other, then so are certain related basis of relative simplicity: i.e., the first hypothesis is simpler than
concepts. It turns out that projectibility is not closed under most the second one. This kind of relative simplicity is computational as
logical operators. For example, it is not closed under disjunction or opposed to syntactic or semantic. If scientists are interested in
negation: i.e., if the concepts A and B are projectible with regard to determining the value of C when the value of P is 6, it is easier to
concept C, then it does not follow that (A v B) is projectible with use the first hypothesis than the second hypothesis to arrive at the
regard to concept C; and if the concept A is projectible with regard answer. The calculations are less involved. This kind of relative
to the concept B, then it does not follow that -A is projectible simplicity also depends on the interests of scientists. If we want to
with regard to concept B. Second, Pollock stresses that projectibility determine the value of R when P is 6, where R is equal to the
is a problem for all forms of probabilistic and inductive reasoning, value of C divided by the value of C on the second hypothesis, it is
not just induction by simple enumeration. We also need to restrict easier to calculate the answer with the second hypothesis. Indeed,
statistical induction, direct inference, statistical inference, and the we can do it in a flash: R = 1. However, if scientists are not
statistical syllogism to projectible concepts. For example, logic interested in this result, then the second hypothesis does not count
textbooks invariably formulate the statistical syllogism as "Most A as simpler than the first hypothesis. While the computational view
are B, this is an A, therefore it is a B. ,, If we do not restrict A and makes relative simplicity into a practical matter by connecting it
B so that A is projectible with regard to B, then we can let A be a with how easily scientists can get answers to their questions,
disjunctive predicate like "things that are either birds or giant sea Harman believes it still promotes relative simplicity as an indicator
tortoises." Our statistical syllogism would then be: "Most things of verisimilitude. If one hypothesis is simpler than another, this is a
that are either birds or giant sea tortoises are things that can fly, practical reason to believe the hypothesis and (with no difference
this creature is a giant sea tortoise, therefore this creature is between believing something and believing that it is true) this is
something that can fly." The problem with this reasoning is not a automatically a reason to believe that the hypothesis is true.
false premise. This odd bird/tortoise generalization is actually true There seems to be a straightforward difference between the two
because there are so many birds, so few giant sea tortoises, and predicates "grue" and "green": viz., the former is a disjunctive
most birds can fly. Rather, the problem is the projectibility of predicate while the latter is not. When we explain what "grue"
"things that are either a bird or a giant sea tortoise" with regard to means, the explanation takes the form of a disjunction in which
"things that can fly." The first concept is not projectible with each disjunct is a conjunction of a color term ("green," "blue")
regard to the second. and a temporal term ("before t/, "after t',). Goodman believes this
While there are about twenty different kinds of solutions to the difference is only a relative difference. We are starting with "green"
new riddle in the literature, the simplicity solution is among the and "blue" as basic or primitive terms. If we start with "grue" and
most popular. Even Goodman has wondered if his entrenchment "bleen" as basic or primitive terms, then our explanation of
criterion isn't really just a simplicity criterion. The generic form of "green" will take the form of a disjunction. Something will be
this solution is that we should prefer "All emeralds are green" to green if it is examined before t and determined to be grue, or it is
"All emeralds are grue" because the green hypothesis is simpler not examined before t and it is bleen, where something is bleen if it
than the grue one. In the ninth selection, "Simplicity as a is examined before t and determined to be blue, or it is not
Pragmatic Criterion for Deciding What Hypotheses to Take examined before t and it is green. David Sanford claims there is
Seriously," Gilbert Harman develops a simplicity solution to a more to the disjunctiveness issue than these syntactic similarities.
