## 1. Life


Henry Nelson Goodman was born on August 7, 1906, in Somerville,
Massachusetts (USA), to Sarah Elizabeth (Woodbury) Goodman and Henry
L. Goodman. In the 1920s he enrolled at Harvard University and
studied under
 Clarence Irving Lewis (who later became his Ph.D. supervisor),
 Alfred North Whitehead, 
Harry Scheffer, W.E. Hooking, and Ralph Barton Perry. Goodman
graduated from Harvard in 1928. It took him, however, 12 more years
until he finished his Ph.D. in 1941 with *A Study of Qualities*
(SQ). There are several possible reasons for the lateness of his
Ph.D. Maybe the most important was that Goodman was Jewish, and
therefore not eligible for a graduate fellowship at Harvard (Schwartz
1999; Elgin 2000a; Scholz 2005). He had to work outside the university
to finance his studies. From 1928 until 1940, Goodman worked as the
director of the *Walker-Goodman Art Gallery* at Copley Square,
Boston. This interest and activity in the artworld is more frequently
cited as a reason for the lateness of his Ph.D. During his graduate
studies Goodman was also a regular participant in W.V. Quine's
seminars on the philosophy of the
 Vienna Circle 
(in particular of Rudolf Carnap). Goodman also worked closely with
Henry Leonard, who wrote his Ph.D. at the same time under Alfred North
Whitehead's supervision. After military service, Goodman taught
briefly as "instructor in philosophy" at Tufts College,
and was then hired as associate professor (1946-51) and later as
full professor (1951-64) at the University of Pennsylvania. He
served briefly as Harry Austryn Wolfson Professor of Philosophy at
Brandeis University (1964-67), finally returning to Harvard in
1968, where he taught philosophy until 1977. At Harvard, he
founded *Project-Zero*, a center to study and improve education
in the arts. Besides being an art gallery director as a graduate
student, and private art collector throughout his life, Goodman was
also involved in the production of three multimedia-performance
events, *Hockey Seen: A Nightmare in Three Periods and
Sudden Death* (1972), *Rabbit, Run* (1973),
and *Variations: An Illustrated Lecture Concert* (1985) (Carter
2000, 2009).


Goodman was more interested in solving philosophical problems than
in his celebrity as a philosopher. He authorized only two interviews
(Goodman 1980, 2005), did not write an autobiography, and rejected the
invitation to be honored with a volume in the prestigious *Schilpp
Library of Living Philosophers* (Elgin 2000a, 2). Sparse bits of
information about his personal life can only be gathered from the
autobiographies of his contemporaries and their published
correspondences (e.g., Quine 1985; Creath 1990) or his obituaries
(e.g., Carter 2000; Elgin 1999 (Other Internet Resources), 2000a,
2000b; Elgin et al. 1999; Mitchell 1999; Scheffler 2001; Scholz 2005;
Schwartz 1999). Goodman died on November 25, 1998, in Needham,
Massachusetts, at the age of 92, after a stroke.


## 2. Anti-Absolutism


Nelson Goodman's philosophy synthesizes German/Austrian Logical
Empiricism, as developed and practiced by philosophers like Rudolf
Carnap and Carl Hempel, with American Pragmatism of the kind practiced
and advocated by C.I. Lewis. Goodman, however, departs from both
traditions considerably. As we will see, he departs from Lewis's
pragmatism in dismissing the idea of an indubitable given in
experience. He departs from logical empiricism in giving up a
principled analytic/synthetic distinction.


### 2.1 The Myth of the Given in Experience


Goodman's philosophy--especially his epistemology--is
usually considered to be in opposition to the philosophy of the
Logical Positivists, and of Rudolf Carnap in particular. But this
characterization overlooks an important continuity between the
philosophy of the Logical Positivists and Goodman's work. The received
view, that Goodman's main work, *The Structure of Appearance*
was intended as an anti-foundationalist reconception of
Carnap's *Der logische Aufbau der Welt* (cf. Elgin 2001;
Hellman 1977) is particularly misleading here.


In fact, Goodman was quite aware that Carnap's work was itself
anti-foundationalist in the same respect as his. Already in his
dissertation thesis *A Study of Qualities* (which was later
developed into *The Structure of Appearance*), Goodman
writes:



> 
> [...] Carnap has made it clear that what we take as ground
> elements [for a constitutional system] is a matter of choice. They are
> not dignified as the atomic units from which others must be built;
> they simply constitute one possible starting point. [...] In
> choosing erlebs, Carnap is plainly seeking to approximate as closely
> as possible what he regards the original epistemological state
> [...] Yet whether it does so or not is no test of the
> system. [...] Hence [...] argument concerning whether the
> elements selected are really primitive in knowledge is extraneous to
> the major purpose of the system. (SQ, 96-98)
> 
> 
> 


The quote makes it obvious that Goodman himself did not consider
his constructionalist approach in *A Study of Qualities* as an
epistemological alternative to Carnap's. Insofar as criticism of a
foundationalist epistemology does play a role in *The Structure of
Appearance* or *A Study of Qualities*, this criticism was
rather directed at the philosophy of C.I. Lewis, who was Goodman's
teacher at Harvard. Lewis indeed held the view that empiricism must
presuppose the incorrigibility and indubitability of what is given in
experience. According to Lewis, I might need to revise, for example,
that I saw a plane crossing the sky when I learn that what I mistook
for a plane was Superman. However, nothing can make me revise that
there was a blue and a red spot in the center of my visual field that
then led to the (false) belief that there was a plane.


*A Study of Qualities*, on the other hand, begins with the
argument that even the simplest judgments of this sort--as the
one about a blue and a red spot in the center of my visual
field--might be revised in the light of new evidence. My judgment
that I had a blue spot in the middle of my visual field a few seconds
ago when I looked at a ripe apple under normal conditions might be
revised when I now judge that I have a red spot in my visual field,
looking at the same object under the same conditions and know that it
could not have changed its color. However, if such revisions can be
made in retrospect, nothing of the "given" is indubitable
or incorrigible. Judgments about qualia, in this sense, are decrees;
which judgments are accepted is a matter of the overall coherence of
my system of beliefs and my other qualia judgments. 



> 
> The literal unverifiabilty of such quale-recognition is,
> nevertheless, in the last analysis beyond question. If I say the green
> presented by that grass now is the same as the green presented by it
> at a certain past moment, I cannot truly verify that statement because
> I cannot revive that past moment. The statement therefore constitutes
> an arbitrary and supreme decree. But a decree, simply because it is
> arbitrary, is not therefore necessarily haphazard. My
> quale-identifications are influenced; I do not feel equally inclined
> to identify the color presented by the grass now with the color
> presented by a cherry a moment ago, though such a decree if made would
> be equally supreme and unchallengeable on strict grounds. We are all
> much in the same position of absolute but sane monarchs; our
> pronouncements are law, but we use our heads in making them. (SQ, 17;
> cmp. SA (2nd ed.), 134)
> 
> 
> 


Also in this respect Goodman is following Carnap and the logical
empiricists. C.I. Lewis emphasizes this in his "Logical
Positivism and Pragmatism" (Lewis 1941). There he explains that
the main difference between the empiricism of the pragmatists and the
empiricism of the logical positivists (especially the Carnap
of *Philosophy and Logical Syntax* (1935)) is that the latter
were ready to analyze empirical knowledge fully in the so-called
"formal mode". Accordingly, they analyze empirical
knowledge as more or less coherent systems of accepted sentences, some
of which are "protocols", some are sentences of
mathematics and logic, some are generalizations, etc. In particular,
the formal mode would not distinguish between statements such as
"This object looks red" and "This object is
red".


For Lewis, this sort of empiricism is not worthy of the name. After
all, the experiential element does not seem to show up at all in this
kind of formal analysis. Lewis claims instead that a proper empiricism
must treat sentences of the form "This looks red." as
special, indubitable statements. We might err when classifying things
as being red, but we cannot err when it comes to recognizing things as
looking red. This is "the given" in experience, the
phenomenal states we find ourselves in when making
experiences. Without such an indubitable element, Lewis fears that our
epistemology would necessarily collapse into a coherence theory of
truth (Lewis 1952). Goodman, on the other hand, is ready to bite that
bullet when throwing away the indubitable given. Lewis, the major
advocate of pragmatism, comments on this move by Goodman that his
"proposal is, I fear, a little more pragmatic than I dare to
be" (Lewis 1952, 118).


