Donald Cary Williams
Hist-Analytic would like to express its gratitude to the Editor of Review of Metaphysics for permission to webify Williams' important paper, "The Elements of Being." The Review of Metaphysics is owed a great deal by those of us who have followed the development of analytical philosophy and it's implications for metaphysics over the last several decades. Williams' paper is among the most important papers in analytical ontology ever written and the Review of Metaphysics has displayed an understanding of the importance of making it available to the international Internet community. This page is a work in progress and hopefully further details of Williams' life will become available in the future. Thanks also go to Charles Pigden of the University of Otago, New Zealand, and Keith Campbell for his insightful introduction to the paper.
Little is known about D. C. Williams. He was Chairman of Harvard's Philosophy Department and has been written about briefly by Willard Van Orman Quine: "Donald Cary Williams." Proceedings and Addresses of the American Philosophical Association1983), 57:245-248. Williams was a Guggenheim Foundation fellow in 1937. Hopefully, later I will be able to add to the details surrounding the life and influence of this first rate thinker and philosophical stylist.
"The Principle of alternation." Monist. 33. 1923. 586-600.
"The definition of yellow and of good." J. Phil. 27. 1930. 515-527.
"On Having Ideas in the Head." J. Phil. 29. 1932. 113-121.
"Ethics as Pure Postulate." Phil. Rev. 42. 1933. 399-411.
"The Innocence of the Given." J. Phil. 30. 1933. 617-628.
"The Inductive Argument for Subjectivism." Monist. 44. 1934. 80-107.
"Mr. Stace's 'Refutation of Realism." Mind. ns. 43. 1934. 357-358.
"Scientific Method and the Existence of Consciousness." Psychol. Rev. 41. 1934. 461-479.
"The Nature and Variety of the Apriori." Analysis. 5. 1938. 85-94.
"Induction and the External World." Phil. Sci. 5. 1938. 181-188.
"William James and the Facts of Knowledge." In Commemoration of William James, 1842-1942. 1941. Columbia U. Press. 95-126.
"Naturalism and the Nature of Things." Phil. Rev. 53. 1944. 417-443.
"Realism" (poem). J. of Phil. 42. 1945. 577.
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The Ground of Induction. Cambridge. Harvard U. Press. Russell and Russell. 1947.
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"Probability, Induction, and the Provident Man." Philosophic Thought in France and the United States. ed. Marvin Farber. U. of Buffalo Press. 1950.
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"Review of Reichenbach: The Theory of Probability." Phil. Phenomenol. Res. 11. 252-257.
"The Sea Fight Tomorrow." In Paul Henle and H. Kallen and S. K. Langer: Structure, Method, and Meaning. 1951.
"The Myth of Passage." J. Phil. 1951. 457-472.
"Prof. Carnap's Philosophy of Probability." Phil. Phenomenol. Res. 13. 1952. 103-121.
"On the Direct Probability of Induction." Mind. 62. 465-483.
"On the Elements of Being." Rev. Metaphysics. 7. 1953. 3-18, 171-192.
"Prof. Linsky on Aristotle." Phil. Rev. 63. 1954. 253-255.
"More on the Ordinariness of History." J. Phil. 1955. 52. 646-651.
"Form and Matter." Phil. Rev. 64. 1958. 291-312, 499-421.
"Mind as a Matter of Fact." Rev. Metaphysics. 13. 1959. 203-225.
Principles of Empirical Realism. 1965. Springfield Ill. C. C. Thomas.
"Universals and Existents." Australasian Journal of Philosophy Vol. 64. No. 1. March. 1986.
Universals and Predication by Bruce Aune
Tropes Online (Stanford)
Excerpt from The Ground of Induction
"Tropes and Time" by Kathe Trettin
"Why There are No Tropes," by Jerrold Levinson
"Two Dogmas of Ontology," by Francesco Orilia
Determinables as Universals, by Ingvar Johannson
Acton, H. B. "The Theory of Concrete Universals, 1." Mind Vol.XLV. Oct. 1936. pp. 2842.
Acton, H. B. "The Theory of Concrete Universals, 1." Mind Vol.XLVI. Jan. 1937. pp. 1-13.
Alexander, S. "Universal, Particular, and Individual." in Space, Time and Deity: The Gifford Lectures at Glasgow, 1916-1918. Vol. 1. Macmillan. 1927. pp. 208-233.
Armstrong, D. M. Nominalism and Realism: Universals and Scientific Realism. vol. 1. Cambridge U. Press. 1978.
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Armstrong, D. M. A World of States of Affairs. Cambridge U. Press. 1997.
Beck, R. Loyd. "John Cook Wilson's Doctrine of the Universal," Monist. Vol. XLI. Oct. 1931. pp. 552-582.
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Bosanquet B. "The Concrete Universal." The Principle of Individuality and Value. Macmillan. London. 1927. pp. 3-81.
Brownstein, D. Aspects of the Problem of Universal. U. of Kansas. 1973.
Butchvarov, P. Resemblance and Identity: An Examination of the Problem of Universals. Indiana University Press. 1966.
Butchvarov, P. Being Qua Being: A Theory of Identity, Existence, and Predication. Indiana University Press. 1979.
Campbell, Keith. Abstract Particulars. Oxford. 1990.
Campbell, Keith "The Metaphysics of Abstract Particulars." Midwest Studies in Philosophy. Vol. VI. The Foundations of Analytical Philosophy edited by P. French, Theodore E. Uehling, Jr. and H. Wettstein. U. of Minn. Press. 1981.
Bergmann, G. Realism: A Critique of Brentano and Meinong. University of Wisconsin. Chpt. V 1967.
Bergmann, G. "The Ontology of Edmund Husserl." Methodos 12. 1960. 359-92. reprinted in Logic and Reality. U. of Wisconsin Press. 1967.
Dawes-Hicks, G. "Are the Characteristics of Particular Things Universal or Particular?" Proceedings of the Aristotelian Society. Supplementary Volume III. 1923. reprinted in Van Iten.
Hochberg, H. "Bergmann's Realism and the Critique of Bundle and Tropic Ontologies." in The Positivist and the Ontologist: Bergmann, Carnap and Logical Realism. Rudopi. 2001.
Hochberg, H. "Particulars as Universals: Russell's Ontolological Assay of Particularity and Phenomenological Space-Time." Journal of Philosophical Research Vol. XX, 1995. pp. 84-111.
Husserl, E. Logical Investigations trns. J. N. Findlay. Vol. 1 pp. 402-432; Vol. 2. pp. 436-470. Humanities Press. 1970 (1913).
Jones, J. R. "Are the Qualities of Particular Things Universals?" Philosophical Review Vol. LVII. 1949. pp. 152-170.
Knight, Helen "Stout on Universals." Mind Vol. XLV. Jan. 1936. pp. 45-60.
McColl, Storrs "Abstract Individuals." Dialogue, vol. V. no. 2. 1966. pp. 217-231.
McGilvary, E. B. "Relations in General and Universals in Particular." Journal of Philosophy Jan. 1939. reprinted in Towards a Perspective Realism ed. Ramsperger. Open Court. 1956.
Moore, G. E. "Are the Characteristics of Particular Things Universal or Particular?" Proceedings of the Aristotelian Society. Supplementary Volume III. 1923. reprinted in Moore's Philosophical Papers Collier Books. New York. 1962. pp. 17-32.
Moore, G. E. Some Main Problems of Philosophy esp. chpts XVIII, XIX, XX, George Allen & Unwin. 1953.
Moore, G. E. "Identity." Proc. Arist. Soc. 1900-01. pp. 103-127.
Simons, P. "Relational Tropes." in Analytical Phenomenology: Essays in Honour of Guido Kung. ed. T. Harflinger and P. Simons. Dordrecht. (to appear).
Martin, C. B. "Substance Substantiated." Australasian Journal of Philosophy 58. 1980.
Prior, A. N. "Determinables, Determinates, and Determinants I, II" Mind Vol. LVIII. Jan 1949. p. 1-20, and April. 1949. pp. 178-194.
Stout, G. F. "Are the Characteristics of Particular Things Universal or Particular?" Proceedings of the Aristotelian Society. Supplementary Volume III. 1923.
Stout, G. F. The Nature of Universals and Propositions Oxford U. Press. 1921 see, also, Studies in Philosophy and Psychology Macmillan. 1930.
Stout, G. F. "Universals Again." Proc. Arist. Soc. Vol. 15. 1936. Van Iten, R. The Problem of Universals Appleton-Century-Crofts. 1970.
Hist-Analytic is most grateful to Keith Campbell and the Editor of the
The Modern Schoolman. for permission
to use an earlier version of this brief introduction (The Modern Schoolman,
Vol 79 (2002) 151-162) to Williams' paper.
Many philosophers have admitted the existence of abstract particulars, properties that occur as particulars, or, as Donald Williams dubed them, ‘tropes’. Anyone who accepts Peirce’s type/token distinction as holding for the colors, for example, accepts instances of properties as particulars. Anyone who, like Locke, adheres to a substance-property ontology, but also insists that all things are always only particular, affirms that properties are particulars – that is, tropes.
