Concepts and Propositions, David Kelley 2025 by The Atlas Society

ConceptsandPropositions

Propositions are the units of thought and speech. They are the contents of knowledge and belief, of premises and conclusions, of questions and hypotheses, of hopes and fears. That dogs are animals, that the movie I saw last night was terrible, that a comet struck the Earth about 70 million years ago—the first is a biological fact, the second a value judgment, the third a scientific hypothesis, but each of them is a proposition. Understanding the nature of propositions is foundational in epistemology, with ramifications in other branches of philosophy.

This paper deals with two core issues.

Unity: On the face of it, a proposition has components put together in a certain structure. The proposition that dogs are animals is built from the concepts DOG and ANIMAL, as reflected in the fact that the English sentence expressing the proposition is built from the words “dog” and “animal.” But the proposition has a unity as the content of a complete thought, expressed in a grammatical sentence; and that unity goes beyond the mere combination of elements. A proposition can be either true or false, whereas its components are neither; the concepts DOG and ANIMAL designate categories of things, but neither makes a claim that is true or false. What explains the unity of a complete thought or complete sentence?

Truth: Philosophers who embrace a broadly realist view, in which our knowledge is about reality, typically hold that truth means correspondence to facts. Yet the correspondence theory of truth has been notoriously difficult to defend, or even to state clearly, because of difficulties in accurate understanding of two concepts: facts as the things true propositions correspond to, and correspondence as a relation between true propositions and facts.

Both issues have been the subject of philosophical analysis since ancient Greek philosophy and both of them remain active topics in contemporary philosophy. This paper will address the issues from the framework of the Objectivist epistemology. This view dates back to the work of Ayn Rand—in particular, her work Introduction to Objectivist Epistemology, 2 which dealt with the nature of concepts. The theory has developed further in the decades since but is still not well-known.3

2 Ayn Rand, Introduction to Objectivist Epistemology, in The Objectivist, 1966–67. This work was republished with extensive questions and Rand’s answers: Introduction to Objectivist Epistemology, expanded 2nd ed., edited by Harry Binswanger and Leonard Peikoff (Penguin, 1979, 1990). IOE hereafter.

3 For further development in Objectivist epistemology, see cited works by Harry Binswanger, Allan Gotthelf, David Kelley, James Lennox, and Gregory Salmieri.

As Rand noted, “The organization of concepts into propositions, and the wider principles of language . . . are outside the scope of this work.”4 The goal of this paper is to develop an Objectivist theory of propositions.

Section I will outline the existing framework of the Objectivist epistemology, including its fundamental tenets, its theory of abstraction and concept formation, and its view that consciousness is an active process. Section II will start to extend that framework, discussing the nature of the conceptual level of consciousness more broadly, including propositions and language. Section III will cover the structure of propositions, including a new account of their unity. Sections IV and V will address issues about truth, including the nature of correspondence and the ontology of facts. Along the way, I will comment on historical and contemporary work where relevant, but my focus will be on developing a theory of propositions on an Objectivist basis.

I. The Objectivist Framework

The Objectivist epistemology—to locate it in the philosophical landscape—subscribes to epistemological realism and to empiricism.

Realism holds that reality—the world of things with their properties, actions, and relationships—exists independently of human knowers. The nature of a thing does not depend on what we believe about it, or whether we know about it at all. Reality is not constructed by, or malleable by, our consciousness. (Of course we can change and create things by action, but not by thought alone.) This view, which Rand called “the primacy of existence,” holds not only that the objects of awareness do not depend on our awareness, but also that the function of consciousness is to identify what exists and the nature of existents. Cognition is inherently relational; it is of or about something. And that “something” is ultimately something in reality. Cognition is radically dependent on reality: it can only combine and integrate content derived from what’s real. It is of course possible to combine elements mistakenly, to mis-integrate, but not to generate the elements out of whole cloth.5

Realism has a long history in philosophy, as does its opposite number, idealism (which Rand called “the primacy of consciousness”). Both views have taken many different forms, with some attempts to combine

4 IOE, 75.

5 Ayn Rand, “The Metaphysical Versus the Man-Made,” in Philosophy: Who Needs It (Bobbs-Merrill, 1982), 29. Rand held that the primacy of existence is self-evident and inescapable. See IOE (1979), 240ff. Also Leonard Peikoff, Objectivism: The Philosophy of Ayn Rand, 19 ff. For a detailed exposition and analysis, see David Kelley, chaps. 1 and 6 in The Evidence of the Senses (Louisiana State University Press, 1988).

page 4 of 35 them. To avoid confusion with other uses of “realism” in philosophy, I will use “the primacy of existence” hereafter for the Objectivist thesis described above.

Empiricism holds that all knowledge is grounded in, derived from, and justified by sense-perception. For our purposes, the most important aspect of empiricism is its bearing on concepts. If knowledge is propositional in form, and if propositions are structured from concepts, it stands to reason that a theory of propositions should be guided by an analysis of concepts. An empiricist theory of knowledge needs a theory of how concepts are formed from and grounded in the perception of particulars by some process of abstraction.

