Goodman, Nelson (1906–1998)

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Nelson Goodman, the distinguished American philosopher of science and language, was born in Massachusetts in 1906. He received a bachelor of science degree from Harvard in 1928 and took his Ph.D. in philosophy there in 1941. After an instructorship at Tufts College (19451946), he was appointed associate professor at the University of Pennsylvania (19461951) and then professor (19511964). From 1964 to 1967 Goodman was the Harry Austryn Wolfson professor of philosophy at Brandeis University. In 1967 he became a professor of philosophy at Harvard. He died in 1998.

Goodman's delineations of certain strategic problems in epistemology, philosophy of science, and constructional methods, as well as the results of his own inquiries, are fundamental in the areas in which he worked. Specifically, these include theories of inductive logic or confirmation, problems concerning the nature of causal or lawlike regularity, theories of the structural or logical simplicity of theories, and constructions of linguistic systems within which philosophical problems may be solved, as well as theories of the adequacy or accuracy of such systems. Because of his achievements any further significant contributions to these areas may be expected to rest, in some measure, upon his work.

In this brief compass no attempt will be made either to give a comprehensive account of Goodman's ramified views or to rehearse in full detail any one of his major achievements. Instead, we will give an account of a few aspects of his major contributions in just sufficient detail to make their general import intelligible and to show something of their interconnections.

Our order of presentation of topics is quite independent of their chronology in Goodman's philosophical development. We begin with those of his important studies with which there appears to be widest familiarity.

Inductive Theory

One of Goodman's characterizations of the task of inductive theory is that it consists in "formulating rules that define the difference between valid and invalid inductive inferences." On this usage a set of rules for discriminating valid acceptances or nonacceptances of hypotheses from those which are invalid constitutes an inductive theory, or, alternatively, a theory of confirmation or a theory of projection.

Goodman's contribution to the provision of such inductive canons has been threefold. First, he provided an analysis of the character of philosophical problems about induction. Second, he furnished a critique of the problems still to be solved and of the versions of confirmation theory which have been at all fully elaborated (notably those of Rudolf Carnap and Carl Gustav Hempel; see Fact, Fiction and Forecast, especially pp. 2434, 4851, and 6886, and also the published exchanges between Carnap and Goodman to which reference is made on p. 86). Third, he made advances, explicitly in the form of a discussion of a theory of projection, toward the solution of some of the problems thus delineated. Where induction is construed narrowly as inference about future cases on the basis of examined cases, projection is, by contrast, inference about any unexamined cases on the basis of examined ones. We will consider each of these three aspects of his contribution in turn.

the "problem of induction"

Goodman argues that the so-called problem of induction, when it is construed as the problem of justifying induction, is one that may be "dissolved" as soon as we see what is at issue. Moreover, this "dissolution" highlights all the more clearly the bona fide problem that he calls the new riddle of induction. As he sees it the problem is not to justify induction but to be able to distinguish valid from invalid inductions. On Goodman's view the dissolution of the old problem of induction, that is, of the problem of justifying induction, is accomplished when we come to understand that a genetic or descriptive account of our inductive behavior, such as the one that David Hume almost brought ff, furnishes the basis of such a justification. That this is a cogent view, he points out, can be seen when we raise the question of justifying deduction. How do we justify a deductive inference? By showing that it conforms to specific logical rules of deduction. By the same token, an inductive inference can be justified by showing that it conforms to a specific rule of induction.

One may immediately ask, however, what justification we have for adopting a set of rules of induction as valid. Of course, the same question might be asked concerning a set of deductive rules. The answer may be indicated by furnishing a parable.

Consider the situation of an imaginary philosopher to whom we may give the name "Aristotle." Aristotle has a keen interest in the area of deductive inference. In this area, he finds that although there is already an established practice among humans of making deductive inferences and although there is already a practice of discriminating, among ostensible inferences of this type, those that are correct from those that are not, nevertheless no one has yet made explicit or systematically codified the implicit rules upon which such discriminations appear to be based.

Our imaginary philosopher decides to undertake this task and eventually comes forward with such a codification. Using his codification people are enabled to make explicit their reasons for discriminating valid from invalid deductions by referring to the explicit rules that Aristotle has placed conveniently at hand. Of course no one would have paid any attention at all to these rules if they did not, with fair accuracy, reflect established practicethis is indeed what constitutes their validity as a set of rules. In the course of many years, however, other philosophers come forward to point out anomalies in Aristotle's set of rules. They point out that in certain cases some of his rules yield unacceptable inferences, and these philosophers suggest amendments which will remove the anomalies. When the amendments are incorporated they, in turn, have the effect of modifying practice. As Goodman puts it:

[Deductive] inferences are justified by their conformity to valid general rules, and general rules are justified by their conformity to valid inferences. But this circle is a virtuous one. The point is that rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences." (Fact, Fiction and Forecast, p. 67)

If we return our attention to induction we see that an analogous situation obtains. Particular inductive inferences are justified by reference to rules of induction, and rules of induction are justified by reference to particular practices of inducing. Hume was on the right track in giving a descriptive account of inductive practice and in explicating rules of causal inference that he held to be in conformity with this practice. Those who have criticized him for this have been wrong.