Indeed, Goodman's early and later philosophy is
anti-foundationalist. This is truly a characteristic of his work on
induction, metaphysics, logic and even the languages of art. It
should, however, not be interpreted as a counter program to logical
positivism. What Goodman did--in all these areas--is better
understood as a continuation and enlargement of Carnap's program. This
is obvious if we consider Goodman's relativism and irrealism. It is
also apparent when we think about his pluralism in logic and his
insistence that there are more cognitively valuable representation
systems than just the sciences, namely the languages of
art.

 His anti-foundationalism therefore is more than just a
restatement that there is no "bedrock" for
knowledge--as was argued by Karl Popper and Otto Neurath,
but also that there are no fundamental ontological objects, that there
are no fundamental logical principles, and that there are no
privileged representation systems. All of these echo Rudolf Carnap's
famous Principles of Tolerance (Carnap 1934): tolerance with regards
to ontology, to logical principles, and to representation systems in
general. 


### 2.2 The Analytic/Synthetic Distinction and Likeness of Meaning


Goodman did, however, considerably depart from the logical
positivists in denying the comprehensibility of the analytic/synthetic
distinction. This rejection and Goodman's gradual account of synonymy
(or, rather, likeness of meaning) developed out of an exchange of
letters between Morton White, Quine, and Goodman, which is also the
historical background of Quine's famous "Two Dogmas of
Empiricism" (Quine 1951a).


On 25 May 1947, Morton White wrote a letter to Quine asking for
advice on a paper in which he tried to deal with a solution to C.H.
Langford's paradox of analysis proposed by Alonzo Church. White was
especially unhappy with Church's invocation of abstract objects in
order to explicate the notion of synonymy. White sent his
discontentment with the proposed solution to Quine (White's original
paper appeared in print in 1948 under the title "On the
Church-Frege Solution of the Paradox of Analysis") and
then sent Quine's answer to Goodman. In 1947 the three discussed the
matter by letter, until White was eventually chosen to write a survey
of their discussion, which appeared in 1950 under the title "The
Analytic and the Synthetic: An Untenable Dualism". Quine
presented his view on the matter in an address to the American
Philosophical Association, which was published in 1951 as "Two
Dogmas of Empiricism" (Quine 1951a).


At that time the postulation of new abstract objects, such as
Fregean senses or other intensional objects, in order to explicate a
certain notion of synonymy seemed an unacceptable move for someone
with nominalist leanings such as Quine and a purist such as White. For
Quine, an explication of "synonymy" or
"analyticity" and the like should rather be given in
behavioristic terms. The explication should tell us in what way
"analyticity" and "synonymy" make a difference
in speaker behavior. To learn that the difference lies in postulated
abstract objects did not seem to explicate the notions in any
promising way.


Goodman's original discontentment with the whole situation was more
serious. In a letter to White and Quine he claimed that not only did
he find the explications of "synonymy" and
"analyticity" so far provided to be problematic, but he
did not even understand what these terms were supposed to mean
pre-theoretically:



> 
> When I say I don't understand the meaning of "analytic"
> I mean that very literally. I mean that I don't even know how to apply
> the terms. I do not accept the analogy with the problem of defining,
> say, confirmation. I don't understand what confirmation is, or let us
> say projectibility, in the sense that I can't frame any adequate
> definition; but give me any predicate and (usually) I can tell you
> whether it is projectible or not. I understand the term in
> extension. But "analytic" I don't even understand this
> far; give me a sentence and I can't tell you whether it is analytic
> because I haven't even implicit criteria.... I can't look for a
> definition when I don't know what it is I am defining. (Goodman in a
> letter to Quine and White, 2 July 1947, in White 1999, 347)
> 


Goodman's remark is instructive, since it undermines a move that
Grice and Strawson would later make against Quine's argumentation in
"Two Dogmas of Empiricism". In their "In Defense of
a Dogma" (Grice and Strawson 1956) they argue that Quine's
skepticism about the analytic-synthetic distinction as such is
undermotivated in light of our pre-theoretic grasp of the
distinction. Goodman's claim is that there in fact is no such
pre-theoretic grasp of the distinction.


The official result of the exchange between White, Goodman, and
Quine was that any sharp analytic-synthetic distinction is
untenable and should just be abandoned:



> 
> I think that the problem is clear, and that all considerations
> point to the need for dropping the myth of a sharp distinction between
> essential and accidental predication (to use the language of the older
> Aristotelians) as well as its contemporary formulation--the sharp
> distinction between analytic and synthetic. (White 1950, 330)
> 


Goodman's view on the matter had already appeared in print in 1949
under the title "On Likeness of Meaning". In this paper
Goodman proposes a purely extensional analysis of meaning, the upshot
of which is that no two different expressions in a language are
synonymous. He discusses several objections to theories of meaning
that rely on intensional entities (such as, for example, Fregean
senses) to explicate the notion of synonymy in non-circular ways, such
that the question of whether two terms are "synonymous" is
comprehensible as well as scrutable. Goodman eventually rejects
intensional approaches and opts for an extensional theory for sameness
of meaning. According to such an extensional theory, two expressions
have the same meaning if and only if they have the same
extension. This criterion is certainly intelligible, but also
scrutable; we can



> decide by induction, conjecture, or other means
> that two predicates have the same extension without knowing exactly
> all the things they apply to. (PP, 225)


But an extensional theory is, of course, not thereby free of
problems. Consider, for example, the expression "unicorn"
and "centaur", which have the same extension (namely the
null-extension) but differ in meaning. Hence, whereas sameness of
extension is a necessary condition for sameness of meaning, sameness
of extension does not seem to be sufficient for sameness of meaning.
Goodman proposes an extensional fix to this problem that gives
necessary and sufficient conditions for sameness of meaning. He
observes that although "unicorn" and "centaur"
have the same extension, simply because of the trivial fact that they
denote nothing, "centaur-picture" and
"unicorn-picture" do have different extensions. Clearly,
not all centaur-pictures are unicorn-pictures and *vice
versa*. Thus the flight to compounds makes an extensional
criterion possible:



> [I]f we call the extension of a predicate by
> itself its primary extension, and the extension of its compounds as
> secondary extension, the thesis is as follows: Two terms have the same
> meaning iff they have the same primary and secondary extensions. (PP,
> 227)


 The primary extensions of "unicorn"
 and "centaur" are the same (the null-extension), but
 their secondary extensions do differ: the compounds
 "unicorn-picture" and "centaur-picture"
 differ in extension.


If we allow all kinds of compounds equally, we arrive immediately
at the result that by our new criterion no two different expressions
have the same meaning. Consider the expressions "bachelor"
and "unmarried man": "is a bachelor but not an
unmarried man" is a bachelor description that is not an
unmarried-man description. Hence, by Goodman's criterion, the
secondary extensions of "bachelor" and "unmarried
man" differ because the primary extensions of at least one of
their compounds do. Since the same trick can be pulled with any two
expressions, Goodman is left with the result that no two different
expressions are synonymous, but he is ready to bite this bullet.
*P*-descriptions that are not *Q*-descriptions are easy to construct for
any *P* and *Q* (provided these are different terms) and
these constructions might well be relatively uninteresting. If only
such uninteresting constructs are available to make a difference in
secondary extension, *P* and *Q*, despite being not strictly
synonymous, might be more synonymous than a pair of predicates for
which we are able to find interesting compounds (as in the case of
"centaur" and "unicorn"). This turns sameness
of meaning of different terms into likeness of meaning, and synonymy
and analyticity into a matter of degree.