quantitative version of the new riddle. Harman considers the He develops an objective, semantic analysis of disjunctive predicates
12 Introduction Introduction 13
in the tenth selection, "A Grue Thought in a Eleen Shade: 'Grue' instances, and some undetermined instances, Goodman says it is
as a Disjunctive Predicate." Sanford distinguishes between actually projected. When a predicate is used in doing this-actually
exclusively disjunctive predicates and inclusively disjunctive projecting a hypothesis-it earns (as opposed to inherits)
predicates. He also distinguishes two kinds of exclusively entrenchment. Goodman also refers to this as actually projecting
disjunctive predicates, disjoint predicates and disconnected the predicate. Since the predicate "green" has been used in actual
predicates. If a predicate ccp)) is equivalent to a disjunction of projections longer and more often than the artificial predicate
incompatible, nonempty predicates and and everything "grue," it has earned much more entrenchment than "grue" and
((G)) ((HJ)
on the boundary of ((G)) or ((H)) is also on the boundary of ccp, )) makes the green hypothesis better entrenched than the grue
then ccpJ) is a disconnected predicate. Sanford notes that "grue" is a hypothesis. Ian Hacking, who has published extensively on the
disconnected predicate. He also notes that this does not provide an topic of statistical inference as well as the history of statistics, agrees
adequate solution to the new riddle. We can easily introduce with Goodman about the importance of entrenchment. In the
grue-like predicates that are neither disjoint nor disconnected, such eleventh selection, "Entrenchment," Hacking introduces a
as the predicate "supergrue." Something is supergrue if it is two-dimensional view of using a predicate. If we view using a
examined before t and determined to be green, or it is not predicate longitudinally, then we are concerned with its record of
examined before t and it is blue or bluish-green. A predicate like past uses. Goodman takes this view with his notion of
"supergrue" shows that we can have a new riddle without an entrenchment. If we view using a predicate latitudinally, then we
exclusively disjunctive predicate-that is, we can have a new riddle are concerned with how easily we can use the predicate now.
with an inclusively disjunctive predicate. Sanford analyzes Hacking maintains that we cannot seriously use the predicate
inclusively disjunctive predicates in terms of independent "grue" at the present time. He claims that if we seriously use a
predicates. He introduces three types of independence: logical, predicate, then we must be willing to project that predicate. That is,
minimal, and genuine. He maintains that we can see a relevant, we must be willing to use the predicate not only in classifying but
objective difference between "grue" and "green'' in connection also in making predictions and generalizations. According to
with genuine independence. A pair of predicates and are Hacking, it is simply an ethnographic fact that we cannot use
cccJ) ccHJ)
genuinely independent if and only if they are logically independent, "grue" in these ways-no matter how much we mention the
minimally independent, and each distinct boundary of one predicate and no matter how many mental gyrations we go
predicate intersects each distinct boundary of the other predicate at through. The problem is not, he argues, a logical, cognitive,
one, and only one, distinct point of intersection. Sanford argues translational, or "transcendental" one. Hacking also maintains that
that if we express "green" and "grue" in a certain logical the new riddle involves a false dichotomy: viz., that we can either
form-ccA and C, or Band not CJJ_then an objective difference use a predicate to classify or we can use it to generalize, and so we
appears. The predicate "green" is equivalent to "green and first can first classify things as members of a kind and then later go on
examined before t) or green and not first examined before t. )) The to generalize about them. Hacking emphatically denies that there is
predicate "grue" is equivalent to "grue and first examined before t, sharp distinction between classifying and generalizing. He believes
or grue and not first examined before t. )) Here the predicates that we have not realized this because we tend to view concept
"green" and "first examined before t1) are genuinely independent, acquisition in terms of grouping or collecting, because we are aware
as are the predicates "green" and "not first examined before t. )) of an independent profession (natural history) devoted to
However, the predicates "grue" and "not first examined before t1) taxonomy, and because we make an issue of how a word acquires an
are not genuinely independent. extension and whether it acquires an extension before an intension.
Goodman solves the new riddle by comparing hypotheses for Elliott Sober, who is noted for his work in philosophy of
entrenchment. This involves determining whether one hypothesis biology, takes a probabilistic approach to the new riddle in the
has a much better entrenched predicate than the other, where twelfth selection, "No Model, No Inference: A Bayesian Primer on
entrenchment is connected with how often a predicate has been the Grue Problem." Sober views the new riddle as a matter of
used in actually projecting hypotheses. When a hypothesis is comparing the probabilities of the relevant hypotheses given our
adopted because it has some positive instances, no negative observations about the color of emeralds up to time t. This involves