Both in the Aristotelian tradition, and in the modern tradition from Locke to Mill, one will find many attempts to provide a theory of abstraction—using the term “abstraction” in the broadest sense to mean a cognitive process that starts with the perceptual awareness of particular things and results in concepts for kinds of things and for their qualities, actions, and relationships. Berkeley and Hume, of course, attacked the very notion of “abstract ideas,” but even they tried to explain how words, at least, could come to be associated with classes of particulars and thus function abstractly. In this very broad sense, empiricism is committed by its nature to abstraction from sense-perception, precisely because it rejects the claim that abstract concepts are innate.

Concept-formation

Rand developed an innovative theory of abstraction that avoids many of the problems encountered by previous theories. Concept-formation involves the conscious, deliberate integration of perceptual awareness. In briefest summary, we form a concept like TABLE in two stages. First, we observe that certain objects are similar in shape and function, by contrast with other objects—chairs, sofas, lamps—that differ in these respects. When we group things together mentally as similar, Rand refers to them as “units.” Her great insight was that similarity is a quantitative relationship. Similar things possess the same characteristic, but in different degree or measure. Tables are similar in shape, but their shapes vary quantitatively; one table is taller than another, one is larger in surface area, etc. 6 Birds fly, and the many determinately different ways of flying differ along dimensions such as rate of wing-beat, and ratio of beating to soaring (hummingbird vs. 6 On this view, the similarity between two things is not given directly. It is grasped by their common difference from a contrast object. “When A and B are seen as differing less than either does from C, . . . A and B are seen as differing quantitatively in a respect in which both differ qualitatively from C. The difference in shape between the two tables is quantitative, as opposed to the qualitative difference in shape between either table and the chair. Correspondingly, the similarity between the two tables is essentially the fact that they are commensurable: ‘similarity, in this context, is the relationship between two or more existents which possess the same characteristic(s), but in different measure or degree.’” David Kelley, A Theory of Abstraction, 2nd ed. (The Atlas Society, 2015), 14, quoting Rand, IOE, 15–16.

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condor); speed of flight (crow vs. falcon); height (chickadee vs. hawk) and amount of flying (chicken vs. Arctic tern).

The second stage of the process is the omission of the measurements of the units. Since the units differ only in degree, we can abstract from the differences and thereby treat the units as identical. We integrate the units into a new mental unit, the concept TABLE, on the principle that a given table must have some specific shape but may have any shape within a specific range.

Universality and abstractness are two essential features of concepts.

 A concept is universal because it subsumes a range of numerically distinct units, an open-ended set of existents. The concept DOG is not a name for a specific dog; it stands indefinitely for any and all dogs, past, present, and future.

 A concept is abstract because it omits the specific measurements of its units; it subsumes an open-ended range of qualitatively distinct things, an open-ended range of identities. A dog can have any identity within certain limits. When we describe a Chihuahua and an Alsatian as dogs, we are treating them as identical, despite their evident differences in specific characteristics. When we say that dogs bark, we are treating the sounds as identical, despite the differences among the particular sounds. When we say that birds fly, we are treating their different modes of flight as identical.

This view of concepts holds that there is no such thing in reality, apart from our minds, as an abstract table lacking specific measurements. Nor is there a universal category table existing apart from our mental processes. Things do not group themselves, or shed their measurements, on their own. In other words, Objectivism does not subscribe to a realist theory of universals in either the Platonic or the Aristotelian sense. Concept-formation does not reveal abstract kinds or features that exist independently in the objects themselves; it integrates and transforms the awareness of a network of determinate similarities and differences among the concrete, determinate properties of objects in such a way that we can grasp those properties in an abstract form, i.e., conceptually.

Identity of cognitive processes and states

An important thesis in the theory of concepts, but applicable to any form of cognition, is that consciousness itself has a definite identity as something that exists. Conscious awareness does not occur by magic. It is not a sheer revelation of what is outside the mind. It is a function performed by living organisms exercising specific biological organs and processes. Cognition in all its forms is the result of the interaction between the things known and the knower's faculties. This view is therefore not a form of “naïve realism.”

In perception, the processes that produce percepts are physiological, and the result is that we always perceive an object in a specific form—the object must appear to us in a specific way—determined by the

page 6 of 35 operation of the sensory systems. There is no way for us to step out from behind our senses to see how things “really” look, or “ought” to look. A thing can only look the way it actually does in a given set of circumstances, and this appearance is the means by which we are aware of its actual identity.7 But there is still a one-to-one relationship between the percept and its object. Not so at the conceptual level, because any concept is universal: a concept is a single cognitive unit designating an open-ended number of objects.

Like perception, however, conceptual knowledge has a particular identity that results from the nature and operations of our own cognitive capacities. The validity of conceptual cognition is not compromised by the fact that the abstractness and universality of our concepts are not mirrored in universal, abstract essences existing in the things themselves. Objectivity in cognition does not require that the contents of our mind mirror what is outside. This requirement, which many philosophers have implicitly imposed on cognition, is the product of a false model of the mind as a diaphanous medium.8 The objectivity of concepts derives from the fact that they are based on similarities and differences that do exist independently of us, in the things themselves; and from the fact that we process these similarities and differences in a manner required by the nature of our faculties.