What marks off a trope metaphysic from others is to be found in what the ontology denies, rather than in what it affirms. A trope metaphysic gets its importance from the primacy that it accords to them. Its bite comes from the claim that these are the basic elements, the ‘alphabet of being’, as Donald Williams has it. This claim involves as an essential element the denial of the existence of genuine universals. This is a first and most significant dimension of economy. Further, in Williams’ theory, the primacy of tropes is coupled with a bundle theory of complex concrete particulars. So the theory also involves the denial of the reality of substances as substrata bearing the properties that inhere in them, or acting as an essential principle of individuation. Here is a second significant dimension of economy.
This search for ontic economy drives trope theory. Williams’s ontology admits but a single basic category, the abstract particular or trope. It is worth emphasizing that this position is not any form of Nominalism, where that term implies the denial of the existence of properties (and relations). Quite the contrary: trope theory affirms that Reality consists in nothing but (monadic or polyadic) properties. Rather than a Nominalism, this view is better described as a strict Particularism – it does not deny that there are properties, but denies that properties are Universals.
Nor does trope theory deny the existence of simple or complex individuals. It does not admit substance as a distinct category, but individual basic tropes are substances in the Humean sense – they are capable of independent existence. They do not require an underlying substratum to bear them. It is one of this ontology’s great attractions that it can in this way dispense with the Inherence relation, together with all its attendant difficulties.
In this classic paper, Donald Williams pioneers the trope metaphysic, providing us, in beguiling rhetoric, and a most admirable independence of mind, an original view of a perennial crux in metaphyics.
*****Keith Campbell is Emeritus Professor of Philosophy at the University of Sidney, Australia.
The following essay is taken from "On the Elements of Being." Rev. Metaphysics. 7. 1953. 3-18, 171-192. The pagination of the original is indicated in square brackets. There is some discrepency between the original and later publication of this paper, consequently some caution is advised in relying on the pagination, following p. 189.
First philosophy, according to the traditional schedule, is analytic ontology, examining the traits necessary to whatever is, in this or any other possible world. Its cardinal problem is that of substance and attribute, or at any rate something cognate with this in that family of ideas which contains also subsistence and inherence, subject and predicate, particular and universal, singular and general, individual and class, and matter and form. It is the question how a thing can be an instance of many properties while a property may inhere in many instances, the question how everything is a case of a kind, a this-such, an essence endowed with existence, an existent differentiated by essence, and so forth. Concerned with what it means to be a thing or a kind at all, it is some wise prior to and independent of the other great branch of metaphysics, speculative cosmology: what kinds of things are there, what stuff are they made of, how are they strung together?
Although "analytic ontology" is not much practiced as a unit under that name today, its problems, and especially the problem of substance and inherence, are as much alive in the latest manifestos of the logical analysts, who pretend to believe neither in substances nor in universals, as they were in the counsels of Athens and of Paris. Nothing is clear until that topic is clear, and in this essay I hope to do something to clarify it in terms of a theory or schema which over a good many years I have found so serviceable that it may well be true.
Metaphysics is the thoroughly empirical science. Every item of experience must be an exemplar and test case for the categories of analytical ontology. Technically, therefore, one example ought for our present theme to be as good as another. The more dignified examples, however, are darkened with a patina of tradition and partisanship, while some frivolous ones are peculiarly perspicuous. Let us, therefore imagine three lollipops, made by a candy man who buys sticks from a big supplier and molds candy knobs on them. Lollipop No. 1 has a red, round, peppermint head, No. 2 a brown, round, chocolate head, No. 3 a red, square, peppermint head. The circumstance here which mainly provokes theories of subsistence and inherence is similarity with difference: each lollipop is partially similar to each other and partially different from it. If we can give a good account of this circumstance in this affair we shall have the instrument to expose the anatomy of everything, from an electron or an apple to archangels and the World All.
My chief proposal to that end may be put, to begin with, as nothing more tremendous than that we admit literally and seriously that to say that a is partially similar to b is to say that a part of a is wholly or completely similar to a part of b. This is a truism when we construe it with respect to ordinary concrete parts, for example, the sticks in the lollipops. On physical grounds, to be sure, it is not likely that any three solid objects, not even three sticks turned out by mass industry, are exactly similar, but they often look as if they were, and we can intelligibly stipulate for our argument that our exemplary sticks do exactly resemble each other through and through. To say then that each of the lollipops is partially similar to each other, that is, with respect to stick, is to say that there is a stick in each which is perfectly similar to the stick in every other, even though each stick remains as particular and distinct an individual as the whole lollipop. We would seldom give a proper name to a lollipop and still more seldom to the stick in one, but we might easily do so - "Heraplem" for lollipop No. 1, for example, "Paraplete" for its stick, "Boanerp" for No. 2, and "Merrinel" for its stick. Heraplem and Boanerp then are partially similar because Paraplete and Merrinel are perfectly similar.
What now of the rest of each lollipop and what of their more subtle similarities, of color, shape, and flavor? My proposal is that we treat them in exactly the same way. Since we cannot find more parts of the usual gross sort, like the stick, to be wholly similar from lollipop to lollipop, let us discriminate subtler and  thinner or more diffuse parts till we find some of these which are wholly similar. This odd-sounding assignment, of course, is no more than we are accustomed to do, easily and without noticing.
Just as we can distinguish in the lollipops, Heraplem and Boanerp, the gross parts called “sticks,” namely Paraplete and Merrinel, so we can distinguish in each lollipop a finer part which we are used to call its “color” and another called its “shape” – not its kind of color or shape, mind you, but these particular cases, this reddening, this occurrence or occasion of roundness, each as uniquely itself as a man, an earthquake, or a yell. With only a little more hardihood than christened the lollipops and sticks, we can christen our finer components, let us say, and “Hamis” and “Borcas” for the respective shape components.
In these four new names, the first and last letters are initials of “Heraplem” and “Boanerp,” and of “color” and “shape,” respectively, but this is a mnemonic device for us, irrelevant to their force as names. “Harlac,” for example, is not to be taken as an abbreviation for the description, “the color component of Heraplem.” In a real situation like the one we are imagining, “Harlac” is defined ostensively, as one baptizes a child or introduces a man, present in the flesh; the descriptive phrase is only a scaffolding, a temporary device to bring attention to bear on the particular, entity being denoted, as a mother of twins might admonish the vicar, “Boadicea is the cross-looking one.”
Heraplem and Boanerp are partially similar, then, not merely because the respective gross parts Paraplete and Merrinel (their sticks) are wholly similar but also because the respective fine parts, Hamis and Borcas (their “shapes”), are wholly similar – all this without prejudice to the fact that Hamis is as numerically distinct from Borcas, to which it is wholly similar, and from Harlac, with which it is conjoined, and as the stick Paraplete is from the stick Merrinel, and as the whole lollipop, Heraplem, is from the whole Boanerp. The sense in which Heraplem and Boanerp “have the same shape” and in which “the shape of one is identical with the shape of the other” is the sense in which two soldiers “wear the same uniform” or in which a son “has a father’s nose” or our candy man might say “I use the same ident ical stick, Ledbetter’s Triple-X, in all my lollipops.” They do not have the same shape in the sense in which two children have the same father, or two streets have the same manhole in the middle of their intersection, or two college boys wear the same tuxedo (and so cannot go to the same dances together). But while similar in the indicated respects, Heraplem and Boanerp are partially dissimilar, and these are partially dissimilar because some of their finer points, for example, their colors, are dissimilar.
In like manner, to proceed, we note that Harlac, the color component of No. 1 (Heraplem), though numerically distinct from, is wholly similar to, the color component of No. 3. But No. 1 has not only a color component which is perfectly similar to the color component of No. 3; it has also a flavor component perfectly similar to the flavor component of No. 3. (It does not matter whether we think of the flavor as a phenomenal quality or as a molecular structure in the stuff of the candy.) The flavor-plus-color of No. 1 (and likewise of No. 3) is a complex whose own constituents are the flavor and the color, and so on for innumerable selections and combinations of parts, both gross and fine, which are embedded in any one such object or any collection of them.
Crucial here, of course, is the admission of a fine or subtle part, a diffuse or permeating one, such as a resident color or occurrent shape, to at least as good standing among the actual individual items of the world’s furniture as a gross part such as a stick. The fact that one part is thus finer and more diffuse than another and that it is more susceptible of similarity no more militates against its individual actuality than the fact that mice are smaller and more numerous than elephants makes them any the less real. To borrow now an old but pretty appropriate term, a gross part, like the stick is “concrete,” as the whole lollipop is, while a fine or diffuse part, like the color component or shape component, is “abstract.” The color-plus-shape is less abstract or more nearly concrete than the color alone, but it is more abstract or less concrete than color-plus-shape-plus-flavor, and so on up till we get to the total complex which is wholly is wholly concrete.