## 3. Nominalism and Mereology


### 3.1 Nominalisms


"Nominalism" can refer to a variety of different,
albeit related, positions. In most cases, it either refers to the
rejection of universals or of abstract objects. What nominalism means
for Goodman undergoes two radical changes. In his Ph.D. thesis, *A
Study of Qualities*, he uses the label "nominalist" to
describe constructional systems whose constructional basis does not
include abstracta, such as Carnap's system in the *Aufbau*
(Carnap 1928). Whether classes are used in the construction, as
Carnap's *Aufbau* indeed does, is irrelevant for the
characterization of these systems as
"nominalist". Nominalism is not an issue of discussion
here; "nominalist" merely occurs as a classification (for
more details on constructional systems see
 section 4
below.)


Goodman first endorses a nominalist position in his famous joint article
with W.V. Quine, "Steps Toward a Constructive Nominalism"
(1947). Goodman and Quine set the agenda in the very first sentence
of the article: "We do not believe in abstract
objects". And they conclude the first paragraph: "Any
system that countenances abstract entities we deem unsatisfactory as
a final philosophy" (Goodman and Quine 1947, 105).


Goodman and Quine first discuss nominalistically acceptable
reductions of platonist statements. "Platonist" here
refers to the use of terms for classes, numbers, properties, and
relations--in short, anything that is not a concrete particular. 
The first examples are straightforward and their resolutions are
well-known today. "Class \(A\) is included in
class \(B\)" can be rendered as "Everything that is
an \(A\) is a \(B\)" (where "\(A\)"
and "\(B\)" now stand for the appropriate predicates,
rather than for classes). "Class \(C\) has two
members", or "The number of \(C\)s is 2", is
rendered as "There are two \(C\)s", and spelt out
formally (based on Russell's theory of definite 
 descriptions--see
 the discussion in the entry on Russell)
 as:



\[

\exists x \exists y(x \ne y \land \forall z(Cz \equiv (z = x \lor z = y)))

\]

No recourse to classes or other abstract entities (e.g., numbers)
is necessary. However, this strategy does not deliver a general recipe
to account for statements that are typically expressed in a
straightforward set-theoretic way. For instance, it seems to Goodman
and Quine that there is no general recipe for expressing statements
like "There are more cats than dogs" in a nominalistically
acceptable fashion. If the total number of dogs were known, then, in
principle, the quantifier strategy above could be used--albeit
that, with hundreds of millions of dogs alive today, it would
certainly not be practical. Quine and Goodman suggest a translation
into the language of mereology with an additional auxiliary predicate
"bigger than"; while this provides a surprisingly
versatile solution for many cases, it is still not completely general
(Goodman and Quine 1947, 110-11). Further, a general
definition of the *ancestral* of a relation 
(as first given by Gottlob Frege 1879, SS26) seemed to Quine and
Goodman at the time to be out of reach for the nominalist. Leon
Henkin (1962, 188-89) finds an elegant solution, quantifying
over lists of successive inscriptions. Goodman later (PP, 153)
suggests that his technique to formulate the ancestral of matching
(SA, SSSSIX-X) could also solve the problem. We note
that if second-order logic can be made palatable to the
nominalist--perhaps by adopting a plural interpretation of
second-order logic 
 (Boolos 1984, 1985), or a proof-theoretic semantics, 
or in any other way--Frege's original definition (which is not
formulated in set theory, but in his version of second-order logic)
can be employed (Rossberg and Cohnitz 2009).


Even though these two particularly pressing gaps appear to be
capable of being closed, a general recipe for recasting platonist
statements appears out of reach, in particular, when we consider
statements of pure mathematics itself. Without such a nominalist
recasting, Goodman and Quine hold, platonist mathematical
statements cannot be deemed intelligible from a strictly nominalist
perspective. The question becomes, according to Goodman and Quine,



> 
> 
> how, if we regard the sentences of mathematics merely as strings of
> marks without meaning, we can account for the fact that mathematicians
> can proceed with such remarkable agreement as to methods and
> results. Our answer is that such intelligibility as mathematics
> possesses derives from the syntactical or metamathematical rules
> governing those marks. (Goodman and Quine 1947, 111)
> 
> 




Goodman and Quine construct a theory of syntax for the
set-theoretic language and a proof theory based on the Calculus of
 Individuals (see
 section 3.2 below) 
 supplemented with a token-concatenation theory. The tokens in question
are concrete, particular inscriptions of the logical symbols,
variable-letters, parentheses, and the "\(\in\)" (for
set-membership) that are use to formulate the language of set
theory. Primitive predicates are introduced to categorize the
different primitive symbols: all concrete, particular
"\(\in\)"-inscriptions, for instance, fall under the
predicate "Ep". Concrete complex formulae, e.g., 
"\(x \in y\)", are concatenations of concrete primitive
symbols--in our case the concatenation of
"\(x\)" and "\(\in\)" and
"\(y\)". Bit by bit, Goodman and Quine define their
way up to which concrete inscriptions count as correctly formed
sentences of the language of set theory, and finally which concrete
inscriptions count as proofs and theorems. Goodman and Quine argue
that in this way the nominalist can explain the "remarkable
agreement" of mathematicians mentioned above.


Since Quine and Goodman not only impose nominalistic strictures,
but also finitism in their joint article (Quine and Goodman 1947,
SS2), the syntactic and proof-theoretic notions defined still fall
short of the usual platonist counterparts. Even if any given sentence
or proof is finite in length, the platonist would hold that there are
sentences and proofs of any finite length, and thus sentences and
proofs that are too long to have a concrete inscription in a given
finite universe. Moreover, there are infinitely many (and indeed
uncountably many) truths of mathematics, but--in particular, in a
finite universe--there will only ever be finitely many
inscriptions of theorems. Even if the universe is in fact infinite,
perhaps a theory of syntax and proof should not make itself hostage to
this circumstance.


Platonists and nominalists will likely disagree whether Goodman and
Quine successfully argue their case in their joint paper. Goodman and
Quine will be able to account for any actual mathematical proof and
any theorem actually proven, since there are at any stage only
finitely many of them, each of which is small enough to fit in our
universe comfortably. Thus, arguably, they reach their goal of
explaining the agreement in mathematical practice without presupposing
mathematical platonism. Due to its finitistic nature, however, the
account radically falls short of giving explications that are
extensionally equivalent to the platonists' conceptions (see Rossberg
and Cohnitz 2009 for discussion and a landscape of possible
solutions). Goodman later (1956) explains that nominalism is not
incompatible with the rejection of finitism; it is



>  at most incongruous [...]. The nominalist is
> unlikely to be a non-finitist only in much the way a bricklayer is
> unlikely to be a ballet dancer. (PP, 166; on the question of finitism
> see also MM, 53; Field 1980; Hellman 2001; Mancosu
> 2005)
> 
> 


Given the ardent pronouncements in the 1947 article with Quine, the
common misunderstanding that Goodman's mature nominalism encompasses,
or is motivated by, the rejection of abstract objects is
understandable. Nonetheless, it is incorrect. Goodman does not reject
all abstract objects: in *The Structure of Appearance*, he
embraces qualia as abstract objects (see
 section 4 below), 
some of which (in fact all but moments) are universals (SA,
SSVII.8). Goodman's mature nominalism, from *The Structure of
Appearance* onwards, is a rejection of the use of *sets*
(and objects constructed from them) in constructional systems, and no
blanket rejection of all universals or abstract particulars. To be
sure, Goodman also refuses to acknowledge properties and other
non-extensional objects, but the reason for his rejection of such entities is
independent, and in fact more fundamental, than his nominalism: it is
his strict requirement of extensionality (WW, 95n3; see also
 section 6 below). 
Goodman does occasionally include extensionalism in his nominalism
(see LA, xiii, 74; under the entry "nominalism" the index
of LA references some passage which discusses properties ; see also
MM, 51; WW, 10n14). Strictly speaking, however, nominalism for Goodman
is the refusal to use class terms in a constructional system--no
more, and no less.