Unit economy

An important aspect of the identity of concept follows from the well-known limit on the span of conscious attention. We can hold only a relatively few things in mind at once, whether perceived objects, random letters or numbers, etc.9 That fact is the basis for Rand’s principle of unit-economy:

Since consciousness is a specific faculty, it has a specific nature or identity and, therefore, its range is limited: it cannot perceive everything at once; . . . Whether the units with which one deals are percepts or concepts, the range of what man can hold in the focus of his conscious awareness at any given moment, is limited. The essence, therefore, of man’s incomparable cognitive power is the ability to reduce a vast amount of information to a minimal number of units—which is the task performed by his conceptual faculty. And the principle of unit-economy is one of that faculty’s essential guiding principles….

7 Kelley, Evidence of the Senses, chap. 3.

8 Ibid., 378 ff

9 G. A. Miller, “The Magical Number Seven, Plus or Minus Two: Some limits on Our Capacity for Processing Information,” Psychological Review 63, no. 2 ( 1956): 81–97. For an extended account of Miller’s insight and Rand’s principle of unit-economy, see Robert Campbell, “Ayn Rand and The Cognitive Revolution in Psychology,” Journal of Ayn Rand Studies 1, no. 1 (1999), 107–134.

Conceptualization is a method of expanding man’s consciousness by reducing the number of its content’s units—a systematic means to an unlimited integration of cognitive data.

A concept substitutes one symbol (one word) for the enormity of the perceptual aggregate of the concretes it subsumes.10

Unit-economy is the essential function of concepts, the cognitive advantage we gain by forming concepts through measurement-omission. As we will see in Section V, the principle of unit-economy extends to propositions as well.

II: The Conceptual Level

Propositions and concepts go hand-in-hand as partners in the conceptual level of cognition. Propositions are composed of concepts; a concept for a category or feature is a “file folder” (to use Rand’s analogy) for storing the propositional knowledge about things in the category or possessing the feature.

Consider two ways in which the conceptual level of cognition differs from the perceptual. The first is the retention of the concept. When I perceive a car passing my house, the perceptual awareness occurs at a specific point in time. It lasts for a specific duration, a brief one, and then it is over. I might retain some image of the car that I could recall as a perceptual memory. But if I do recall it, I will experience it as a memory—the content will be experienced as something from the past—rather than as a percept. When I form a concept, however, I retain the concept as a product. In the process of concept-formation, I become aware of a category of things, such as tables or apples, or of an attribute that things have in common (in different degrees) such as length. The concept is a way of detaching the category or the attribute, as a content of a cognitive action occurring at a specific moment, and retaining it as a cognitive content over time. My concept of apple is not a memory of the original act of concept-formation; it is a permanent possession, even when I am not actively employing it. In this respect, a concept is to concept-formation as a marriage is to the wedding.

In the same way, the propositional knowledge that whales are mammals was acquired in the form of a conscious judgment, when I first learned this fact, but is retained as knowledge over time, even when I am not thinking about it. The conscious judgment occurs at a specific point in time, and involves a conscious integration of the concepts WHALE and MAMMAL. But this action of mind produces the new content— the proposition that whales are mammals—along with the acceptance of that content as true. Both the content and the acceptance remain as more or less permanent deposits, available to me the next time I think about the subject.

10 IOE, 63–4. See also 165.

(This claim must be qualified somewhat. As Harry Binswanger notes, “A concept is a permanent file folder, but the majority of the propositions one forms are about particular, transient circumstances. . . . Such propositions are used but not stored.”11 That’s largely true. Estimates of an adult’s vocabulary range up to 50,000 words; the number of concepts is less after discounting for synonyms and other redundancies. By contrast, the best estimate of the number of propositions we process is 10,000 to 20,000 per day. Even if we have to reduce that number by an order of magnitude, it still vastly exceeds the number of concepts we possess. Nevertheless, many propositions are permanent: Laws and provisions of the Constitution, scientific laws, philosophical principles, and on and on, including all the knowledge we have acquired from education and experience.)

The permanence of concepts and propositions is the first relevant difference between the conceptual level and perception. The second difference is that concepts and propositions can be held in common by different people and communicated among people. Perceptual awareness occurs in an individual mind. You and I may perceive the same car, but our perceptual experiences are distinct; I have private access to my experience and you to yours. We can share them only by expressing them in words, i.e., conceptually, but not at the perceptual level. The same is true for our acts of concept-formation or judgment. But you and I may possess a concept with the same content: the category or attribute that we are aware of. And we may possess the same propositional knowledge of a fact.

Both of these differences—the retention and communication of conceptual content—are made possible by language. The process of forming a concept, Rand says, “is not complete until its constituent units have been integrated into a single mental unit by means of a specific word.”12 If one did not complete the process, there would be no way to retain the conceptual awareness over time; one would have to reenact the process of concept-formation each time one wanted to think about the category or attribute. (It may be possible to retain some simple concepts in the form of images, but this is a marginal and for our purposes irrelevant possibility.) And of course there would be no way to communicate one's conceptual awareness to another person without a concrete symbol that can be spoken or written. In the same way, the propositional grasp of a fact must be formulated in language in order to be retained and communicated.