I propose now that entities like our fine parts or abstract components are the primary constituents of this or any possible world, the very alphabet of being. They not only are actual but are the only actualities, in just this sense, that whereas entities of all other categories are literally composed of them, they are not in general composed of any other sort of entity. That such a crucial category has no regular name is quite characteristic of first principles and is one reason why the latter are worth pursuing. A description of it in good old phraseology has a paradoxical ring: our thin parts are “abstract particulars.” We shall have occasion to use “parts” for concrete entities and “components” for abstract ones (and “constituent” for both), as some British philosophers have used “component” for property and “constituent” for concrete part. Recalling, however, that Santayana used “trope” to stand for the essence of an occurrence, 1 I shall divert the word, which is almost useless in either his or its dictionary sense, to stand for the abstract particular which is, so to speak, the occurrence of an essence.
A trope then is a particular entity either abstract or consisting of one or more concrete entities in combination with an abstraction. Thus, Napoleon and Napoleon’s forelock are not tropes, but Napoleon’s posture is a trope, and so is the whole whose constituents are his forelock and his posture, and so is residing on Elba.
Turning now briefly from the alphabet of being to a glimpse
1Santayana, George: The Realm of Matter in Works, New York, Scribners, 1937, Vol. 14. pp. 288-304.
of its syllabary, we observe two fundamental ways in which tropes may be connected with one another: the way of location and the way of similarity. These are categorially different and indeed systematic counterparts of one another - mirror images, as it were. Location is external in the sense that two tropes per se do not entail or necessitate or determine their location with respect to one another, while similarity is internal in the sense that given any two tropes, there are entailed or necessitated or determined whether and how they are similar. (What further this prima facie difference amounts to we cannot pursue here.) Location is easiest thought of as position in physical space-time, but I intend the notion to include also all the analogous spreads and  arrangements which we find in different conscious fields and indeed in any realm of existence which we can conceive - the whole interior stretch and structure of a Leibnizian monad, for example. Both modes of connection are describable in terms of distance and direction.
We are familiar in a general way with the numberless distances and directions which compose locations in space and time, but not so used to thinking of the limiting value of such location (though very familiar with the phenomenon itself) - namely, being in the same place at the same time, the unique collection and interpenetration which we call "belonging to or inhering in, or characterizing, the same thing." Russell calls this "compresence"; I shall follow Whitehead, Keynes, and Mill in calling it "concurrence." Plainly, what I called "color-plus-shape," in the second paragraph back, is not just the sum of a color and a shape but their sum in concurrence; we might have said "color-cum-shape." We can now explain furthermore that Harlac and Bantic, our lollipop colors, are really complex, each consisting of a knob-color and a stick-color in a certain relative location, and similarly for the shapes. Since there are no short words (like "red" and "square") which describe such complex colors and shapes, I shall ignore the sticks (supposed to be all alike) and use our trope names just for the qualities in the respective knobs.
It will not matter if the reader regards the use of "distance"
and "direction" for resemblance relations as metaphorical so long as he gets the idea. Here we have no trouble with the notion of the limiting value, zero distance or precise similarity, but may need to think a little more about the lesser similarity or greater difference which holds, e.g., between a red and a purple, and still more, unless we are psychologists or phenomenologists, about such elaborate similarity distances and directions as are mapped on the color cone.
Any possible world, and hence, of course, this one is completely constituted by its tropes and their connections of location and similarity, and any others there may be. (I think there are few others or none, but that is not necessary to the theory of tropes.) Location and similarity (or whatever else there is) provide all the relations, as the tropes provide the terms, but the total of the relations is not something over and above the total of terms, for a relation R between tropes a and b is a constitutive trope of the complex r'(a,b) (e.g., the concurrence-sum of Harlac and Hamis), while conversely the terms a and b will be in general composed of constituents in relation - though perhaps  no more than the spread of a "smooth" quality, a "quale," such as a color.
Any trope belongs to as many sets or sums of tropes as there are ways of combining it with other tropes in the world. Of special interest however are (1) the set or sum of tropes which have to it the relation of concurrence (the limiting value of location), and (2) the set or sum of those which have to it the relation of precise similarity (the limiting value of similarity, sometimes mischievously called "identity"). Speaking roughly now, the set or sum of tropes concurrent with a trope, such as our color component Harlac, is the concrete particular or thing which it may be said to characterize, in our example the lollipop Heraplem, or, to simplify the affair, the knob of the lollipop at a moment. By parallel, speaking roughly again, the set or sum of tropes precisely similar to a given trope, say Harlac again, may be supposed to be, or at least to correspond formally to, the abstract universal or "essence" which it may be said to exemplify, in our illustration a definite shade of redness.
(The tropes approximately similar to the given one provide a less definite universal.)
the phrase "set or sum" above is a deliberate hedge. A set is a class of which the terms are members; a sum is a whole of which the terms are parts, in the very primitive sense of "part" dealt with by recent calculi of individuals. In the accompanying figure, for instance, the class of six square, the class of three
rows, and the class of two columns are different from each other and from one figure; but the sum of squares, the sum of rows, and the sum of columns are identical with one another and with the whole.
What a difference of logical "type" amounts to, particularly in the philosophy of tropes, is far from clear, but  everybody agrees that a sum is of the same type with its terms, as a whole is of the same type with its parts, a man of the same type with his arms and legs. The concept of a class or set, on the other hand, is notably more complex and questionable. A class has not been shown to be in any clear sense an abstract entity, but there is some excuse for considering it of a different type from its members. Convinced that a concrete thing is composed of tropes in a manner logically no different from that in which it is composed of any other exhaustive batch of parts, we have every incentive to say that a concrete thing is not a set but a sum of tropes; and let us so describe it. Whether the counterpart concept of the universal can be defined as the sum of similars - all merely grammatical difficulties aside - is not so clear; there is little doubt that the set or class will do the job.
All the paradoxes which attend the fashionable effort to equate the universal humanity, for example, with the class of concrete men (including such absurdities as that being a feathered biped is then the same as having a sense of humor) disappear when we equate it rather with our new set, the class of abstract
particular humanities - the class whose members are not Socrates, Napoleon, and so forth. Still wilder paradoxes resulted from the more radical nominalistic device of substituting the sum of concrete men for their class, and though most of these also are obviated by taking our sum of similar tropes instead, I am sure that some remain. Because concurrence and similarity are such symmetrical counterparts, I shall not be surprised if it turns out that while the concurrence complex must be a sum, the similarity complex must be a set.
In suggesting how both particulars and abstract universals are composed of or "constructed from" tropes, I aver that those two categories do not divide the world between them. It does not consist of concrete particulars in addition to abstract universals, as the old scheme had it, nor need we admit that it must be constructible either from concrete particulars or from abstract universals, as recent innovators argue. The notions of the abstract and the universal (and hence of the concrete and the particular) are so far independent that their combinations box the logical compass. Socrates is a concrete particular. The component of him which is his wisdom is an abstract particular or "trope." The one general wisdom of which all such wisdoms are members or examples is an abstract universal. The total Socratesity of which all creatures exactly like him are parts or members is a "concrete universal," not in the idealistic but in a strictly accurate sense.
Having thus sorted out the rubrics, we can almost automatically do much to dispel the ancient mystery of predication, so influential in the idea of logical types. The prevalent theory has been that if y can be predicated of x, or inheres in or characterizes x, or if x is an instance of y, then x and y must be sundered by a unique logical and ontological abyss. Most of the horror of this, however, which has recently impelled some logicians to graceless contortions of language, is due to taking predication as one indissoluble and inscrutable operation and vanishes when our principles reveal predication to be composed of two distinct but intelligible phases. "Socrates is wise," or
generally "a is φ," means that the concurrence sum (Socrates) includes a trope which is a member of the similarity set (wisdom-in-general). When we contrast a thing with a property or characteristic of it, a substantive with an adjective, we may intend either or both of these connections.
The particular wisdom in Socrates is in  one sense a characteristic, i.e., it is a component, of him. This is the sense in which G. F. Stout held, quite properly to my way of thinking, that "characters are abstract particulars which are predicable of concrete particulars."2 The universal wisdom is in the second sense the characteristic of each such wisdom - this is the sense in which G. E. Moore could hold plausibly that even an event, such as a sneeze, has characteristics and is not one. 3 In the third or ordinary sense, however, the universal wisdom characterizes the whole Socrates. From this complication emerge at least two senses of "instance," the sense in which Socrates is a (concrete) instance of wisdom-in-general and that in which his wisdom component is an (abstract) instance of it, and the two notions of class, the ordinary concreta class consisting of Socrates, Plato, and all other whole wise creatures, and the abstracta class of their wisdoms, our similarity set.