Goodman presents two positive considerations for the rejection of a
set-theoretic language (not counting the remarks in Goodman and Quine
1947, 105). Methodologically, nominalistic constructions have the
advantage that they do not use any resources that the platonist could
not accept (Goodman 1958; PP, 171). The advantage of a nominalistic
construction is thus one of parsimony:



> 
> As originally presented in *A Study of Qualities* [...]
> the system was not nominalistic. I feel that the recasting to meet
> nominalistic demands has resulted not only in a sparser ontology but
> also in a considerable gain in simplicity and clarity. Moreover,
> anyone who dislikes the change may be assured that the process of
> replatonizing the system--unlike the converse process--is
> obvious and automatic; and this in itself is an advantage of a
> nominalistic formulation. (SA, Original Introduction, page L of the
> 3rd. ed.; regarding the simplicity remark see SA, SSIII.7)
> 
> 
> 


All resources employed by the nominalist are (or should be)
acceptable to the platonist, while the converse may not be the case
(see also Goodman 1956, 31 (PP, 171); MM, 50).


By the time he writes *The Structure of Appearance*, Goodman
has come around to a different criterion for whether or not a system
obeys nominalistic structures: the predicates present in the whole
system (SA, SSII.3). This is as opposed to merely considering the
basis of the system in answer to this question as he does in *A
Study of Qualities* (as mentioned above). In Goodman 1958 (see
also SA, SSIII.7), he suggests a different, perhaps more precise,
way to characterize nominalistic systems in terms of the
system's *generating relation*:



> 
> System *S* is *nominalistic* iff *S* does not
> generate more than one entity from exactly the same *atoms*
> of *S*.
> 
> 
> 


Goodman describes the criterion as demanding that "sameness
of content" entails identity. Systems that have only
mereological means of "generating" composite objects (see
section
 3.2 Mereology below) 
count as nominalistic according to this criterion. Parthood is
transitive, so from atoms *a* and *b* only one further
object can be "generated", the mereological sum
of *a* and *b*. A set-forming operation, however, will
distinguish, for instance, between {*a*, *b*} (the set
of *a* and *b*) and {{*a*, *b*}} (the set
containing the set of *a* and *b*) and {{*a*},
{*b*}} (the set containing the singleton set of *a* and
the singleton set of *b*). None of the these three are pairwise
identical. Membership is not transitive. The first and third contain
two members, but not the same members (both *a* and *b*
are members of the first set, but not of the third), while the second
set has only one member (namely the first set). All three (and
infinitely many others) are generated from the same atoms, however, or
as Goodman might put it, they have the same content: *a*
and *b*. A system featuring a set-theoretic generating relation
thus does not count as nominalistic.


The sameness-of-content criterion was criticized by David Lewis
(1991, 40) as question-begging. Lewis suggests that the only
alternatives for generating relations that Goodman allows are
mereological, set-theoretical, or a combination of the two, and that
only mereological generation passes the test. Unless one rejects set
theory already, Lewis contends, one would not find the criterion
plausible. There are, however, non-extensional mereological systems
that violate the sameness-of-content criterion as well (see entry
on mereology). Moreover, the
sameness-of-content criterion may be understood as a version of 
Ockham's Razor, demanding not to multiply entities beyond necessity.


### 3.2 Mereology


The Polish logician Stanislaw Lesniewski (1886-1939) must
surely count as the father of mereology--the theory of parts and
wholes--but around 1930, Goodman re-invents the theory together
with his fellow graduate student Henry S. Leonard
(1905-1967). Only in 1935 do Goodman and Leonard learn of
Lesniewski's work through one of their fellow students, W.V. Quine
(Quine 1985, 122). An early version of Leonard and Goodman's system is
contained in Leonard's Ph.D. thesis, *Singular Terms* (Leonard
1930). In 1936, Leonard and Goodman present their mature system at a
meeting of the Association of Symbolic Logic; the corresponding paper
is published four years later under the title "The Calculus of
Individuals and Its Uses" (Leonard and Goodman
1940). Subsequently, Goodman uses the calculus in his own
Ph.D. thesis, *A Study of Qualities* (SQ), and a version of it
in *The Structure of Appearance* (SA). Little is known about
the nature of Goodman and Leonard's cooperation on the calculus.
Goodman attributes the first thought for the collaborative project to
Leonard (PP, 149). Leonard, more concretely, suggests in a (still)
unpublished note:



> 
> If responsibilities can be divided in a collaborative enterprise, I
> believe that it may be fairly stated that the major responsibility for
> the formal calculus [...] was mine, while the major
> responsibility for discussions of applications [...] lay with
> Goodman. (Leonard 1967)
> 
> 
> 


Quine only mentions that he himself "was able to help them on
a technical problem" (Quine 1985, 122). Leonard's system
of *Singular Terms* is significantly different from, and indeed
in philosophically interesting ways weaker than, the Calculus of
Individuals (Rossberg 2009), but the exact extent of Goodman's
technical contribution to the calculus remains unknown.


Perhaps surprisingly, nominalistic scruples were not the driving
force behind the development the Calculus of Individuals. Instead, their goal is to
solve a technical problem in Carnap's *Aufbau* (1928) (see
 section 4 below), 
and to this end they employ both set-theoretic and mereological
notions. Leonard, in his Ph.D. thesis (supervised by Alfred North
Whitehead), presents his calculus as "an interpolation in
Whitehead and Russell's *Principia Mathematica* between \*14 and
\*20" (Leonard 1967), and makes liberal use of class-terms in the
formulation (Leonard 1930). Also the joint
paper of Leonard and Goodman is formulated using class terms, as is
the system Goodman used in his own Ph.D. thesis, *A Study of
Qualities* (1941, SQ). It is not until his joint article with
Quine (Goodman and Quine 1947) and his *Structure of
Appearance* (1951, SA) that Goodman eschews the use of set theory
to formulate the Calculus of Individuals.


As mentioned above, parthood, as opposed to the set-theoretic
notion of membership, is transitive: if *a* is a part
of *b* and *b* is a part of *c*, then *a*
is a part of *c*. Neither the system Leonard and Goodman
present in their 1940 article, nor the version in Goodman's *A
Study of Qualities*, nor the calculus he uses in *The Structure
of Appearance*, take "part" as primitive. Rather, it
is in all three cases defined based on the sole primitive notion
adopted: *overlap* in SA, and *discreteness* in the
other two systems. Overlap can pre-systematically be understood as
sharing a part in common; discreteness as sharing no part in
common. All three systems indeed define parthood so that these two
pre-systematic understandings come out as theorems.


The Calculus of Individuals in all its formulations contains
principles of mereological summation and mereological fusion.
Mereological summation is a binary function of individuals, so that
the sum *s* of two individuals *a* and *b* is
such that both *a* and *b*, and all their parts, are
parts of *s*--and also all sums of parts of *a*
and *b* and are parts of *s.* Mereological fusion is a
generalization of the mereological summation. In Leonard and Goodman
1940 fusion is defined using sets: all the members of a set a
are "fused" in the sense that they, and all their parts,
and all the fusions amongst their parts, end up being parts of the
individual that is the fusion of set a.


The technical details of the different versions of the Calculus of
Individuals can be found in this supplementary document:
The Calculus of Individuals in its different versions
 (see also entry on 
 mereology).


Unrestricted mereological fusion has been widely criticized as too
permissive. 
It allows for so-called scattered objects (e.g., the sum of the Eiffel
Tower and the Moon) and in the case of Goodman's construction
in *The Structure of Appearance* for sums of radically
different kinds of objects, like sounds and colors. W.V. Quine, after
endorsing this principle in a joint paper with Goodman (Goodman and
Quine 1947), becomes one of its first critics in his review of *The
Structure of Appearance*:



> 
> part, clear initially as a spatio-temporal concept, is here
> understood only by spatio-temporal analogy. [...] When finally we
> proceed to sums of heterogeneous qualia, say a color and two sounds
> and a position and a moment, the analogy tries the imagination. (Quine
> 1951b, 559)
> 
> 
> 


Goodman (1956) maintains that the criticism is disingenuous if put
forward by a platonist: set-theoretic "composition" is as
least as permissive as mereological fusion. Whenever there is a fusion
of scattered concrete objects, there is also a set of them (see Simons
1987 or van Inwagen 1990 for prominent criticisms of unrestricted
composition).