A concept is not identical with a word, nor a proposition with a sentence. The same concept may be expressed in different words—“table” in English, “mensa” in Latin, and “trapeza” in Greek all refer to tables. The same proposition may be formulated in many different sentences, not only across different languages but within a given language, using variations in grammatical structure. “John opened the door”

11 Binswanger, How We Know, 183.

12 Rand, IOE, 19.

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and “The door was opened by John” express the same proposition and assert the same fact. Yet words and concepts, sentences and propositions, are not really distinct, either. A concept is not fully formed, as we noted, until it is associated with a concrete physical symbol. Conversely, the physical concretes—e.g., the letters t,a,b,l,e as marks on paper—are merely marks on paper and not a word if they are divorced from the concept. The relationship between a concept and a word can best be described using the Objectivist theory of concepts: a concept must have some verbal form but may have any (within limits set by the requirements of speech and writing). When we speak of a concept, we are abstracting from the particular verbal form in which it is concretized in order to focus on the identification of certain units through an integrative process of measurement-omission.

The same pattern holds for propositions and sentences. A proposition is not a linguistic phenomenon per se. When we speak of a proposition, we abstract from the particular verbal form of a sentence to focus on the cognitive content of the thought it expresses. Divorced from that cognitive content, a sentence would simply be sounds or marks on paper, without content, meaning, or reference. On the other hand, we cannot divorce the proposition from its verbal expression. We think in language; the same thought may be formulated in any of a range of possible sentences, but must be formulated in some particular sentence.

In other words, the basic semantic properties of language derive from the cognitive content of concepts and propositions, which in turn depend on the exercise of capacities for awareness and integration by knowers. Words and sentences do not have autonomous semantic properties of their own. They have such properties only in virtue of the way in which humans use these symbols to represent reality and express their understanding of it. In this respect, the framework I have described is in line with recent “activist” views that analyze propositions in terms of the cognitive acts of knowers.13 The Objectivist view, however, differs from these activist theories on many points. The most important is that, while some of these theories include the categories and properties of objects as components in their analysis of propositions, none offer a theory of how we form concepts for those categories and properties. As we will see, the epistemology of concepts provides the essential basis for understanding the unity of propositions.

On the basis of these presuppositions, let us turn to the new analysis of propositions and their unity.

III. The Unity of Propositions

An individual word usually gives us no clue to the cognitive structure of the concept, the nature of the cognitive integration by which units are integrated into a new mental unit. But the presence of grammatical

13 Jeffrey C. King, “Propositional unity: what’s the problem, who has it and who solves it?” Philosophical Studies (2013); Scott Soames, “Cognitive Propositions,” Philosophical Perspectives (2013); Peter Hanks, Propositional Content (2015), 4.

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structure in sentences does give us such a clue to the cognitive structure of the proposition. (In what follows, I will rely on the grammar of English sentences, which have a normal subject-predicate structure, as do sentences in many other languages, despite differences in other grammatical features such as word order, inflection, etc. But my concern is with propositions, not their linguistic expression.)

The basic type of proposition, out of which all the others are composed, has a simple subject-predicate structure: “I am cold,” “The man in the corner is bald,” “Whales are mammals,” “The first human being set foot on the moon in July 1969.” The subject is a noun, pronoun, or noun phrase indicating what the sentence is about. The predicate is the verb or verb phrase, including any complement or object of the verb, that attributes something to the referent of the subject. Such sentences differ from words or phrases that stand alone: “cold,” “July 1969.” Subject and predicate play different roles in a sentence, and both are necessary. A sentence cannot have two subjects without a predicate—e.g., “The whale mammals”—and cannot have two predicates without a subject—e.g., “Am cold, is bald.”

A sentence expresses a complete thought, whereas their components by themselves do not. But what does this mean? What makes a thought complete? The answer seems clear enough at one level. A sentence can make an assertion, declaring that something is the case. A word or phrase by itself asserts nothing. The word “whale,” for example, designates a category of animals. The concept it expresses is the locus for our propositional knowledge about whales, but the word in and of itself does not say anything about them. The phrase “set foot on the moon in July 1969” designates an action, but in and of itself does not say who or what did that action.

Unity of propositions

A sentence thus seems to have a unity arising from the way in which subject and predicate complement each other, a unity that is a feature of the sentence as a whole, as a grammatical structure, and not of the component words. At the turn of the 20th century, Gottlob Frege and Bertrand Russell wrestled with this issue. In a famous passage, Russell put the issue this way:

Consider . . . the proposition “A differs from B.” The constituents of this proposition, if we analyze it, appear to be only A, difference, B. Yet these constituents, thus placed side by side, do not reconstitute the proposition. . . . A proposition, in fact, is essentially a unity, and when analysis has destroyed the unity, no enumeration of constituents will restore the proposition.

Frege introduced the term “saturated” to explain this unity: The predicate of a proposition is “unsaturated” without a subject (or bound variable, in his logical system) to complete it.15 But Frege and Russell thought the explanation of unity lay primarily in the sentence or proposition itself, independent of the person

14 Bertrand Russell and Alfred North Whitehead, Principia Mathematica, 1912; 1963, 49–50.

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uttering or hearing it. Both the Objectivist epistemology and the activist view differ. It is the knower who combines subject and predicate to make an assertion (or to entertain a possible claim). Cognitive activities by the knower are the primary source of a proposition’s unity.