We are thus quits with the old problem of induction, but the new, very formidable "riddle of induction" still remains. For although Hume was right in turning to description of actual practice, his description was insufficiently precise. He pointed out that observed regularities give rise to habits of expectation and that predictions based on such regularities are "normal or valid." But the defect in Hume's account, Goodman shows, lies in his failure to note "that some regularities do and some do not establish such habits; that predictions based on some regularities are valid while predictions based on other regularities are not. To say that valid predictions are those based on past regularities is thus quite pointless" (ibid., pp. 8182). Accordingly, the new riddle of induction consists in finding a set of rules of inductive logic that will do for us what Hume failed to do. Thus, the problem is not to justify induction but adequately to codify it. An adequate codification would presumably stand to inductive practice very much as the codification of deduction, accomplished by our mythical Aristotle, stood to deductive practice as described in our parable above. In particular, it would presumably consist of a set of rules the appeal to which would serve to validate specific acceptances or rejections of scientific hypotheses or theories.

critique of confirmation theory

In "The Problem of Counterfactual Conditionals" (reprinted without major change as Chapter 1 of Fact, Fiction and Forecast ) Goodman was able to show that a solution to the problem of achieving an adequate interpretation of counterfactuals is intimately connected with many of the other crucial questions of the philosophy of science and that such a solution could be achieved only if various critical questions about the nature of scientific laws and of confirmation theory could be answered.

He shows, in particular, that the problem of furnishing adequate criteria for distinguishing true from false counterfactual conditionals has as a constituent the problem of adequately defining "scientific law," that this requires us to distinguish those hypotheses which are confirmed by their instances from those which are not, and that this, in turn, requires the fashioning of an adequate theory of confirmation. It is together the burden of the last part of "The Problem of Counterfactual Conditionals," of two brief articles on confirmation theory and of several passages in Chapter 3 of Fact, Fiction and Forecast that extant confirmation theories are defective, for they provide no means (except such as vitiate the theories through question-begging stipulations about what primitive predicates may be comprised in confirmable hypotheses) to distinguish the hypotheses to which such theories may be applied. Goodman, for example, points out that extant provisions of criteria for what constitutes a confirming instance in such defective theories either have the consequence that "any statement will confirm any statement" (ibid., p. 81) or make question-begging assumptions, mentioned before, about the recognizability of "purely qualitative predicates" which are held to be the only permissible ones that may occur in (thus distinguishable) confirmable hypotheses. He shows, in short, that a desideratum of theories of confirmation is a definition of "confirmable hypothesis." In the final chapter of Fact, Fiction and Forecast he attempts to fill this need through advances on the problem of defining "projectible" as a predicate of hypotheses.

theory of projection

In earlier discussions Goodman had shown that certain dispositional terms (other than projectible ) may be adequately defined by projecting them over the extensions of (that is, by defining them in terms of) certain carefully specified nondispositional or manifest predicates. Such earlier successes provide important paradigms. If on their model the meaning of the term projectible can be clarified, it will be feasible to decide to which hypotheses the term applies, and a crucial desideratum of heretofore defective theories of confirmation will have been taken care of.

Inasmuch as the term projectible is itself a dispositional predicate we may expect that among the manifest predicates that will occur in any candidate definiens will be the corresponding manifest predicate: "projected." However, defining projectible in terms of "projected" offers some very special difficulties which do not arise in the case of many dispositional predicates. The predicate "projectible" is like "desirable." It is not the case that every hypothesis that has been actually projected ought to have been or ought to be projected. (A hypothesis is characterized as having been actually projected if "it is adopted after some of its instances have been examined and determined to be true, and before the rest have been examined"; ibid., p. 90.)

Goodman, perhaps unlike J. S. Mill in confronting "desirable" is explicitly aware of the trap, and although his task is thereby enormously complicated, he avoids falling into it. He proposes, eventually, an explication of "projectibility" that provides criteria for discriminating projectible hypotheses based on past projections and certain other characteristics of our actual linguistic habits. In particular, attention to actual projections of hypotheses enables Goodman to explicate a relevant sense of projected predicate (a predicate occurring in an actually projected hypothesis). This, in turn, leads to his explication of a concept that becomes pivotal to his theory of projection: the concept of "entrenchment"more specifically, the concept "is a much better entrenched predicate than."