## 4. The Structure of Appearance


*The Structure of Appearance* is perhaps Goodman's main
work, although it is less widely known than, for
example, *Languages of Art*. It is, in fact, a heavily revised
version of Goodman's Ph.D. thesis, *A Study of Qualities*. SA
is a constitutional system, which, just like Rudolf Carnap's *Der
logische Aufbau der Welt*, shows how from a basis of primitive
objects and a basic relation between those objects all other objects
can be obtained by definitions alone. We commented above already on
the anti-foundationalist nature of both Carnap's and Goodman's
constitutional systems. For them, the point of carrying out such a
construction was not to provide a foundationalist reduction to some
privileged basis (of experience or ontology), but rather to study the
nature and logic of constitutional systems as such. In this sense,
Goodman's interest in other "world versions", such as the
languages of art, should be seen as a continuation of his project in
SA.


### 4.1 Goodman on Analysis


Because Goodman is interested in the nature and logic of
constitutional systems as such, he begins his discussion in *The
Structure of Appearance* with meta-theoretical considerations.
Since the project of SA is to develop a constitutional system that
defines other notions from a predetermined basis, the question is
which conditions of adequacy should be in place for evaluating the
definitions. Constitutional systems are systems of *rational
reconstruction*, i.e., the concepts, objects, or truths that get
constituted by definition from the basis are supposedly counterparts
of concepts, objects or truths that we accept already
pre-theoretically.


One might think that such a reconstruction is only successful
if *definiens* and *definienda* are synonymous. However,
Goodman argues that the *definiens* of an accurate definition
need have neither the same intension nor even the same extension as
the *definiendum*; thus, taking as an example Alfred North
Whitehead's analysis of geometrical points, points in space may be
defined equally well as certain classes of straight lines or as
certain infinite convergent sets of concentric spheres; but these
alternative *definientia* are neither cointensive (synonymous)
nor coextensive with each other. A set of sets of straight lines is
just not the same set of objects as a set of infinite convergent sets
of concentric spheres. Hence, their accuracy notwithstanding, the
respective definitions are not coextensive with, let alone synonymous
with, the *definiendum*. Accuracy of constructional definitions
amounts to no more than a certain homomorphism of
the *definiens* with the *definiendum*. This means that
the concepts of the constructional system must provide a structural
model for the explicanda in the sense that for every connection
between entities that is describable in terms of the explicanda, there
must obtain a matching connection, stateable in terms of the
respective explicata or *definientia*, among the counterparts
that the entities in question have within the system. In this way the
two different definitions of "point" serve their purpose
equally well. The objects in the sets generated--although being
very different in kind--stand in just the right relations to one
another within the sets to serve as an explicatum for
"point" as geometry demands. This rather pragmatic
criterion of adequacy for philosophical analyses serves Goodman well
for a number of reasons. The most important is perhaps that Goodman
does not believe there was any such thing as identity in meaning of
two different expressions (see our discussion of likeness of meaning
above). Thus, if synonymy was made the criterion of adequacy, no
analysis could ever satisfy it. But relaxing the criteria of adequacy
for philosophical analyses to structure-preservation also supports
Goodman's more radical theses in epistemology and metaphysics,
especially in his later philosophy. One of his reasons to replace the
notion of truth with that of "rightness of symbolic
function", the notion of certainty with that of
"adoption", and the notion of knowledge with that of
understanding is the thought that the new system of concepts preserves
the structural relations of the old without preserving the
philosophical puzzles related to truth, certainty and knowledge (RP,
chapter X).


### 4.2 The Critique of Carnap's *Aufbau*


Goodman's predecessor in studying a constitutional system by the
means of modern formal logic is, as we already said, Rudolf Carnap,
who follows a very similar project as Goodman in his *Der logische
Aufbau der Welt* (Carnap 1928). In this book Carnap investigates
the example of a world built up from primitive temporal parts of the
totality of experiences of a subject (the so-called "elementary
experiences" or just "erlebs") and thus faces the
problem of abstraction: how can qualities, properties and their
objects in the world be abstracted from our phenomenal
experiences.


Carnap tries to show that by using the method of
"quasi-analysis" all the structure can be retained from
the basis if the "erlebs" are ordered by a simple relation
of part-similarity. Very roughly, the idea is that, although the
individual temporal slices of our totality of experience are not
structured (and thus have no parts), we can, via quasi-analysis, get
to their quasi-parts, the "qualities" they share with
other time-slices with which they are part-similar. Of course, time
slices of the totality of our experiences can be part-similar with
each other in a variety of ways. Perhaps two slices are similar with
respect to what is in our visual field at the time in question, or
they are similar with respect to what we hear or smell. However, since
the time-slices are primitives in the system, we cannot yet even talk
about these respects or ways in which the slices should be similar in
order to, for example, be considered experiences of the same
color. Carnap's ingenious idea is to group exactly those erlebs
together that are mutually part-similar, thereby grouping exactly
those that share (pre-theoretically speaking) a property. For simple
cases the quasi-analysis seems to give exactly the right
results. Consider the following group of erlebs that,
pre-theoretically have different colors.



![[6 vertical
colored bars, labeled A through F, A bar is green on the top half and
black on the bottom half, B bar is all black, C bar is black on top
half and red on bottom half, D bar is all red, E bar is all green, F
bar is green on top third, black in middle third, and red on bottom
third]](fig1a.png)
Figure 1a.



However, we do not yet know that there are such things as
colors. In fact the only thing we know about the erlebs
(*A*-*F*) is that they are part similar as displayed
in the following graph (where part-similarity between erlebs is
indicated by a line):



![[Graph: A and E
on first row (2nd and 4th columns respectively), B and F on second row
(1st and 3rd columns respectively), C and D on third row (2nd and 4th
columns respectively).  A has lines connecting it to B, C, F, and E.
B has lines connecting it to A, F, and C.  C has lines connecting it
to B, A, D, and F.  D has lines connecting it to C and F. E has lines
connecting it to A and F F has lines connecting it to all others.]](fig1b.png)
Figure 1b.





If we take the graph and now group exactly those erlebs together
that are mutually part-similar, we get the following sets:



\[
\{A, B, C, F\}, \{A, E, F\}, \{C, D, F\}
\]

But, of course, these sets correspond exactly to the extensions of
the colors in our example (viz. black, green, and red). Thus, by
knowing about the part-similarity between erlebs alone, we seem to be
able to reconstruct their properties with the method of
quasi-analysis.


Goodman observes, however, that in unfavorable circumstances
quasi-analysis will lead to the wrong results. Consider the following
situation:



![[6 vertical
colored bars, labeled A through F, A bar is green on the top half and
black on the bottom half, B bar is all black, C bar is black on top
half and red on bottom half, D bar is all red, E bar is black on the
top half and green on the bottom half, F bar is green on top third,
black in middle third, and red on bottom third]](fig2a.png)
Figure 2a.



This corresponds to the following graph:



![[Graph: A on
first row 3rd column, B and F on second row (1st and 5th columns
respectively), D on third row, 6th column, E and C on fourth row (2nd
and 4th columns respectively).  A has lines connecting it to B, C, F,
and E.  B has lines connecting it to A, F, C, and E.  C has lines
connecting it to all others.  D has lines connecting it to C and F. E
has lines connecting it to B, A, F, and C F has lines connecting it to
all others.]](fig2b.png)
Figure 2b.



If we use Carnap's rule for quasi-analysis, we will obtain all
color classes except \(\{A, E, F\}\), the color class for
"green", because green only occurs in "constant
companionship" with the color "black". Goodman calls
this the "constant companionship difficulty".


A second problem can be illustrated with the following example of
erlebs:



![[6 vertical
colored bars, labeled A through F, A bar is green on the top half and
black on the bottom half, B bar is all black, C bar is black on top
half and red on bottom half, D bar is all red, E bar is all green, F
bar is green on top half and red on the bottom half]](fig3a.png)
Figure 3a.