Some Objectivist philosophers deny that propositions have a unity to be explained. Binswanger, for example, says,

[A] proposition does not have the kind of unity that a concept has. Propositions are not integrations— not in the sense that concepts are. A proposition is an organized combination of concepts (or proper names) not an integration of them: the parts of a proposition—the individual words—remain apparent as components.16

Of course the words (concepts) are apparent, along with the grammatical structure. But that does not mean propositions have no unity. Consider a chemical analogy—the distinction between a compound and a mixture. Both are composed of elements. But:

 In a compound, elements are chemically bonded; in a mixture they are not.

 The elements in a compound have a fixed ratio (e.g., H2O); the elements in a mixture can vary in ratio.

 A compound can have properties in virtue of the bonding of elements.

By analogy, the elements in a proposition—the subject and predicate—are bonded, as opposed to being a list of concepts in random order. Those elements must be connected in a specific way grammatically (their “ratio,” by analogy). And a proposition has properties not found in the concepts that are its components: It is a complete thought, expressed in a complete sentence; it can be true or false; and it can be a premise or conclusion in inferences.

Binswanger is right that a concept has a special kind of unity. Like a chemical element, it is the simplest unit of the conceptual level of cognition; a concept C can be defined, and it can presuppose other concepts required to form and understand C, but it has its own unity in designating a category or property. In a proposition, as in a chemical compound, we can identify the components. But we cannot unbind them without destroying the proposition.

If a proposition is the product of an integrative cognitive action that binds the proposition together, then the question of unity is really an epistemological one, and the Objectivist epistemology suggests an answer.

15 Gottlob Frege, “On Concept and Object,” 179–80. It is not clear why the term “saturated” provides an explanation of unity rather than a re-description of it. That is not relevant to my view, however, so I will not pursue it here.

16 Binswanger, 183.

One aspect of the primacy of existence is the principle that cognition is identification: the awareness of the identity of what exists. This is a corollary of the law of identity. To be is to be something definite; whatever exists must have an identity. Indeed, an existent is its identity; it is what it is. There is no metaphysical gap or distinction between its existence and its identity, its being and its being something, as if its identity were a suit of clothes it could remove. The function of cognition, accordingly, is to grasp the identities of things. In any form of awareness, from the simplest sensation to the most advanced scientific theory, there is always something we are aware of, something that exists. And that something is something—it has some identity that we grasp.

At the perceptual level, the unity of existence and identity is reflected in the unitary character of perceiving: we never perceive a free-floating identity on the one hand, nor a characterless existent (a “bare particular”) on the other. Such things do not exist to be perceived. Perception is the awareness of entities, which we discriminate as units from their background. To be discriminated, an entity must differ qualitatively from its background in some dimension—color, texture, depth, etc.—and the perceiver must be aware of this qualitative difference. We therefore perceive the entity as an existent in and through our awareness of (some aspects of) its identity. 17

The process of concept-formation, however, allows us to abstract in varying degrees from the identity of a thing, on the principle that a given unit must have some specific identity in each relevant respect but may have any. Thus the concept “human” abstracts from a wide range of attributes that are part of the identity of any particular human being, such as hair color, intelligence, or political views; the concept “animal” abstracts from a wider range of variation in identity; the concept “organism” abstracts even further; and so on. We reach the limit of such abstraction in the concept of “existent” itself. At the same time, concepts allow us to abstract a given feature or dimension of identity—an attribute like length or wisdom, an action like running or flying, a relationship like marriage—from the existents that possess the attribute, perform the action, engage in the relationship. Once again, the principle is that a feature or dimension of identity must be the identity of some existent, but may characterize any existent within a given range. We reach the limit of abstraction with the concept of “identity.”

In varying degrees, therefore, concepts abstract existents from the identities they possess, and identities from the existents possessing them. But there is no distinction between existence and identity in reality. To make an assertion, one must restore the unity explicitly. This is the basis for the subject-predicate structure of a proposition. It has traditionally, and correctly, been held that the function of the subject is to refer, that of the predicate to describe or characterize what is referred to. This difference in function underlies the grammatical differences. A subject expression like “all whales” cannot function as a predicate: it can

17 Kelley, The Evidence of the Senses, chap. 5.

designate certain things but does not say anything about them. A predicate expression like “are aquatic mammals” cannot function as a subject: it can attribute something but does not refer. The subject of a proposition specifies one or more existents as the objects of awareness, the predicate specifies some aspect of their identity, and the proposition as a whole attributes that identity to the existents. As a result, every proposition is a particular expression of the law of identity: a thing is what it is.18

A possible objection is that “A thing is what it is” is itself a proposition, with its own unity as a proposition. What is the basis of its unity? Doesn’t it need explanation? Are we just pushing the question of unity to a higher level—like turtles all the way down, propositions all the way up?