Raying out around the problem of predication is many another half magical notion about essence and existence which we now can prosily clarify. As the obscurity of the essence or general character, for example, is mostly resolved by looking at it stereoscopically, to distinguish the dimensions of the universal and of the abstract, so too dark mingling of glory and degradation which haunts the existence of the individual is mostly resolved by the ideas of concreteness and particularity. The individual is hallowed both by the utter self-identity and self-existence of the particular occurrent and by the inexhaustible richness and the inimitability of the concrete. At the same time, however, it is debased by the very same factors. It seems ignobly arbitrary and accidental, qua particular, with respect to its mere
2 In Proc. Arist. Soc., Sup., 3:114, 1923. Stout's theory, in its fundamentals, is almost identical with the one I am defending.
3 Ibid., p. 98.
self in its external relations, because it thus shirks the resemblance role on which classification and generalization are grounded; and it has the confusion and unfathomability of the concrete, wherein every form struggles in a melee of forms so stupendous that the Aristotelians mistook it for formless matter.
A philosophy of tropes calls for completion in a dozen directions at once. Some of these I must ignore for the present because the questions would take us too far, some because I do not know the answers. Of the first sort would be a refinement and completion of our account of substances and of the similarity manifold. Of the second sort would be an assimilation of the very categories of our theory - concurrence, similarity, abstractness, and so forth - to the theory itself, as tropes like the rest, instead of relegating them to the anomalous immunities of "transcendentals" (as the old Scholastics said) and "metalanguage" (as the new scholastics say). What in fact I shall do here is to defend the fundamental notion that there are entities at once abstract, particular, and actual, and this in two ways: the affirmative way of showing how experience and nature evince them over and over,  and the negative way of settling accounts with old dialectical objections to them.
I deliberately did not use the word "abstract" to describe our tropes till we had done our best to identify them in other ways, lest the generally derogatory connotation of the word blind us to the reality of objects as plain as the sunlight (for indeed the sunlight is an abstract existent). The many meanings of "abstract" which make it repulsive to the empirical temper of our age suggest that anything abstract must be the product of some magical feat of mind, or the denizen of some remote immaterial eternity. Dictionaries, journalists, and philosophical writers are almost equally vague and various about it. Santayana has it that "abstract" means imprecise, but also "verbal, unrealisable, or cognitively secondary." 4 The abstract is equated with the abstruse, the ethereal, the mental, the rational, the incorporeal, the ideally perfect, the nontemporal, the primordial or ultimate, the purely theoretical, the precariously speculative
4 Realm of Essence Chap. 3. in Works
and visionary; or again with the empty, the deficient, the non-actual or merely potential, the downright imaginary, and the unreal. In some quarters, "abstract" means symbolical, figurative, or merely representative, in contrast with what is real in its own right.
On the same page the word may connote alternately the two extremes of precious precision and the vague, confused, or indefinite. Mathematics or logic is called "abstract" partly because it is about formal structures, partly because it treats them only hypothetically; but a symbolic calculus is called "abstract" because it it isn't about anything. Semanticists and professors of composition shudder away from statements on such "high levels of abstraction" as "Herbivority is conducive to bovine complacency" in contrast with the "concrete" virility of "Cows like grass," though the two sentences describe exactly the same state of affairs. Logical philosophers proclaim their "renunciation of abstract entities" without making clear either what makes an entity "abstract" or how one goes about "renouncing" an entity.
One wonders, in view of this catalog, if there is anything which would not on occasion be called "abstract." Most people  would deny that a cat is abstract, but an idealist would say that she is. Yet it would be a mistake to infer that "abstract" has been a wholly indiscriminate epithet. All the uses we have observed, and doubtless others, have stemmed from two roots which in turn are related in a very intimate way. They represent what various persons believed, often mistakenly, is implied by those root ideas. One of them is the use of "abstract" to mean transcending individual existence, as a universal, essence, or Platonic idea is supposed to transcend it. But even though this use of "abstract" is probably as old as the word itself, I think it was in fact derived, by natural mistakes which we earlier noted, from the other aboriginal use, more literally in accord with the word's Latin construction, which is virtually identical with our own.
At its broadest the "true" meaning "abstract" is partial, incomplete, or fragmentary, the trait of what is less than its including whole. Since there must be, for everything but the World All, at least something, and indeed many things, of which
it is a proper part, everything but the World All is "abstract" in this broad sense. It is thus that the idealist can denounce a cat as "abstract." The more usual practice of philosophers, however, has been to require for "abstractness" the more special sort of incompleteness which pertains to what we have called the "thin" or "fine" or "diffuse" sort of constituent, like the color or shape of our lollipop, in contrast with the "thick," "gross," or chunky sort of constituent, like the stick in it. 5
If now one looks at things without traditional prepossessions, the existence of abstracta seems as plain as any fact could be. (To call them "abstracta" is bad in so far as the word is artificial, but it helps to avoid the prepossessions, including the implication of transcendent metaphysics, which hang about "abstract entities" and the psychological implication, as if such objects were our own private inventions, of "abstractions.") There is something ironically archaic in the piety with which the new nominalists abhor abstract entities in favor of that "common-sense prejudice pedantically expressed," 6 the dogma of Aristotle that there can be no real beings except "primary substances,"  concrete individuals, as absolute and "essential" units, and thus turn their backs on one of the greatest insights of the Renaissance, that the apparent primacy of such chunky middle-sized objects is only a function of our own middle size and practical motivation. The great modern philosophies have rather sought the real in putative "simple natures" at one end of the scale and the one great ocean of action at the other end.
I have no doubt that whole things like lollipops, trees, and the moon, do exist in full-blooded concreteness, but it is not they which are present to the senses, and it is not awareness of abstracts which is "difficult...not to be attained without pains
5 Although this has been for centuries the root meaning of "abstract," the nearest to a straightforward statement of it which I found is in Dagobert D. Runes: Dictionary of Philosophy, New York, Philosophical Library, 1942, p. 2: "a designation applied to a partial aspect or quality considered in isolation from a total object, which is, in contrast, designated concrete." Even here the word "isolation," as we shall see, is delusive.
6Russell, Bertrand: History of Western Philosophy. New York, Simon and Schuster, 1945, p. 163.
and study." 7 To claim primacy for our knowledge of concrete things is "mysticism" in the strict sense, that is, a claim to such acquaintance with a plethoric being as no conceivable stroke of psychophysics could account for. What we primarily see of the moon, for example, is its shape and color and not at all its whole concrete bulk. If now we impute to it a solidity and an aridity, we do it item by item quite as we impute wheels to a clock or a stomach to a worm. Evaluation is similarly focussed on the abstract. What most men have valued the moon for is its brightness; what a child wants of a lollipop is a certain flavor and endurance. He would much rather have these abstract qualities without the rest of the bulk than the bulk without the qualities.
Integral to the debate between the metaphysical champions of the concrete particular and the abstract universal has been a discussion whether the baby's first experiences are of whole concrete particulars (his ball, his mother, and so forth) or of abstract universals (redness, roundness, and so forth). For what it may be worth, perhaps not much, a little observation of a baby or of oneself in a babyish mood will convince the candid and qualified that the object of such absorption is not the abstract universal (the infant does not "fall from the clouds upon the topmost twig of the tree of Porphry" 8) and certainly not the concrete particular (that "foreign thing and a marvel to the spirit" 9 which a lifetime of observation and twenty centuries of research hardly begins to penetrate), but is in sooth the abstract particular or trope, this redness, this roundness, and so forth.
Through the uses of the trope to account for substances and universals are of special technical interest, the impact of the idea is perhaps greater in those many regions not so staled and obscured by long wont and old opinion and not so well supplied with alternative devices. While substances and universals can
7 Berkeley, George: Principles of Human Knowledge, Introd., Sec. 10.
8 Blanshard, Brand: The Nature of Thought. New York, Macmillan, 1940, Vol. 1, p. 569.
9 Santayana: The Unknowable, Vol. 13, p. 352.
be "constructed" out of tropes, or apostrophized in toto for sundry purposes, the trope cannot be "constructed" out of them and provides the one rubric which is hospitable to a hundred sorts of entity which neither philosophy, science, not common sense can forgo. This is most obvious in any attempt to treat of the mind, just because the mind's forte is the tuning, focussing, or spotlighting - in brief, the abstraction - which brings abstracta into relief against a void or nondescript background. A pain is a trope par excellence, a mysterious bright pain in the night, for example, without conscious context or classification, yet as absolutely and implacably its particular self as the Great Pyramid. But all other distinguishable contents are of essentially the same order: a love, or a sorrow, or a pleasure.
The notion, however, gets its best use in the theory of knowledge. The "sensible species" of the Scholastics, the "ideas" of Locke and Berkeley, the ideas and impressions of Hume, the sense data of later epistemology - once they are understood as tropes, and as neither things nor essences, a hundred riddles about them dissolve, and philistine attacks on theory of knowledge itself lose most of their point. We need not propose that a red sensum, for  example, is perfectly abstract (whatever that might be). But even though it have distinguishable components as a shape and a size as well as a color, and though the color itself involve the "attributes" of hue, brightness, and saturation, still is abstract in comparison with a whole colored solid. According to reputable psychologists, further, there can be data much more abstract, professed empiricists to the contrary notwithstanding: data which have color and no other character, or even hue and no other attribute.