This corresponds to this graph:



![[Graph: A and E
on first row (2nd and 4th columns respectively), B and F on second row
(1st and 3rd columns respectively), C and D on third row (2nd and 4th
columns respectively).  A has lines connecting it to B, C, F, and E.
B has lines connecting it to A and C.  C has lines connecting it to B,
A, D, and F.  D has lines connecting it to C and F. E has lines
connecting it to A and F F has lines connecting it to A, C, E, and
D.]](fig3b.png)
Figure 3b.



But here \(\{A,C,F\}\) should be a color class resulting from
quasi-analysis, although \(A\), \(C\), and \(F\) have in fact
no color in common. Goodman calls this problem "the difficulty
of imperfect community". It is controversial to what extent
these problems are devastating for Carnap's project, but Goodman
considered them to be serious.


### 4.3 Goodman's Own Construction


In contrast to Carnap, Goodman begins from a realist basis,
considering the example of a system built on phenomenal qualities,
so-called qualia (phenomenal colors, phenomenal sounds, etc.) and thus
faced the *problem of concretion*: how can concrete experiences
be built up from abstract particulars?


In the visual realm, a *concretum* is a color-spot moment,
which may be construed as the sum of a color, a visual-field place and
a time, all of which stand in a peculiar relation of togetherness.
Goodman adopts this relation as a primitive and then shows how, by
means of it, it is possible to define the concept of the concrete
individual as well as the various relations of qualification in which
qualia and certain sums of qualia stand to the fully or partially
concrete individuals that exhibit them.


After this is done, Goodman faces his second major constructional
objective. He has to order the qualia into different categories. The
problem is to construct for each of the categories (color, time,
place, and so forth) a map that assigns a unique position to each
quale in the category, and that represents the relative likeness of
qualia by nearness in position. The solution to the problem requires
in each case the specification of a set of terms by means of which the
order at hand can be described, and then the selection of primitives
suitable to define them. Goodman thereby shows how predicates
referring to size and shape of phenomenal concreta may be introduced,
and he suggests briefly some approaches to the definition of the
different categories of qualia by reference to their structural
characteristics.


Goodman shows in SA how using a mereological system can help to
avoid the difficulty of imperfect community for a system built on a
realist base (such as SA), as well as for a system built on a
particularistic base (such as *Der logische Aufbau der Welt*).
The constant companionship difficulty, on the other hand, does not
arise in SA because no two concreta can have all their qualities in
common.


### 4.4 The Significance of *The Structure of Appearance*


Very many of the side issues dealt with in *A Study of
Qualities* and *The Structure of Appearance* reappear in
Goodman's later philosophy. The "grue"-problem (to be
explained in the next section) as a problem of what predicates to use
for projection and the related problem of how to analyze disposition
predicates, as well as the question of how to explicate simplicity,
tense, aboutness, and so on, all have their roots in Goodman's
dissertation. Alas, his most important work is also his most
complicated, which is perhaps the reason why it is so often ignored.
Other writings by Goodman are seemingly more accessible and have thus
attracted a wider readership. However, it is arguable that the
significance of Goodman's "easier" pieces cannot be
assessed adequately without relating them to the problems and projects
of *A Study of Qualities* and *The Structure of
Appearance*.


## 5. The Old and the New Riddle of Induction and their Solution


### 5.1 The Old Problem of Induction is a Pseudo-problem


The old problem of induction is the problem of justifying inductive
inferences. What is traditionally required from such a justification
is an argument that establishes that using inductive inferences does
not lead us astray. Although it seems to be a meaningful question
whether there is such a justification for our inductive practices,
David Hume argues that there can be no such justification (Hume
[1739-40] 2000; see the discussion of Hume in the entry on
 the problem of induction).
It is important to understand that Hume's argument is
*general*. It is not just an argument against a particular
attempt to justify induction in the sense above, but a general argument
that there can be no such justification *at all*.


In order to see the generality of this argument, we have to note
that the same problem also arises for *deduction* (FFF,
SSIII.2). That deduction is in the same predicament is observed by
Goodman and exploited for his solution of Hume's problem of induction.
Thus the upshot of Goodman's understanding of Hume's argument is that
there can be no justification of our inferential practices, if such a
justification requires a reason for their justifiedness. Accordingly,
the old problem of induction, which requires such a justification of
induction, is a pseudo-problem.


### 5.2 Hume's Problem, Logic, and Reflective Equilibrium


If the problem of induction is not how to justify induction in the
sense mentioned above, then what is it? It is helpful here to look at
the case of deduction. Instances of deductive inferences are justified
by showing that they are inferences in accordance with valid rules of
inference. According to Goodman, the rules of logic are in turn valid
because they are more or less in accordance with what we intuitively
accept as instances of a valid deductive inference (FFF, 64).


On the one hand, we have certain intuitions about which deductive
inferences are valid; on the other hand we have rules of inference.
Confronted with an intuitively valid inference, we check whether it
accords to the rules we already accept. If it does not, we might
reject the inference as invalid. If, however, our intuition that the
purported inference is valid is stronger than our confidence that our
logical rules are adequate, we might consider amending the rules. This
soon leads to a complicated process. We have to take into account that
the rules must remain coherent and not too complicated to apply. In
logic, we want the rules to be, for example, topic neutral, i.e.,
applicable to inferences (as far as possible) independent of specific
subject matter. On the other hand, we also want to extract as much
information from premises as possible, so we do not want to risk being
too cautious in accepting rules. In this process we make adjustments
on both sides, slowly bringing our judgments concerning validity into
a *reflective equilibrium* with the rules for valid inferences
until we finally get a stable system of accepted rules. (The term
 "reflective equilibrium"
was introduced by John Rawls (1971) for Goodman's technique.)


Reflective equilibrium is a story about how we *actually*
justify our inferential practices. According to Goodman, nothing more
can be demanded or achieved. It seems, perhaps, *prima facie*
desirable that we also seek a justification in the sense of the old
problem, but Hume's argument suggests that such a justification is
impossible. If this is correct, the remaining problem is to define our
inferential practices by bringing explicit rules into reflective
equilibrium with our tutored intuitions. "Justified" or
"valid" are predicates that are applied to inferences on
this basis.


It thus also becomes clearer how Goodman thought about Hume's
solution--that induction is merely a matter of custom or habit.
Hume's solution might be incomplete, but it is basically correct. The
remaining task is then to explicate the pre-theoretic notion of valid
inductive inference by defining rules of inference that can be brought
into a reflective equilibrium with intuitive judgments of inductive
validity.


### 5.3 The New Riddle of Induction


Before presenting Goodman's solution, we first have to discuss
Goodman's own challenge, the so-called "New Riddle of
Induction".


Consider the following two (supposedly true) statements:


* (B1)
 This piece of copper conducts electricity.
* (B2)
 This man in the room is a third son.


B1 is a confirmation instance of the following regularity
statement:


* (L1)
All pieces of copper conduct electricity.


But does B2 confirm anything like L2?


* (L2)
All men in this room are third sons.


Obviously, it does not. But what makes the difference? Both
regularity statements (L1 and L2) are built according to the exact
same syntactical procedure from the evidence statements. Therefore, it
does not seem to be for a syntactical reason that B1 confirms L1 but
B2 fails to confirm L2. Rather, the reason is that statements like L1
are lawlike, whereas statements like L2 at best express accidentally
true generalizations. Lawlike statements, in contrast to accidentally
true general statements, are confirmed by their instances and support
counterfactuals. L1 supports the counterfactual claim that if this
thing I have in my hand were a piece of copper, it would conduct
electricity. In contrast, supposing that it is indeed true, L2 would
not support that if an arbitrary man were here in the room, he would
be a third son. To tell which statements are lawlike and which
statements are not is therefore of great importance in the philosophy
of science. A satisfactory account of induction (or corroboration -- 
 see the discussion of Popper in the entry on 
 the problem of induction) 
as well as explanation and prediction requires this distinction. 
Goodman, however, shows that this is extremely hard to get.