The objection misses the point. To offer any explanation for the unity of a proposition, we obviously have to use propositional statements. But the explanation is not about those propositions. It is about the facts they identify in reality. Consider a particular case: I am walking in a forest, I see a deer and see that it is brown. The judgment “This deer is brown” is the cognitive form in which I identify the nature of what I see. If we spelled out the cognition, its content would be “The features of what I see fall within the range of measurements of the concepts DEER and BROWN.” My judgment is propositional; it has a subject unified with a predicate. But the judgment is about the deer, and its unity is our conceptual way of grasping its identity. The proposition has parts that we unify in a relational way, joining the subject with the predicate. But there’s no relation between the deer itself and its color, no parts to join together. The deer is its identity. Like any other existent, it is what it is. And the latter statement, “it is what it is,” is the epistemological explanation of the proposition’s unity.

Grammatical structure

So far, I have outlined a theory about propositional unity, but at a high level of abstraction. The grammatical structures of thought and speech allow us to unify subjects and predicates in many different ways. To appreciate that variety, consider a few of the structures that can be used to make propositions of different types.

In the simplest type of proposition, a perceptual judgment like “This is a chair,” the existent is specified by the demonstrative pronoun, which refers to the object I am perceiving. In this case, we see the division of labor between subject and predicate in its purest form. The subject “This” does nothing but refer to a certain existent without characterizing its identity; it is the predicate alone, “is a chair,” that attributes identity. Of course, we cannot specify an existent without any awareness of its identity. In the case of the perceptual judgment, that awareness is provided by the perception of the thing: the reference of the term

18 cf. Peikoff, “The Analytic-Synthetic Dichotomy,” in IOE, 100–101: “Every truth about a given existent(s) reduces, in basic pattern, to: ‘X is: one or more of the things which it is.’”

“this,” as a pronoun, is determined by whatever it is that I have discriminated perceptually. If I then judge “The chair is brown,” the subject refers to the entity not merely as an existent, or as the object of perceptual discrimination, but specifically as a chair. Nevertheless, the subject alone, “the chair,” does not explicitly attribute an identity to the thing. It does so only implicitly, as a result of some prior explicit recognition of it as a chair and does so for the purpose of going on to identify its color

Demonstrative pronouns like “this” and “these” can specify one or more particular existents as individuals; the same is true of names (John Smith, the Smiths). But we also—and indeed, more often—specify existents conceptually, with subjects that contain one or more concepts. In this respect, it is important to distinguish two relationships, designation and reference.

I will use the term “designation” for the relationship a concept bears to its units. Any concept designates its units qua units, i.e., as members of an open-ended category of existents whose measurements (within a given range) are regarded as omitted. It is a uniform relationship, the same for all concepts. The concept MAN designates an open-ended category of things, the concept RED an open-ended category of color qualities, the concept RUNNING an open-ended category of actions, etc. The same is true for phrases, like “brown squirrel”; many propositions have phrases as subject terms to designate a category, especially when we do not have a separate concept for that category. In every case, the concept or phrase designates all its units, qua units. Within a proposition, however, a concept may be used to refer to all or some of its units in many different ways. We use various grammatical devices to “target” certain things and specify precisely what we are talking about. I will use the term “refers” to indicate what a proposition is about, as distinct from the units a concept designates.

Consider the following uses of “man” as the subject of a proposition (“man” is intended to mean male, “person” or “human” to mean humans):

1. “A man is at the door.” “A man” refers to an individual unit of the concept, identified only as an individual unit.

2. “The man in the corner is drunk.” “The man in the corner” refers to an individual whom I previously identified, say by observation, as being in a certain place. This sentence is about a specific person whom I identify, for your convenience, as being in that place.

3. “The man who committed this crime is a fiend.” This is like (2) except that I do not have a specific man in mind; I am referring to whoever fits the description.

4. “Humans are rational animals.” “Human” refers to the category qua category, i.e., as a single unit embracing all the members of the category. This grammatical structure most clearly illustrates Rand's

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analogy between concepts and variables in mathematics. “Human” refers to humans as such, any human, just as the variable x in x + x = 2x refers to a number as such, any number.19

5. “Some people are married.” “Some people” refers to one or more units of the category as distinct units that may have distinct characteristics.

6. “Men have walked on the moon.” This is like (5) in referring to distinct units qua distinct, except that the plural form specifically refers to more than one unit.

7. “All people need oxygen to survive.” This is like (4) in referring to the category as a whole, but does not refer to the category as a single unit; “all people” refers to the individual units of the category, specifying all of them without exception.

These examples illustrate the two chief ways in which the English language allows the subject of a statement to refer specifically to certain units of a concept. The first is the use of quantifiers: “all,” “some,” the plural form, etc. The second is modification, the use of adjectives and adjectival phrases and clauses: “The man in the corner,” “The man who committed this crime.” A concept, as I noted, is universal. It designates a plurality of numerically distinct existents. When a concept is used in the subject of a proposition, we can, so to speak, adjust the exact degree of universality we want through quantifiers and modification.