The person who uses the theory of tropes to sharpen his sight of what really is present and what is not may not credit the allegation of such still more delicate components of the mind as the imageless thought of the old German schools, or the nonimaginal ideas of Descartes, or the pure concepts of the Scholastics, or the ethereal Gestalten of more recent German evangels; but if any of these do exist, they exist as tropes. The same is to be said, I suppose, of the still darker categories of
pure mental act, intentionalities, dispositions, and powers. Such actual but relatively complex mental processes as trains of thought, moral decisions, beliefs, and so forth, taken as particular occurrents, whether comparatively brief or lifelong, and not (as nearly all phrases in this department at least equally suggest) as recurrent kinds, are tropes and compounded of tropes - and the kinds too, of course, are compounds of tropes in their own way. A whole soul or mind, if it is not a unique immaterial substance on its own, is a trope.  In one manner or another everybody grants that there is a very considerable correlation between the components of conscious experience and the processes of the body. The physical correlates of conscious tropes are then in general physical tropes - the patterns of arrangement and motion which behaviorally or physiologically are beliefs, discriminations, perceptions, desires, and the rest. In our happy-go-lucky way however, the human functions we generally speak and think about are "mixed tropes," like the "mixed modes" of the Cartesians. A belief, a sensation, an emotion, a purpose - each is partly the conscious item and partly the behavioral one.
On the model of such mixed tropes we must understand a love affair, an act of contrition, or a piece of impudence. A word or a sentence in a particular occurrence is a trope, mental, physical, or mixed. The "same" word in many occurrences is the corresponding universal. The distinction differs from Peirce's between "token" and "type" inasmuch as it avoids the usual identification of the token with the concrete ink splotch, for example, in which our trope inheres - an ill-timed obsession with substance which is out of accord both with ordinary ideas and with the fact that most verbal tropes cannot plausibly be imputed to any special concrete objects anyhow. A word is not a trope, but the connoisseur who gloats over its form, its texture, or its color is gloating over a trope. A musical performance, a song or a symphony, is a trope, and so is a musical theme - not the kind of theme, the universal which recurs throughout the same work in all its repetitions, but  any single case of it. The idea of the mixed trope may bring some order too into the philosophy of history.
where A. J. Ayer, for example, has wondered whether "the liberal tradition, or the American Constitution" is either a property or an individual." 10
If a bit of perceptual behavior is a trope, so is any response to a stimulus, and so is the stimulus, and so therefore, more generally, is every effect and its cause. When we say that the sunlight caused the blackening of the film we assert a connection between two tropes; when we say that sunlight in general causes blackening in general, we assert a corresponding relation between the corresponding universals. Causation is often said to relate events, and generally speaking any event is a trope: a smile, a sneeze, a scream, and election, a cold snap, a storm, a lightning flash, a conspiracy, perhaps a wave, and so on up to such big and important events that they have proper names, like Lulu, the H-bomb explosion. We have called a trope a "case" of its universal, while the universal is the "kind" of the trope, and so it is no surprise that a medical case is a trope - in the sense, at any rate, in which a person is said to have a case of typhoid fever rather than to be a case of it (for the latter "case" stands for the whole concrete individual). A high-school boy, uncoached, has assured me, "of course there's such a thing as redness - this pencil has a case of it."
When a scientist reports a temperature or a velocity or a viscosity, he is reporting a trope - not a universal, because it is a once-for-all occurrence, but not a concrete thing either, though doubtless a component of one. He is likely to call it an "aspect" of the thing or preferably a "state," and generally speaking, a "state" of a thing or a nation is a trope (though "state" too may mean a kind or preferably a "state," the universal). Recent developments in subatomic physics, a none too reliable oracle, suggest that an electron, e.g., just is an existent state and that the common-sense philosophy of the concrete here abdicates altogether in favor of the trope.
Since events and processes are tropes, and also cases and states, one wonders about "facts," states of affairs," and "what is the case. Mary's beauty is a trope; Mary-being-beautiful, the
10 In Mind, 61:441, 1952.
"fact" which makes "Mary is beautiful" true, seems a similar but queerer business. C. I. Lewis is surely right that a state of affairs is "abstract and adjectival" rather than a "chunk," 11 and it would be delightful to say that a state of affairs stands to its proposition as an ordinary trope does to its property (universal). But I shrink from endowing the theory of tropes with either the assets or the deficits of a theory of facts, of states of affairs, or of propositions.
A variety of trope which has been much entertained by the philosopher unawares is that of geometrical figures, circles, triangles, and so forth. These have been alternatively treated as if they were Platonic universals and as if they were concrete particulars, whereas in fact they are neither. Triangularity, to be sure, is an abstract universal, and a triangular object is a concrete particular, but a triangle is an abstract particular. Since a triangle, a circle, or any of the rest, while being particular, is an abstractum exhausted in one thin but salient character, the propensity of many generations of writers for taking them as typical "things" was perhaps largely responsible for that catastrophic doctrine of real essences by which truly concrete things like men or trees are supposed to be similarly dominated by single essential character in each.
If a geometrical figure is a trope, so is a woman's figure, and so is her complexion or her digestion - in that sense in which she is more concerned to take care of "her figure," "her complexion," "her digestion," than those of anybody else, however similar. Thus too when someone tells her, "I love the sweetness of your voice and the serenity of your brow," he does not mean, if he is wise or faithful, that kind of voice and brow, wherever they occur in the world manifold, but these particular cases. But while the complexion of a face, a smile on it, the whole expression, and the shape of the whole face or of any part of it, all are tropes, the face itself is a surface, and some logical philosophers who shy at "abstract entities" think that surface escapes that epithet. Well,
11 An Analysis of Knowledge and Valuation. La Salle, Ill.: Open Court, 1946. p. 55.
a surface does seem to occupy a sort of borderline status, but this is no more than our doctrine entails, for we have expressly denied that "between the  abstract and the concrete there can be no intervening stages." 12
As the shape is to the surface, perhaps, so the surface is to the solid. The bigger difference is that a surface is "concrete" in two dimensions as a triangle on it is not a concrete at all. This sort of quasiconcreteness, we note, belongs also to an instantaneous three-dimensional solid in comparison with one which is appreciably extended in time. Only an old familiarity with the terms of geometry, I think, makes anyone suppose that a surface or an instantaneous solid has in any fundamental way a more robust being than a four-dimensional shape or temperature. Similar questions and answers may be expected to attend such entities as the equator or a hole.
Many an entity often called "an abstraction," on the other hand, we may observe to be not abstract at all. God is not abstract, nor an angel, if they exist, and certainly the whole world manifold is not. A household is not, nor a church, nor a nation, nor the human race - these, in the usual acceptation are concrete wholes which happen to be much scattered or fissured; or, if some of them are classes, then though they may be still more peculiar in some way or other, they are not peculiar by being less than such a whole, as an abstractum is.
To combat our motley horde of examples of the abstract particular or trope, there are arrayed considerable forces of dialectic. An old indictment, "fallacy of hypostatization" or "reification," has been used against both the doctrine that universals exist and the doctrine that abstracta  exist. It betrays not only the misapprehension that the universal is the abstract (and the particular the concrete) but the misapprehension that those who believe that abstracta (or universals) exist also believe that they are concrete (or particular). To correct the second misapprehension first, what I assert is, of course, that abstract entities exist as well as concrete ones - not that the abstracta are
12 Ibid. p. 475. Lewis, who elsewhere suggests there are degrees of abstractness is here equating abstractness with universality, and concreteness and universality, we know, are just incommensurate.
concrete but not that they exist in addition to the latter either, and certainly not instead of the latter, but that both exist in the way that American countries exist as well as the states, or as yarn exists as well as socks, although all the counties are in states and much of the yarn is in socks.
The first misapprehension, that to be abstract is to be a universal, if left vague and implicit obstructs our thesis by adding to whatever liabilities attached to the idea of real universals, plus the extra liabilities due to the uncritical merger of the two. Made explicit, it frontally repudiates "abstract particular" as a contradiction in terms. Thus Moore replied to Stout that a "particular thing" means the same as "concrete thing," 13 but, strangely enough, that "particular quality" must mean the same as "definite or determinate quality," so that he can make no sense out of Stout's proposal except that no two things have exactly similar shades of red, for example. 14
C. D. Broad, in like vein, declared that it is plain "nonsense" to say that "the characteristics of particular things are particular" and that when McTaggart wrote that the "wisdom of Socrates" is distinct from wisdom in general (in which we can see a suggestion of the principle of the trope), he must mean only to distinguish "the perfectly determinate degree and kind of wisdom which in fact characterized Socrates" from the relativity indefinite or "determinable" wisdom which is to the former as mere redness is to the exact scarlet of a given rose. 15 Partly these demurrers are deductions from whole rival theories of universals, which we can leave aside to take care of themselves, but partly they they are due to less systematic prepossessions such as we have already treated by pointing out their  mistaken origins,
13 In Proc. Arist. Soc., loc. cit. , p. 97.
14 Ibid., pp. 100-103.
15 Broad, Charlie D.: Examination of McTaggart's Philosophy. Cambridge Univer., 1933, Vol. 1, pp. 25, 134. To understand the theory of tropes requires a clear understanding that we do not mean by "the particular redness of the rose" just a perfectly definite value of the determinable redness, which is still a universal, but the one abstract instance of it, numerically as distinct from other instances exactly like it as it is from a trumpet note.
for example, in the double meaning of "characteristic" or "characterize."