Here comes the riddle. Suppose that your research is in gemology.
Your special interest lies in the color properties of certain
gemstones, in particular, emeralds. All emeralds you have examined
before a certain time \(t\) were green (your notebook is full of
evidence statements of the form "Emerald \(x\) found at
place \(y\) date \(z (z \le t)\) is green"). It seems that,
at \(t\), this supports the hypothesis that all emeralds are
green (L3).


Now Goodman introduces the predicate "grue". This
predicate applies to all things examined before some future
time \(t\) just in case they are green but to other things
(observed at or after \(t\)) just in case they are blue:


* (DEF1)  \(x\) is
grue \(=\_{df}\) \(x\) is examined before \(t\) and green [?]
\(x\) is not so examined and blue


Until \(t\) it is obviously the case that for each statement
in your notebook, there is a parallel statement asserting that the
emerald \(x\) found at place \(y\) date \(z (z \le t)\) is
grue. Each of these statements is analytically equivalent with the
corresponding one in your notebook. All these grue-evidence statements
taken together confirm the hypothesis that all emeralds are grue (L4),
and they confirm this hypothesis to the exact same degree as the
green-evidence statements confirmed the hypothesis that all emeralds
are green. But if that is the case, then the following two predictions
are also confirmed to the same degree:


* (P1)
The next emerald first examined after \(t\) will be green.
* (P2)
The next emerald first examined after \(t\) will be grue.


However, to be a grue emerald examined after \(t\) is not to
be a green emerald. An emerald first examined after \(t\) is grue
iff it is blue. We have two mutually incompatible predictions, both
confirmed to the same degree by the past evidence. We could obviously
define infinitely many grue-like predicates that would all lead to
new, similarly incompatible predictions.


The immediate lesson is that we cannot use all kinds of weird
predicates to formulate hypotheses or to classify our evidence. Some
predicates (which are the ones like "green") can be used
for this; other predicates (the ones like "grue") must be
excluded, if induction is supposed to make any sense. This already is
an interesting result. For valid inductive inferences the choice of
predicates matters. 


It is not just that we lack justification for accepting a general
hypothesis as true only on the basis of positive instances and lack of
counterinstances (which was the old problem), or to define what rule
we are using when accepting a general hypothesis as true on these
grounds (which was the problem after Hume). The problem is to explain
why some general statements (such as L3) are confirmed by their
instances, whereas others (such as L4) are not. Again, this is a
matter of the lawlikeness of L3 in contrast to L4, but how are we
supposed to tell the lawlike regularities from the illegitimate
generalizations?


An immediate reply is that the illegitimate generalization L4
involves a temporal restriction, just as L2 was restricted spatially
(see e.g., Carnap 1947). The idea would be that predicates that cannot
be used for induction are analytically "positional", i.e.,
their definitions refer to individual constants (for places or times).
A projectible predicate, i.e., a predicate that can be used for
induction, has no definition which would refer to such individual
constants but is purely qualitative (e.g., because it is a basic
predicate). The trouble is that this reply makes it relative to a
language whether or not a predicate is projectible. If we begin with a
language containing the basic predicates "green" and
"blue" (as in English), "grue" and
"bleen" are positional. "Bleen" is defined as
follows:


* (DEF2)
 \(x\) is bleen \(=\_{df}\) \(x\) is
 examined before \(t\) and blue [?] \(x\) is not so
 examined and green


But if we start with a language that has "bleen" and
"grue" as basic predicates, "green" and
"blue" are positional:


* (DEF3)
\(x\) is green \(=\_{df}\) \(x\) is
 examined before \(t\) and grue [?] \(x\) is not so
 examined and bleen
* (DEF4)
\(x\) is blue \(=\_{df}\) \(x\) is
 examined before \(t\) and bleen [?] \(x\) is not so
 examined and grue




Both languages are symmetrical in all their semantic and
syntactical properties. So the positionality of predicates is not
invariant with respect to linguistically equivalent
transformations. But if this is the case, there is no semantic or
syntactic criterion on whose basis we could draw the line between
projectible predicates and predicates that we cannot use for
induction.


### 5.4 Goodman's Solution


Goodman's solution to the new riddle of induction resembles Hume's
solution in an important way. Instead of providing a theory that would
ultimately justify our choice of predicates for induction, he develops
a theory that provides an account of how we in fact choose predicates
for induction and projection. Goodman observes that predicates like
"green" are favored over predicates like
"grue", because the former are much
better *entrenched*, i.e., in the past we projected many more
hypotheses featuring "green" or predicates co-extensional
with "green" than hypothesis featuring the predicate
"grue". If two hypotheses are the same with respect to
their empirical track-record, then the hypothesis that uses the better
entrenched predicates overrides the alternatives. On the basis of
these considerations, Goodman defines *projectibility* (and
cognates) for hypotheses (FFF, 108):



> 
> A hypothesis is *projectible* iff it is supported,
> unviolated, and unexhausted, and all hypotheses conflicting with it
> are overridden.
> 
> 
> A hypothesis is *unprojectible* iff it is unsupported, exhausted,
> violated, or overridden.
> 
> 
> A hypothesis is *nonprojectible* iff it and a conflicting hypothesis
> are supported, unviolated, unexhausted, and not overridden.
> 
> 
> 


The last definition takes care of situations when we are confronted
with two hypotheses that are in conflict and neither has a better
entrenched predicate. Entrenchment can even be further refined to
account for cases in which a predicate inherits the entrenchment from
another of which it is derivative. (The critical literature on Goodman's
New Riddle is too extensive to do it justice here; see Stalker 1994 
and Elgin 1997c for selections of important essays on the topic. 
Stalker 1994 also contains an annotated bibliography, comprising 
over 300 entries. The discussion of course continued after the 1990s and the
literature is still growing.)




Goodman's solution makes projectibility essentially a matter of
what language we use and *have used* to describe and predict
the behaviour of our world. However, this language-, or better
version-relativism is just another aspect of Goodman's
irrealism.


## 6. Irrealism and Worldmaking


### 6.1 Irrealism


Goodman labels his own position "irrealism". Irrealism,
roughly, is the claim that the world dissolves into versions.
Goodman's irrealism is certainly the most controversial aspect of his
philosophy.


Two lines of argument can be separated in Goodman's writings (Dudau
2002). First, Goodman argues that there are conflicting statements
that cannot be accommodated in a single world version: some truths
conflict (WW, 109-16; MM, 30-44). If that is the case, we
need many worlds, if any, to accommodate the conflicting versions and
bring them in unison with the standard correspondence account of
truth, that is, that the truth of a statement is its being in
correspondence with a world. The second line of argument seems to be
that we need no worlds at all if we need many. If we need a world for
each version, why postulate the worlds over and above the
versions?


Let us first have a closer look at the first line of reasoning. The
Earth stands still, revolves around the Sun, and runs many other
courses as well at the same time. Yet nothing moves while at rest. As
Goodman concedes, the natural response to this is that the
sentences


* (S1)
The Earth is at rest.
* (S2)
 The Earth moves.


should be understood as elliptical for


* (S1')
The Earth is at rest according to the geocentric system.
* (S2')
The Earth moves according to the heliocentric system.


However, according to Goodman, this would be wrong-headed (WW,
112). Consider the following two historiographical sentences:
"The kings of Sparta had two votes" and "The kings
of Sparta had only one vote". The first sentence is part of a
report by Herodotus, the second part of a report by Thucydides. There
is, again, an inclination to understand these sentences as ellipses
for "According to Herodotus, the kings of Sparta had two
votes", and "According to Thucydides, the kings of Sparta
had only one vote". But obviously these latter two sentences do
not tell us anything about Sparta. They only tell us about what
Herodotus and Thucydides said about Sparta. It is true that
"according to Herodotus, the kings of Sparta had two
votes", even if they actually had no vote or had three
votes. The same holds for the relativizations to the geocentric and
the heliocentric systems: it is true that the Earth is at rest
according to the geocentric system, but that still does not inform us
about the world. Thus, if we assume that (S1) and (S2) are both true,
we end up with a contradiction if we take them to be literally true of
one and the same world. If we do not take them to be literally true,
but to be elliptical and implicitly relativized, we end up with two
truths that are not about any world. At least, they are not about the
parts of the world we were interested in. They turn out to be truths
about versions, but not truths about planets. The solution chosen by
Goodman is to claim that they are about two different worlds. Both
state a literal truth about a world, but just not about the same
world.