A predicate per se does not refer, though it may contain elements that do. In a relational statement like “Mickey Mantle hit the ball into the bleachers,” the predicate contains expressions that refer to what he hit (the ball) and the place he hit it to (the bleachers). But the predicate as a whole, “hit the ball into the bleachers,” does not have a referential function; it specifies an action that is being attributed to Mickey Mantle. In other words, just as a subject normally cannot refer to an existent without characterizing its identity, a predicate often cannot characterize something without referring to one or more existents. But reference is the primary function of the subject, to which any implicit attribution is a means; and attribution is the primary function of the predicate, to which any reference it contains is a means.

The function of the predicate, we have seen, is to specify particular aspects of the identity of the existents we are referring to. The great advantage of concepts is that they allow us to break down the identity of a thing, which exists as a single totality in the thing itself, into specific features and dimensions of identity: specific attributes, actions, and relationships. In a proposition, the concepts we use in the predicate allow us to attribute these specific features and dimensions to things. In this sense, to put the matter in basic epistemological terms, a proposition represents the opposite pattern from a concept: in concept-formation, we differentiate a group of similar things from all others in order to integrate them into a new mental unit;

19 Rand, IOE, 18.

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in a judgment, we integrate concepts into a proposition in order to differentiate a particular aspect of the subject's identity from all others.

Since concepts are abstract, a predicate specifies a particular aspect of identity abstractly. The proposition “John is a man” asserts that John's identity falls within the range of omitted measurements for the concept “man”: he bears some quantitative relationship to the other units of the concept, along each relevant dimension of measurement, but may bear any quantitative relationship. The same kind of analysis applies to propositions that specify a particular attribute: “John is tall” asserts that his height is within the range of omitted measurements of the concept “tall.” “John is married” asserts that John's relation (to someone) is within the range of omitted measurements for the concept “marriage.” These propositions repeat the cognitive act of integration involved in forming the predicate concept. We are simply recognizing a new existent as a unit of the concept by omitting the relevant measurements. The same is true for a proposition with an already conceptualized subject, like “Copper is a metal.” Here we locate the units of the concept “copper” within the range of omitted measurements of the concept “metal.”20

But just as we can adjust the degree of universality in what the subject refers to, we can adjust the degree of abstractness with which the predicate specifies identity. Instead of describing John as tall, we can say that he is 6'4" tall, thus reintroducing a measurement omitted in forming the concept “tall,” but reintroducing it in an explicitly conceptual way, as a numerical multiple of a unit of height. Again, instead of saying that he is married, we can say that he has been happily married to Beth for five years. Here again we have filled in some of the measurements that are omitted in forming the concept “married”: whom he is married to, for how long, with what degree of happiness. When we say that copper melts at 1083 degrees Centigrade, we ascribe to the units of “copper” the capacity designated by the concept “melt,” a change of state that must occur at some temperature but may occur at any; but we also specify the specific measurement of temperature at which these units melt.

As an integration of concepts, to summarize, a proposition's cognitive content is a product both of what it integrates—the component concepts (along with names, demonstratives, etc.)—and of the grammatical form of the integration. The basic form is the subject-predicate structure. The function of the subject is to refer, to specify one or more existents, and the grammatical structure of the subject allows us to select the degree of universality in the range of existents referred to. The function of the predicate is to characterize, to specify an identity, and the grammatical structure of the predicate allows us to select the degree of

20 Since we already possess the concepts involved, with their range of omitted measurements, we can also describe what the knower is doing as “measurement-inclusion,” a key term in Binswanger’s (2014) analysis of propositions.

abstractness in the specification of identity. The integration of subject and predicate into an assertion reflects the law of identity—in particular the fact that existence and identity are not distinct.

IV. Propositions and Reality: Cognitive Ontology

The preceding sections were concerned with the internal structure of propositions, both their deep unity in linking a subject as referent with a predicate stating its identity, and the surface varieties in meaning based on grammatical structure and the reference of the component concepts. It is time now to address the other major issue: the relation of propositions to reality—specifically, the nature of truth. I will discuss truth in the next section. In this section, however, we need to set out some preliminaries.

Assertion and truth: So far, I have said little about the distinction between the content of a proposition and the assertion of it as true, nor on the distinction between true and false propositions. I dealt with propositions as asserted, and as being true. That was deliberate. The primacy of existence—in particular the principle that the function of consciousness is to identify things in reality—has a methodological implication. We start by looking at cases in which that function is performed successfully. On that basis we can explain failures by examining how and where the process of knowing goes off the rails. Both distinctions, however, are important.

 Assertion: Propositions are made to be asserted. They are the means for acquiring and retaining knowledge of reality. But of course propositions can also be the content of states that don’t necessarily involve assertion, such as questions, made-up stories, and hopes and fears, among other “propositional attitudes.” We can also entertain a proposition, as with hypotheses in science or accusations in a criminal trial. Indeed, this is an important feature of conceptual-level cognition. The ability to entertain a proposition without asserting it allows us to pose questions for inquiry; it guides the search for evidence that will establish whether the proposition is true and can be claimed as knowledge.