One predicate, P, is said by Goodman to be much better entrenched than another predicate, Q, if P and all predicates coextensive with it have actually been projected much more often than Q and all predicates coextensive with it. Thus, take the predicate "grue" (which applies to any blue thing not examined before some time, t, and also to any thing examined before time t and found to be green). This "highly artificial" predicate, occurring in the hypothesis "The next emerald to be examined (after time t ) will be grue" allows that hypothesis to be equally highly evidenced with the more usual "The next emerald to be examined (after time t ) will be green." But hypotheses employing "grue" (or any term applicable to exactly the things "grue" is applicable to) have, nevertheless, been much less frequently projected (for example, used in making predictions) than have hypotheses using "green" (or any term applicable to exactly the things "green" is applicable to). This is part of the basis upon which "green" is judged a much better-entrenched predicate than is "grue"; and Goodman's theory attempts to show how, although they are equally well evidenced, hypotheses containing much better-entrenched predicates are to be preferred to ones that contain much less well-entrenched predicates. Goodman points out that when we speak of the entrenchment of predicates we are really speaking of the entrenchment of habits of classification. This is to say that talk of the entrenchment of predicates is, in effect, talk of the entrenchment of their extensions. And, a little later on, still referring to his elucidation of entrenchment, he says:

Like Hume, we are appealing here to past recurrences, but to recurrences in the explicit use of terms as well as to recurrent features of what is observed. Somewhat like Kant, we are saying that inductive validity depends not only upon what is presented but also upon how it is organized; but the organization we point to is effected by the use of language and is not attributed to anything inevitable or immutable in the nature of human cognition. To speak very loosely, I might say that in answer to the question what distinguishes those recurrent features of experience that underlie valid projections from those that do not, I am suggesting that the former are those features for which we have adopted predicates that we have habitually projected. (Ibid., pp. 9697)

The import of these considerations is that what constitutes a valid projection, and consequently what comes to constitute a projectible hypothesis, is a result of how we have, as a matter of fact, come to classify.

If Goodman's attempt to define "projectible" is successful, we have at hand the means of solving the problem of distinguishing confirmable from nonconfirmable hypotheses and thereby of surmounting a major obstacle in the way of providing a logic of induction.

These results of Goodman'sboth the critique of extant theories and the positive proposals put forward in 1955 (ibid.)are clearly still being digested by people in the field, if one may judge by the discussions of them that (ten years later) appeared in print with increasing frequency.

Theory of Structural Simplicity

An early version of Goodman's calculus of simplicity (later extensively modified) occurs in Part I, "On the Theory of Systems," of his first book, The Structure of Appearance. There the calculus is exclusively connected with considerations somewhat more general than those involved in, for example, assessing the simplicity of scientific theories. In The Structure of Appearance interest in simplicity is interest in the simplicity of the primitive predicate basis of any constructional system; that is, any constructed linguistic system or axiomatic system which makes explicit what are the primitive (that is, the undefined) terms of the system. The main general problem that Goodman addresses is that of delineating criteria of adequacy for constructional systems generally, rather than for scientific theories in particular. For the constructor of such systems this problem is often posedin part, at leastas the problem of choice among alternative primitive predicate bases. In choosing a primitive basis such considerations as antecedent clarity and "defining power" are obviously to be taken into account, but Goodman shows that the simplicitythe structural or logical simplicityof such bases, is also an at least equally important consideration.

In his later writings on the subject (particularly in "The Test of Simplicity" and Fact, Fiction and Forecast ) Goodman also made clear the relationship of measures of simplicity to the philosophy of science. He maintains that simplicity is a primary consideration guiding choices among scientific theories or systems of hypotheses. It is a mistake to believe that simplicity becomes a factor only after we have first sought a true system and then turn to matters of elegance. He maintains that, on the contrary, our concern with simplicity is an inevitable concomitant of our concern with system. For, he points out, we achieve systematization only to the extent that the basic vocabulary and principles we employ in dealing with some subject matter come to be simplified. The important thing to note is that "when simplicity of basis vanishes to zerothat is, when no term or principle is derived from any of the otherssystem also vanishes to zero. Systematization is the same thing as simplification of basis" ("The Test of Simplicity," p. 1064).