It is crucial for Goodman's argument that in the conflict between
(S1) and (S2) we have (a) an actual conflict between statements, and
(b) no other way to resolve that conflict (like, for example,
rejecting at least one of the two statements in a non-arbitrary
way). Of course, other contemporaries of Goodman, such as Quine and
Carnap, also consider the problem that experience alone might
underdetermine theory-choice, but believed that pragmatic criteria
will in the long run allow us to arrive at one all-encompassing
coherent version of the world. In Quine's (Quine 1981) and Carnap's
(Carnap 1932) philosophies, this is assumed to be a physical version.
But Goodman does not believe in physicalist reductivism. First of all,
there does not currently seem to be any convincing evidence that all
truths are reducible to physics (just consider the problem of reducing
mental truths to physical truths), and, secondly, physics itself does
not even appear to form a coherent system (WW, 5). Hence, for Goodman,
we are stuck with conflicting world versions we consider true. Since,
as we have seen above, relativism is no option for
Goodman--because it would make true statements true about
versions only--we arrive at Goodman's pluralism: conflicting true
versions correspond to different worlds.


The second line of reasoning in Goodman's writings toys with the
idea that there are no worlds that the right versions answer
to--or at the very least that such worlds are not necessary. The
world versions suffice, and are really the only things that are
directly accessible, anyway. The versions can for many purposes be
treated as worlds (WW, 4 and 96; cmp. MM, 30-33).


Goodman of course recognizes a difference between versions and
worlds. A version can be in English and comprise words. Worlds are
neither in English nor comprise words. However, for a version that is
true of a world, the world has to answer to it in a way. A world that
"corresponds" to (S1), for example, is a world with
planets and spacetime that is so arranged that one of the planets,
Earth, is at rest in it. But "planet",
"spacetime", "at rest", and so on are ways to
categorize reality that depend on a version. These predicates are the
ones chosen in this very version. There was no world that came ordered
in correspondence with these predicates before this version was
constructed. Instead, the world corresponds to the version expressed
by (S1), because the world with that structure was made, when that
version was made.


But what are worlds made of? Should we not at least assume Reality
to be some kind of stuff that allows structuring with alternative
versions as dough allows structuring with a cookie-cutter? Does there
not have to be some substance for our versions to project structure
onto? According to Goodman, this "tolerant realist view"
that a plurality of worlds can be versions of a unique underlying
Reality is also nothing but a useless addition. A Reality underlying
the worlds must be unstructured and neutral, and thus serves no
purpose. If there are many equally satisfactory versions of the world
that are mutually incompatible, then there is not very much left that
the "neutral Reality" could be. Reality would have no
planets, no motion, no spacetime, no relations, no points, no
structure at all. One can assume there is such a thing, Goodman seems
to admit, but only because Reality is really not worth fighting for
(or fighting against, for that matter). If we can tell true from false
versions and explain why some are true versions and others false
versions of worlds without assuming anything like an underlying
reality, why assume it then? Parsimony considerations should lead us
to refrain from postulating it.


### 6.2 Worldmaking


While Goodman insists that "there are many worlds, if
any" (MM, 127; see also MM, 31), Goodman's worlds should not be
conflated with possible worlds. There are no merely possible Goodman
worlds, they are all actual (WW, 94 and 104; MM, 31). It is Goodman's
view that worlds are "made" by answering to right
versions, but there are no (merely possible) worlds that correspond to
false versions. It is important to note that this view does not
collapse into irrationalism or a fancy form of cultural relativism
favored by postmodern thinkers. Making a true version is not
trivial. Not surprisingly, it is not any easier than making a true
version is for a realist. How we make true versions is absolutely the
same on both accounts; the difference is only with respect
to *what* we do when we make true versions (see WW and
McCormick 1996 for discussion).


The constraints on worldmaking are strict. We cannot just create
things; predicates must be entrenched and thus there must be some
close continuity with former versions. Simplicity will keep us from
creating new things from scratch, coherence from making anything in
conflict with beliefs with higher initial credibility, and so on.


A world is made by making a world version. So, according to
Goodman, the making of a world version is what has to be understood.
Carnap's *Aufbau*, as already mentioned, presents a world
version, the systems in *A Study of Qualities* and *The
Structure of Appearance* are world versions, and so are scientific
theories. The heliocentric and geocentric worldviews are relatively
primitive world versions, while Einstein's theory of general
relativity is a more sophisticated one. World versions do not have to
be constructed in a formal language, though; indeed, they do not need
to be in a language, formal or informal, at all. The symbol systems
used in the arts--such as in painting, for instance--can be
used in the process of worldmaking too. It is in this sense that
philosophy, science, and art are all epistemically significant; they
all contribute to our understanding; they all help to create
worlds.


Making a world version is difficult. Acknowledging a great number
of them does not make it easier. The hard work lies, for example, in
creating a constructional system that overcomes the problems of its
predecessors, is simple, uses well-entrenched predicates, or
successfully replaces them with new ones (which is even harder),
allows us to make useful predictions and so on. For Goodman,
scientists, artists, and philosophers are faced with analogous
problems in this.


Goodman's insistence that we make worlds when we make their
versions and that we might just as well replace talking about worlds
with talk about versions creates a problem that is not simply solved
by acknowledging that making a true version is very hard. Making a
version and making the objects that the version is about are clearly
two different tasks. As Israel Scheffler writes in the abstract to
"The Wonderful Worlds of Goodman":



> 
> The worldmaking urged by Goodman is elusive: Are worlds to be
> identified with (true) world-versions or do they rather comprise what
> is referred to by such versions? Various passages in [WW] suggest one
> answer, various passages another. That versions are made is easy to
> accept; that the things they refer to are, equally, made, I find
> unacceptable. (Scheffler 1979, 618)
> 
> 
> 


Indeed, Scheffler argues, Goodman confusingly uses
"world" and "worldmaking" both in a versional
and in an objectual sense. As we said above, Goodman's claim is that
we make a world in the objectual sense by making a version of it. The
claim is based on his conviction that the only structure of the world
to which all true versions correspond does not exist independently;
rather, it is only to be found because we project this structure onto
the world with our conceptualizations. His favorite example is the
constellation known as "Big Dipper". Indeed, we
"made" the Big Dipper by picking out one arbitrary
constellation of stars and naming it. (More precisely, it is a
so-called *asterism* that is part of the constellation *Ursa
Major*--but the point still stands.) Which arrangement of
heavenly bodies makes up the Big Dipper is purely conventional and
hence only due to our conceptualization. Hilary Putnam (1992a)
suggests that this idea may have some plausibility for the Big Dipper,
but it does not, for instance, hold true of the stars that constitute
the Big Dipper. True, "star" is a concept with partly
conventional boundaries; however, that the concept "star"
has conventional elements does not make it a matter of convention that
"star" applies to something (and thus merely a matter of
making a world version).


Putnam also points out that there is a tension between Goodman's
notion of worldmaking and his first line of thought that leads to his
irrealism: the idea that there are conflicting statements in different
adequate world versions. As Putnam argues, to say that a statement of
one world version is incompatible with that of another (such that a
single world cannot accommodate both versions) requires that the
expressions in the two versions have the same meaning. However, it is
not clear that our ordinary notion of meaning allows such
inter-version comparison of sameness of meaning (a thought that
Goodman should be sympathetic to, since he already doubts an
intra-version notion of that kind). Moreover, there might be better
ways to compare alternative versions (e.g., by way of
homomorphism-relations between versions, as developed by Goodman in SA
and discussed above in 4.1) and to explain how versions relate despite
their apparent incompatibility (for example, by paying attention to
the practice of scientists who manage to move from one version to
another).