Although the meanings of "abstract" and of "universal" are almost as distinct as being a Methodist and being married, the fact that the words could so often be treated as synonyms is readily explicable by the fact that, just as it might happen that almost all the Methodists we knew were married, and all the married persons we noticed were Methodists, so - on the profounder principles of the arithmetic of combinations and probability which ground the inverse variation of intension and extension - it does happen that almost all the universals we notice are abstract and almost all the abstracta we notice are universals.
This is not to say that, even in point of psychology, we never abstract except to generalize, that is, never attend to an abstractum save to note that or whether it is replicated. A single sudden unique pain, for example, will arrest and absorb any of us. Among the many processes called "abstraction" only the most primitive quite deserve the name: the distinct awareness of the abstractum itself which occurs at the sensory and even the animal level. Hardly higher is a rudimentary generalization, the propensity to treat similar abstracta similarly; but the offices of conception are needed for awareness either that a given abstractum is abstract (and belongs to a concurrence sum) or that it exemplifies a universal (and belongs to a similarity set).
It was perhaps inevitable none the less that in order to master in some degree the staggering abundance of existence, the virtually infinite number of almost infinitely complex things - in order, as our information experts say, to "code" it economically - we should in unphilosophical practice attach our words and ideas not to members of the fundamental and unitary category but to the two derivative categories of unity-in-plurality. Not giving much explicit attention to a trope as such, we use it to identify the vast sum of tropes in which it is concurrent (each of them determining its own similarity set) and the far-flung set of tropes to which it is similar (each of them determining some concrete thing). Vaguely convinced that these two sorts of complexes are the warp and the woof of which is woven the intelligible fabric of things, we forget the intersections  of which
in fact they are composed, as the rows of a chessboard are composed of the squares.
In addition to complaints about the conjunction of particularity and abstractness, there are complaints about particularity and about abstractness separately. Russell, for example, if I understand him, has thought that to admit absolute particulars at all, that is, differences of case which are not differences of kind, is to fall into the occultism of substance. This dread our analysis of substance is calculated to allay, though the supposed logical and empirical claims of the principle of the identity of indiscernibles may eventually need some more adjudication. The arguments which I wish especially to weigh now, however, are those which assert that the status of abstractness itself is incompatible with actual existence. Because our tropes are advocated not as entities additional to concrete things but as constituents of them, any effective denial or defense of them must be an argument, not for or against a transcendental realm of being, but concerning what sorts of constituents are real and which, if any, are not, and hence the rights and significance of analysis.
When the issue is thus narrowed, the principle dialectical objection may be summed up in the old maxim that a true existent must be such as can exist by and in itself, per se and in se. We have called to witness the idealists that if this is taken without reservation, then ordinary concrete things - men's limbs as well as their temperaments, the men as well as their limbs - cannot be real either, for only the world as an eternal whole exists per se and in se. To preserve the advantage of the concrete over the abstract, we must reinterpret "per se" to accommodate the former but not the latter. If we do not altogether beg the question by defining "per se" to mean concrete, the most we can say is that the concrete is comparatively independent of its context and that it can, within wide limits, be moved around without losing its identity. Whereas we can pull the stick or an atom out of a lollipop and even put it back on demand, we cannot strip off its color and shape or extract the pure flavor of it, and still more obviously we cannot assemble a lollipop from such components. 
Even this difference, however, fades out under examination.
It is merely an accident of physical fact, after all, that sticks are not dissipated when removed from lollipops, or wheels from watches, as a volume of chlorine is when let out of a flask. Many concrete parts are physically incapable of removal, as the Mississippi River is from the Mississippi Valley, and most of them which are removable, as a whelk is from its shell, are so damaged by the operation that they are, as we say, not the same thing at all. But whether removable or not in the ordinary sense of "removable," they are always irremovable in the one queer respect which is cardinal to our kind of question. For the actual events which compose the existence of the watch wheel now before me on the table are numerically as distinct from those which compose the wheel inside the watch ten minutes ago, or back inside the watch again two hours from now, as any of these is from my fingers or from Jupiter. Their community consists logically of only a continuity of similar events or states strung between.
To bring this out best let us use the word "constituents" (what "stand together") for parts or components as they exist within a complex object as we describe it, and the word 'ingredients' (what "go into" the object) for those entities with which we operate when we start generating it or when we are through disintegrating it. The wheels of a watch or the stick of a lollipop qua "ingredients" happen to be conspicuously affiliated with the wheels and stick qua "constituents." The milk, sugar, eggs, and flour which went to making a cake, however, or the flaccid and ruined organs dissected our of an animal body, are much less fairly described as "the same as" the constituents of the object while it lasted.
The atomic theory was the great triumph of the feeling that things ought to have concrete parts which are at once constituents and ingredients, but with discontinuous and identityless electrons taking the place of atoms, this reassurance, limited to begin with, has become worth next to nothing. If now we turn back to our abstractions, the situations seems much the same with them. They often cannot be "moved" in even the crude sense in which some concrete things can, but in whatever sense "the same" wheel survives when taken from a watch, in that sense, if we can believe
our eyes, the color of a blouse, for example, may be transferred to the wash  water, or the glare of an electric light survives for a moment in the positive afterimage.
There remains one severe question, whether abstract qualities do not logically or metaphysically require their contexts as concrete entities do not. On the idealist logic of internal relations, everything requires or entails its whole cosmic matrix, but it seems at first sight that even those who deny this extravagance of idealism would have to grant it inconceivable that an abstractum should exist by itself, like the grin left behind by the Cheshire cat, and not as a component of something concrete.
This raises first the question how we define "concrete." If it means merely what does exist unconjoined with further components, then it is a verbalism that whatever exists must be concrete or a component of something concrete. The real question then is whether an entity which is "abstract" in the sense that it is conjoined in something concrete with other abstracta, as the shape of a watch is, for example, may be duplicated elsewhere by an entity precisely similar internally, but not thus conjoined with anything. Our instincts say "No," that there is a sort of cosmic standard of concreteness, a certain degree of richness or thickness, which perhaps is a general maximum that nothing can exceed, but which at any rate is a general minimum that an entity must attain in order, as the Scholastics say, "to be apt for existence," or that, in Aristotle's phrase, it "can exist apart." 16
Plausible though it be, however, that a color or a shape cannot exist by itself, I think we have to reject the notion of a standard concreteness. For it means that from the awareness of even the thinnest abstractum - indeed the thinner the better - we could deduce the presence of the rest of a concrete thing, if not its specific character then at least that there is something concrete there, as Descartes deduced from a conscious state the existence of a spiritual substance in which it inhered. It seems to me an analytic principle that all deduction must be analytic so that while any proper component  is deducible from the composite
16 Metaphysics, 1070b 36.
which contain it, no composite is deducible from any of its paper components, and hence that abstracta must in principle be as independent of their contexts as concrete things are.
Though it has been interesting to observe, for its own sake, that the abstract and the concrete entities are much alike with respect to independence and manipulability, this was nearly superfluous for our main purpose because the actuality of entities does not in any event depend on whether they are independent and manipulable but only on whether they are there. This was the import of our differentiation between constituents and ingredients. The constituents of the universe are not the ingredients of which God made it, if He made it of any, nor the fragments which will supervene when it decomposes, but are the stars and atoms and men, the shapes and tastes and numbers, which are present in it now; and in the same way the constituents of a lollipop, for example, are not the stuffs which went into the kettle, nor the shards which would result from running it through a grinder, but the sectors, the facets, the atoms, the structures, and the qualities which are its current parts and components in situ. That things consist of tropes does not imply either that they can be dismantled by taking tropes apart.
As constituents are not created by being manipulated, so they are not made by being noticed. The processes by which we notice the constituents of things, whether just to distinguish men, the moon, and the trees from one another in the universe at large, or to distinguish the smaller constituents, abstract or concrete, within such standard "things," is variously called "analysis," "division," "discrimination," and so forth. "Abstraction" is the kind of analysis or discrimination which notices abstracta. The whole  topic of analysis is surrounded with dark dissent and confusion, but while the typical allegations against it are in principle as fatal to the admission that a man really has arms and legs, or even that the World All has men in it, as to the thesis that a man's complexion or temperament is a real entity, brute common sense has generally seen to it that abstractive analysis bears the brunt of the critique.