Goodman finds the key to the problem of measuring the structural simplicity of predicate bases in a "meagre and negative" but highly plausible principle: "If every basis like a given one can always be replaced by some basis like a second, then the first is not more complex than the second" (ibid., p. 1066). The relation "always replaceable by" between predicate bases holds in cases where the replacement is a matter of a purely routine procedure that can always be applied (presumably, for example, in case there is available some decision procedure for determining replaceability). Employing this key principle and some results in the theory of relations. Goodman provides a means of effecting the requisite measures. The calculus of simplicity is applicable only to theories that have been at least sufficiently formalized to enable discrimination of their primitive predicates. Its applicability (for example, as a factor in assessing the acceptability of some scientific theory) is thus severely limited for the present by the paucity of scientific theories that have reached this stage of formalization. On the other hand, this situation would be importantly alleviated if some means could be found either to bring more such theories to the requisite stage of formalization or to modify the calculus in such a way that useful applications of it may be made even to less fully formalized systems.

For the time being, applications of the simplicity measures may, however, be made to constructional systems devised for purposes of philosophical explication (for example, see Goodman's own system in The Structure of Appearance ).


Whatever its importance for both philosophy of science and constructional methods, furnishing a way of measuring the simplicity of bases of any constructed systems by no means represents Goodman's only contribution to constructional methods. The first three chapters of The Structure of Appearance (for example) provide also a discussion of the problem of assessing the adequacy and the accuracy of definitional systems. Here an especially significant discussion (for example, in Ch. 1) provides both an illuminating critique of criteria which in the past have been adduced for assessing such systems and a newly developed criterion, extensional isomorphism, for assessing the accuracy of such systems. The development of this criterion throws new light on the entire program of philosophical or logical analysis.

Although full elucidation of the criterion is beyond the scope of the present entry, some general inkling of its import may perhaps be conveyed by pointing out some of its differences from some of the criteria which have been previously offered for the adequacy of philosophical analyses. It has long been recognized that full synonymy of analysandum (the concept or term being subjected to philosophical analysis) and analysans (the concept or term constituting the product of the analysis) is too strong a requirement. Accordingly, weaker criteria (for example, intensional identity or extensional identity of analysandum and analysans) have been proposed. In The Structure of Appearance Goodman argues that even the weakest of theseextensional identityis too strong a requirement to place on tasks of analysis, for none can totally fulfill such a condition. He proposes instead a criterion that does not "square" an analysandum with its analysans in any one-to-one fashion but rather tests the whole system of concepts to which the analysandum belongs against the whole newly constructed system to which the analysans belongs. The meeting of specified and relatively weak extensional correspondences between two such systems is sufficientand indeed is the most that can cogently be requiredto warrant the accuracy of the analysis.

The discussions of new constructional methods in the first chapter of The Structure of Appearance and the presentation of a version of the calculus of individuals which had been developed by H. S. Leonard and Goodman (in "The Calculus of Individuals and Its Uses") are well supplemented by the specific application of these and other devices to a detailed critique of Carnap's Der logische Aufbau der Welt (in Ch. 5). An important application is also provided by the construction (in Chs. 611) of his own systematic explication of phenomenal concepts or predicates.

Phenomenalism and Nominalism

Goodman's actual work upon, and his defenses of work upon, phenomenalistic systems lead many observers to conclude that he subscribes to phenomenalism as a philosophical position. The fact is, however, that he wrote in full and explicit detail about the relative unimportance and the opacity of questions about the epistemological priority of the phenomenal (and "rival," for example, physicalistic) systems, and there seems to be no good reason to doubt the sincerity of his disavowals of that kind of philosophical commitment. (See The Structure of Appearance, Ch. 4 and passim, and "The Revision of Philosophy.") All of this is notwithstanding the fact that he made contributions to the solution of many very complex problems that are involved in the construction of a phenomenalistic system.

If phenomenalism represented, for him, no particular philosophical commitment, nominalism, on the other hand, surely did. His major writings on this topic (in his and W. V. Quine's "Steps Toward a Constructive Nominalism" and in his The Structure of Appearance; Fact, Fiction and Forecast ; and "A World of Individuals") obviously constitute a fundamental philosophical conviction. Although Goodman's and Quine's nominalism coincide importantly (for example, in their mutual rejection of classes, see "Steps toward a Constructive Nominalism"but note, however, that in later writings Quine appears no longer to embrace such views) it should nevertheless be observed that their nominalistic positions are quite disparate. Thus, Quine apparently rejects, so to speak, classes on account of their being abstract entities; whereas Goodman rejects, so to speak, classes not on account of their being abstract entities (his system in Structure, indeed, refers to abstract entities categorematically) but rather on account of their being nonindividuals. It is the notion of a nonindividual that Goodman finds unintelligible, and he is conscientious in avoiding any philosophical or logical method which presupposes or extorts the claim that there exist any nonindividuals. The consequent austerity in bases chosen and logical tools available to him have had, in fact, fruitful results in eliciting complex, ingenious, and far-reaching techniques or methods of constructional analysis.