Few persons perhaps would say outright that analysis must literally take its object apart, that where it cannot it fails altogether, and that when it does it destroys and belies the object; yet this is in effect what many quite responsible and sophisticated philosophers assume. "Analysis" itself is pure Greek for dissolution; "anatomy" means cutting up; "division," "partition," "composition," "made of," and so forth; all suggest assembling or disassembling. The root meaning of "abstract" as of "pick out" is to take away, so that Lewis quite innocently could describe an abstraction as an "excised element," Blanshard, a bit less innocently, refers to abstracta as "disjecta membra," and Wordsworth, with frank malice, charged that "we murder to dissect." 17
It is true that the analytic act of attention is sometimes facilitated by operating on the objects. Among abstracta, we may attract a child's notice to the color of a thing by varying the color while keeping the rest the same, or vice versa. Among concrete things we may sharpen awareness of the more discrete parts of a watch or frog by taking a specimen to pieces. The goal, however, is not a description of the debris but an inference from it concerning the original constitution of the thing and of other things like it.
The critic is perhaps less confused by the actual mayhem incidental to some analysis than by the notion that analytic attention itself literally "makes the distinction" which it pretends to  discover: it "draws lines," "picks out," "separates," "isolates." The supposed implication that the entities thus discerned were not there before their discernment is grounded partly in the general subjectivist maxim that to be is to be perceived, but it is grounded too in the immense overlapping and interlocking variety of distinctions among which the mind can select, so immense that the selection seems even to a realist a little like arbitrary creation. Anything, however, or anything at least which is big enough to be observable, must be analysable and truly analysable into innumerable different set of parts, as our figure
Poetical Works, London, Oxford Univers., 1950, p. 377 - respectively.
on page 81 as truly consists of the two vertical columns as it does of the three horizontal rows or of the six squares, and similarly for countless other sets of fantastic and filigreed sectors of it which do not happen to coincide with differences of inking. Different interests can fasten upon different sets of parts because they are all truly there to be fastened upon.
It is easy to understand how the mind can and must ignore most of the distinctions which actually exist; it is hard to conceive, and it must be rare, that the mind "makes" a distinction which does not exist. In brief, there is no more reason to suppose that we create the constituents we discern, whether concrete or abstract, than that a hunter engenders the tiger he tracks down and draws a bead on; and as any concrete object can and does truly consist of or contain many different sets of abstract components.
Something, of course, happens when we discern constituents, and the frequent phrase that we then "conceive" or "describe" them "in isolation" or "in abstraction from the whole" provokes the illusion that to discriminate an item is to falsify it because it is to consider it otherwise than as it exists (for it exists in the whole). But this is another trick of language. When we take account of a constituent (whether a concrete man or an abstract shape) "without" its context, we at worst only take account of it without taking account of it in its context; we not only do not remove it from its context, we never deny the context, and more often we take account of it in its context, acknowledging at once their distinctness and their mutual involvement. 
General consideration about analysis having left the abstract and the concrete quite on a level, without impugning either, we are returned to the purview of ontology with a strong prima facie case that the one great obvious difference between abstract constituents and concrete ones which we grasped immediately from examples, and which we indicated by such figurative words as the "fine" and "gross," is the only difference and that this is no more warrants a scruple lest the abstract "exist" less truly than the concrete, or "exist" in a queer mode or mitigated degree, or even belong to a different "type," than the fact that a horse is more
intelligent than a motorcycle but not so fast bestows on either of them a more intense being. It was the idealists again who were mainly responsible for the notion that what is not the complete reality is not completely real, so that the less an existent the less it exists. Yet even by this criterion, which has so little excuse, it is arguable that something big and abstract, such as the pattern of the solar system, might be more existent than something small and concrete, such as one's finger nail.
The idealists and other holists, at any rate, including the pragmatists and many common-sense pundit, unduly discredit the abstract by much overdoing its "thinness." Thus Blanshard summarizes a widespread impression when he belittles abstracta not merely as "disjecta membra of nature" but as "withered now and mummified," 18 as if they were like cast snake skins. In fact, of course, they not merely remain staunchly wedged in their concrete settings; they would not be at all withered or washed out if they could be removed. They are the very stuff of things, as brilliant or urgent as the case provides. The redness of the rose, though not all of the rose, is just exactly all of its real blazing redness.
The strength of a girder or the sweetness of a bonbon is a strength or a sweetness, no more, no less. What the complainant has in mind when he thinks abstracta must be withered or washed out is perhaps the rationalistic preference for the abstraction of structures, and especially spatiotemporal structures, rather than qualities. Thus the abstract has been identified with the "form" rather than the  "matter"; poetry is sometimes said to be more "concrete" than logical prose because it imparts sensuous quality rather than conceptual structure. Logical philosophers like Lewis and Russell have sometimes used "abstract" to stand for structures, such as the rotundity of a ball, to the exclusion of qualia, such as its redness. But whether or not a relational structure is properly called "withered," it is not in our usage any more distinctly abstract than a quale is.
18 Loc. cit., pp. 483-484. Cf. Henri Bergson: An Introduction to Metaphysics, New York, Putnam, 1912, p.20: "The concept extracted from the object has no weight, being only the shadow of a body."
The adjective "mummified" revives the ancient allegation that the abstract must be static, inactive, and ineffective, but nothing of course could be further from the truth. Our ideas of them may be somewhat supine, but the actual strength of a girder is what holds the bridge up; the heat of an atomic explosion scorches a city; and in fact, as we have observed, all of the efficacies we know are of the abstract on the abstract. The rush of a hurricane, a tantrum, the tempo of a dance, an action, a motion, a hurry itself, are tropes.
I am with those who believe that the mind is capable of the analytic attention by which a clear understanding of certain sorts of propositions, like some arithmetic and ontology, eked out perhaps by an example or two, suffices to verify them far better than a great deal of sampling and hypothesizing. Thus I am content with the rudiments of the theory of tropes as instanced by the lollipops. The catalog of miscellaneous applications and the expose of dialectical doubts about the abstract only confirm for me its aptness and the harmlessness of the opposition.
Some will prefer the test of formalization to ascertain whether what I have rather defiantly called the "elements of being" can be the values of variables in a neatly logical language. It is easy to shrug off this demand on the ground that no part of such a linguistic construction could possibly be more patent than the presence of tropes in a lollipop, nor the construction as a whole half so patent, and indeed the existence of an entity can in no wise be more affected by whether it can be a value of a variable than the birth of a man must wait on whether the haberdasher has a hat to fit him.  Nevertheless there is a certain macabre interest in the process of axiomatization as a disclosure of some of the systematic properties of our category, and I should welcome such a test. A similarly systematic but more philosophical way to put the principle through its paces would be to use it for the grounding and compounding of a whole world view, including a theory of perception and meaning and one of cosmic pattern and destiny. I can attempt neither of those here, but I shall point out something of what difference it makes, to the very
texture of our thought and the nature of things, that they are composed of tropes.
All the constituents of knowledge, we saw, are by our account of the same ontic denomination. Sensations, concepts, words, operations, each of them occurs primarily as an abstract particular, each determines its universal. A concept, whatever else it may be, not in itself either more abstract or more universal than a sensation, and while in its use it may signify an abstract particular, each determines its universal. A concept, whatever else it may be, is not in itself either more abstract or more universal than a sensation, and while in its use it may signify an abstract universal, it may equally signify a concrete particular - for just these are the two categories of entity which cannot be wholly present to the senses. There can be now at any rate be no ontological mystery about how general ideas are abstracted from experience or how general principles are induced from it, or of how they both apply to and can be true of further objects, concrete or abstract, in experience or outside.
Since ulterior objects, if they exist, must be woven of tropes just as the perceptual content is, there is no logical or ontological obstacle to the supposition that our impressions and ideas are caused by them and copy them. They may copy them by being similar to them structurally or even by being like them in quality. More than that, however, the perceptual datum may be not just similar to but numerically identical with a component of the object. Santayana and  Nelson Goodman, for example, thus are wrong since a conscious datum, a red patch, say, has no further concurrents in consciousness, it can have no concurrents at all. 19 It is possible to question that a datum must reveal all of its content; it is not possible to question that it cannot reveal its context - not even whether it has a context.
The doctrine of tropes thus accommodates, neither precludes nor entailing, the thesis of neorealism that the red sensum had when one looks at a rose, for example, is at the same time a
19 "...An actual appearance cannot be a part of a substance that does not appear; the given image has only the given relations." Thus Santayana: Scepticism and Animal Faith, in Works, Vol. 13. p. 53, and hence the debacle of "Nothing given exists." Goodman, who assumes throughout that iesse est percipi, decrees by definition that a visual red patch is concrete and precludes further concurrents. The Structure of Appearance, Cambridge, Massachusetts, Harvard Univer., 1951. p. 183.
member of the mind's fabric and a component of the physical rose, and it explains also why such direct awareness of the object after all tells us so little about it. While destroying a chief incentive to psychological dualism by suggesting how the odd apparent immateriality of mental content is mostly, at any rate, its mere abstractness, it nevertheless also accommodates what is essentially the Cartesian theory, that the tropes of the mind although like those of the body and its environing objects in being abstract particulars, are of remarkably different quality and structure and in fact constitute a closed complex, causally connected with physical processes perhaps, but not overlapping with any and indeed not in the same locational order with them.
Finally, of course, while the theory of tropes reduces the incentive to phenomenalism  or positivism by satisfying some of their principal motives, notably by accounting for both substances and essences without alleging anything more transcended than occurrent properties, it is perfectly consistent with those philosophies and as helpful to their formulation as to that of any other intelligible doctrine. The questions at stake among epistemological alternatives are thus adjourned from the high-priori venue to the ordinary jurisdiction of evidence and hypothesis. When we have thus seen that the problem of perception is not insoluble in some dreadful special way but only as an ordinary mundane problem is when the current evidence is consistent with pseudo problem and to dispose of the sense-datum language which is supposed to be responsible for it. Those are as if an amateur detective, at the stage where it is impossible to fasten upon the culprit among a half dozen suspects, decreed that, after all, the properly subtle disposal would be to assert that a murder is an indissoluble whole and that to split it into villain and victim is to be misled by a mistaken verbalism of the lawyers.
While our philosophy of tropes is so akin to empiricism in its intentions and apparatus and though it settles as little as possible by mere armchair analysis, it is an affirmative empiricism which gives the inquiring intellect a purchase on things that the most
thorough rationalism might envy. It is only the other side of the same coin that the theory, by taking seriously the idea of the whole and its constituents, declares for the real and literal validity of analysis against all kinds of romantic holism, whether revolutionary or reactionary, linguistic or metaphysical. If our language is not composed of elements which correspond one to one elements of its objects, it could be and ought to be, and I think that in fact it is. Except for the basest enclitics there are no syncategorematic words, and when allowance is made for accidental vagaries of grammar, the words of a discourse are names which stand substantivally for the several components of the  objects. With language, experience, and things at large thus intelligibly fragmentized and correlated, we can denounce as a fatal barrier to understanding the absolutism which declares that we know and understand nothing except as we know and understand everything.
Our scheme justifies a very skeptical view of the new cults of "appearing" which hope to work a philosophical reformation by substituting for the substantival reference of "There is a red sensum" the internal accusative of the "The thing looks red" or the absolute adverb of "I see redly." It is inimical to the "objective relativism" which transmutes qualities into relations and into relations irreducible to location and similarity, and is similarly skeptical of all other forms of contextualism. While explaining the sort of interfusion and compensation of abstracta which called forth the intuitionist metaphors of Bergson and James, it disposes of their misconception that this is a mystic marriage in violation of the laws of logic and the validity of concepts. It helps obviate also that more ancient principle of obfuscation, the Aristotelian and Scholastic notion that there is a surd element of indeterminateness, nonactuality, and accident in the essence of things, and the neo-Thomist idea that there is a prodigious extra bounty and enigma in their existence.
To take seriously and generally that as the whole consists of its constituents, so it contains its proper parts but they do not contain it, is to guarantee to analysis a real direction. There are real degrees of complexity and simplicity and corresponding
degrees of similarity. There is also a real difference between content and context, so that we had promptly to restore the sharp line, transgressed by the organicist and relativist, between those properties of a thing, like its shape or its color, which are literally to it and wholly compose it, and those which are relational, like being east of Suez or owning a television set, which literally are exterior to it and not among its components (though among the components of more inclusive things of which it is a part). This is one of the reasons we had no truck with location as a principle of individuation.
When therefore we say that a thing consists of its properties or that one property is contained in another, we mean it, as when we say that a library consists of  books or that a girl is contained in a daisy chain. When we say that it is an analytic truth that Middlesex County is part of Massachusetts or that disks are round, we mean this too: Massachusetts contain Middlesex County and a diskiness actually contains a roundness. To know what "disk" means, and to be acquainted with one disky trope, is to know that it has a round trope as a proper component and that every other disky trope, and its including concrete object, will contain a round trope too. The same simple-minded principle, however, which thus makes a part or component deducible from its whole forbids anything else to be deducible from anything. Part does not depend on part, nor whole on whole, nor part on whole. That whole does depend on part is so for the trivial reason that the whole is at least the sum of its parts.
It will be an act of justice, in conclusion, but also a further explanation and justification of the theory of tropes, if we consider briefly the anticipation of it in recent and classical philosophy. It is common intellectual currency in as much as almost everyone says things which presuppose it, most philosophers resort to it half explicitly to deal with occasions where the old categories of abstract universal and concrete particular are flagrantly incompetent, and quite a number have enunciated it in so many words. Yet it has had no continuing life in the history of philosophy and does not exist as an entity in the textbooks, so that discovery is one of those which ruminative persons have had to make over again and for themselves.
The doctrine is a natural child of the modern and empiricist view that a thing consists of its properties, or is the bundle of its characters, from which it varies by making explicit that this does not mean that the thing consists of universals (as about two-thirds of the bundle philosophers have asserted or implied) not that it consists of its appearances (as a different two-thirds have assumed). When William James wrote that experience "is made of that, of just what appears, of space, of intensity, of flatness, brownness, heaviness, or what not," 20 he seemed to sanction the thesis of the new realisms that the datum is a neutral entity or universal essence, 21 but I think he meant this flatness, this brownness, and so forth, i.e., the tropes. The simple ideas and sensible modes of Locke, and their counterparts in Hume's philosophy, since they certainly are not concrete though energetically denied to be universals, must be, if sooth were said, abstract particulars. Many of the "modes," "essences," and "natures" mentioned by Descartes, Spinoza, and Leibniz can be construed only as tropes.
Aristotle is generally interpreted today as having believed that the forms of things exist in them, not as universals, numerically the same in all their instances, but as distinct particulars; and when a neo-Thomist tells us that the "quiddity" in a thing is neither universal nor particular, he seems to intend the same idea. 22 Raphael Demos has explained how Plato himself distinguished between the rational form which is the true prototypal essence and the empirical form in the concrete instance. 23 It is
20Essays in Radical Empiricism, p. 27. See his Principles of Psychology, New York, Holt 1890, Vol. 1, p. 473, where he rejects Dewey's assumptions that "an abstract must eo ipso be a universal," and his criticism of Berkeley, Ibid, p. 469.
21 For a system of neutral entities, see Hold, Edwin B. : The Concept of Consciousness, London, Allen, 1914, and for the datum as essence, Santayana, op. cit..
22 See Maritain, Jacques: Introduction to Philosophy. New York. Longmans, 1930, pp. 172, 206. This seems to be the scholastics' position generally. It is because they specify a distinctive intellectual process to turn the quiddity into a universal but none to make it a particular, and also because I think that what's not a universal must be a particular, that I say the quiddity must be a trope to start with.
23 "Note on Plato's Theory of Ideas," Phil. phenomenol. Res., 8:456-460, 1948.
very difficult, indeed, to be sure of more than a verbal difference, though of some importance still, between our thesis that the world consists wholly of abstract particulars, linked piecemeal by a unique nexus of similarity, and an immanent realism for which the world consists wholly of universalia in rebus, linked thing wise by a unique nexus of compresence or togetherness. To see that a thing is exhausted in its abstract components is more than half the struggle.
Most of the recent "analytic philosophies" are so suspicious of abstract entities - are, in other words, so opposed to analysis, strictly speaking - that their use of the idea of the trope is only covert. A similar prejudice kept the philosophies of events from being frank that their elements are abstract particulars, but the Cambridge realists who declared that there are "two fundamentally different kinds of particulars, viz., occurrents and continuants" 24 almost openly accepted the notion of tropes, and A. C. Benjamin went a step further with "abstract occurrents." 25 I have cited Stout as preeminently the author of an unequivocal theory of tropes, but almost as clear in the cardinal recognition that the abstract need not be general or a universal have been H. W. B. Joseph, Dickinson S. Miller, William Savery, and more recently the doctrine, I think eventually got a good deal from McGilvary's "Relations in General and Universals in Particular." 26 The most that can be done by a thesis in first philosophy like ours is to prepare the way for more concrete and synoptic inquiry. We are only beginning to philosophize till we turn from the bloodless proposition that things in any possible world must consist of tropes to specific studies of the sorts of tropes of which the things in this world actually consist. it is a virtue of our thesis
24 Broad: Examination of McTaggart's Philosophy. Vol. 1, p. 139.
25 Benjamin, Abram C. : The Logical Structure of Science. London, Kegan Paul, 1936, pp. 73-76. He is right, I think, that in principle the distinction between occurrent and continuent cuts across that of abstract and concrete. What I said about events as tropes must be understood in the light of this.
26 J. Phil., 36:5-15, 29-40, 1939.
that it does not strangle or eviscerate the great problem in the philosophical cradle but keeps them alive to face the test of experience and logic. It will be a further virtue if it assists, as I think it will, in their formulation and appraisal. Are there only physical objects and energies, or only minds or spirits, or are they both? How, specifically, is a physical object constituted, and how a mind, and how are they related? These topics of gigantic hypothesis are the last of philosophy for which the first is made.