We have indicated that there are differences between what might be called G-nominalism (Goodman's position)the view, on the one hand, that there are no nonindividualsand the position that might be called Q-nominalismthe view that there are no abstract entities, on the other. While it would, again, be beyond the scope of this entry to give a detailed account of G-nominalism, it may yet be illuminating to remind the reader that Goodman himself characterized his position as a sort of "super-extensionalism." The usual or classical extensionalist position prohibited some otherwise indiscriminate multiplication of entities by imposing a principle to the effect that two entities (say, two classes) that have, so to speak, the same proximate constituents are identical. G-nominalism goes further; it imposes the condition that any two things which have the same systematically ultimate constituents are identical.

Thus, consider the systematic atoms (things not having anything else in the system as possible constituents) a, b, c, and d. Suppose in a (classically) extensional system A we discriminated the classes of pairs {a,c } and {b,d }, and suppose in system B we discriminated the classes {a,b } and {c,d }. For classical extensionalism, systems A and B would not be identical; that is, the proximate constituentsthe two classes of pairsare different, and hence the world's population on this account is increased by two more classes. The G-nominalist, however, has a stronger condition for diversity. For him there are not, say, the eight different entities consisting of the four atoms and the four classes of pairs of them. Rather, there are only four entitiesthe ultimate atoms of the system themselves. The cogency of this view is argued with great vigor and clarity in "A World of Individuals."

Work in Progress

Goodman's interest appears to be an analysis of representationalism in a very broad sense of this concept taken presystematically. Thus, the focus of his attention is not only upon representation as a phenomenon involving, for example, paintings in aesthetics but also upon the representational aspects or functions of maps, graphs, musical scores, and choreographic notations, and, in addition, theories and other descriptions. His deep and abiding interest in this topic is evidenced too as a recurrent thread in many of his works, from very early ones on. The articles in which this concern is most obviously expressed are "On Likeness of Meaning," "Sense and Certainty," "The Way the World Is," and "About." The concern is also dominantly present in his John Locke lectures (given at Oxford in 1962), published as The Languages of Art.

See also Aesthetics, History of; Aesthetics, Problems of; Aristotle; Carnap, Rudolf; Counterfactuals; Hempel, Carl Gustav; Hume, David; Induction; Kant, Immanuel; Mill, John Stuart; Nominalism, Modern; Phenomenalism; Philosophy of Science, Problems of; Projectivism; Quine, Willard Van Orman.


works by goodman

"The Calculus of Individuals and Its Uses." Journal of Symbolic Logic 5 (1940): 4555. In collaboration with H. S. Leonard.

"A Query on Confirmation." Journal of Philosophy 43 (1946): 383385.

"On Infirmities of Confirmation-Theory." Philosophy and Phenomenological Research 8 (1947): 149151.

"Steps toward a Constructive Nominalism." Journal of Symbolic Logic 12 (1947): 105122. In collaboration with W. V. Quine.

"On Likeness of Meaning." Analysis 10 (1949): 17.

"An Improvement in the Theory of Simplicity." Journal of Symbolic Logic 14 (1950): 228229.

The Structure of Appearance. Cambridge, MA: Harvard University Press, 1951.

"Sense and Certainty." Philosophical Review 61 (1952): 160167.

Fact, Fiction and Forecast. London, 1954; Cambridge, MA: Harvard University Press, 1955.

"Axiomatic Measurement of Simplicity." Journal of Philosophy 52 (1955): 709722.

"The Revision of Philosophy." In American Philosophers at Work, edited by Sidney Hook, 7592. New York, 1956.

"A World of Individuals." In The Problem of Universals, 1331. Notre Dame, IN, 1956.

"The Test of Simplicity." Science 128 (1958): 10641069.

"Recent Developments in the Theory of Simplicity." Philosophy and Phenomenological Research 19 (1959): 429446.

"The Way the World Is." Review of Metaphysics 14 (1960): 160167.

"Positionality and Pictures." Philosophical Review 69 (1960): 523525.

"About." Mind 70 (1961): 124.

"Safety, Strength, Simplicity." Philosophy of Science 28 (1961): 150151.

The Languages of Art. Indianapolis: Bobbs Merrill, 1968.

Richard S. Rudner (1967)

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