 Truth: A percept cannot be evaluated as deceptive, true or false, veridical or non-veridical. Perceptual awareness is the result of causal interactions between the object and our sensory systems. Choice and inference are not involved. By contrast, the conceptual level does involve choice and inference, and the scope of failure is huge. There are many ways of “going off the rails,” through cognitive bias, fallacious reasoning, misinformation, and poorly formed concepts, to name a few sources of error. So the analysis of truth has to take account of the ways in which propositions can be false. The proposition that “water runs uphill,” for example, is not the awareness of a fact. But the concepts in that proposition designate real existents, and the proposition has a meaning. Someone who asserted that proposition would purport to assert it as true. How could a false assertion have that much going for it? We will address that issue in the next section.

Identity in cognition

The main preliminary, however, is a set of issues about what we can call cognitive ontology: the ontological status of cognitive states and their objects in the world. As explained in Section 1, the primacy of existence is not a form of naïve realism. Every mode of cognition has an identity due to the nature and operation of the cognitive faculty. For perception, the interaction of sensory systems with objects and with the conditions of perception results in the awareness of the object in a specific form—the way the object appears to the perceiver. In the case of concepts, the essential identity is their universality and abstractness, so that conceptual awareness of things takes the form of grasping them as members of universal categories and instances of abstract properties.

What is the ontological status of these elements of cognition: form in perception, categories and properties for concepts? Many philosophers have assumed that there are just two alternatives: they are either in the mind or in the world. Their ontological status is either subjective or objective—where “objective” means mind-independent. To say that something is objective, on this assumption, is to say it exists in the world apart from minds, and would exist even if there were no minds, no conscious awareness. But in the world apart from minds there are only particular, concrete entities, attributes, actions, and relationships. I am speaking here of concrete particulars, not abstractions, and not tropes (concrete but repeatable properties21):

A particular tree in a forest, not the categories tree or forest; the specific green color of the tree, not the abstract attribute green, nor even the specific shade as a color (trope) some other tree might have; the swaying of the tree in the wind, not swaying in general as an abstract type of action; the tree’s position in the forest as a concrete relationship, not location or spatial position in general.

Where do perceptual appearances, categories and properties fit in the traditional subjective/objective dichotomy? Some philosophers have held that (abstract, universal) properties exist in the world apart from minds. Among those who reject that realist theory of universals, while accepting the subject/objective dichotomy, a common view is what I call the representationalist model of cognition, in analogy with or generalization from the representational theory of perception.

The representational view of perception has taken many forms, but these are its essential tenets: 1. There is some element that represents the thing, property, or event in the external world that we perceive. For the traditional representationalist theory of perception, this element is an idea, image, or sense-datum that is the immediate object of awareness. The essential point here is that there’s something in perceptual experience that does the representing.

21 Anna-Sofia Maurin, “Tropes,” Stanford Encyclopedia of Philosophy

2. The representational content is internal to the perceiver’s experience. It is subjective in the sense of being in the mind, or a feature of conscious experience, as distinct from the real, external, independent existence of the external object in the world. 22

Generalizing from the representationalist theory of perception to conceptual modes of cognition, this model holds: i) that a cognitive state has an inner content which can exist or occur in the absence of any external object; and ii) that such states may also bear a relation to external objects. The distinction between the inner, subjective content and the objective external object is variously described as sense vs. reference, connotation vs. denotation, intension vs. extension, etc. Representationalist theories in perception attempt to isolate the effects of our own faculties on the way things appear, and to reify these effects as a separate (immediate) object of awareness. In the same way, representationalist views of concepts attempt to isolate the effects of our mode of conceptual cognition—the fact that we abstract from concrete objects and their specific characteristics to form abstract concepts of categories and properties—and to reify these effects into separate internal objects. The representationalist theory of perception says that since we perceive objects in virtue of the way they appear, those appearances are the immediate contents of awareness. In the same way, representational theories of concepts hold that since we grasp objects conceptually in virtue of their attributes, those attributes are the immediate cognitive content of our terms—their sense or intension.

There are many variations of this theory in the philosophical literature, and many critiques. I will not pursue those variations and objections further. I mention the approach only to contrast it with the Objectivist view.

The subjective-objective distinction as normally conceived does not exhaust the alternatives. A third alternative is that perceptual appearances, and categories and properties, are aspects of things’ identities as grasped by consciousness through certain cognitive processes. This is an ontological status arising from the fact that consciousness has a specific identity, and in particular from the fact that conceptual awareness operates by a specific process of integration by measurement-omission. In the Objectivist epistemology, this ontological status is called “objective,” taking its name from the epistemological concept of objectivity, which means a focus on reality and the proper use of concept-formation, logic and evidence in reaching conclusions. The mind-independent status commonly assigned to that term is better called “intrinsic”: the specific, concrete objects, characteristics, actions, and relationships intrinsic in the world apart from our awareness.

By contrast with the representationalist model, objective phenomena are not inner objects. They are relational. In perception, the way an object appears to a perceiver—the form of his perceptual awareness— is not a mental content. It is the product of the interaction between the object and the perceiver’s sensory system; it cannot be located in the object apart from the perceiver’s awareness nor in the perceiver’s

22 cf Evidence of the Senses, 10–29 and chap. 4.

awareness apart from the object. As with other kinds of relations, the relation cannot be located, ontologically, in either of the relata. 23

A parallel point applies to the conceptual level. A concept for a category of things is the awareness of those things in a universal and abstract way, based on their identity as existents and on the nature of our capacity to form concepts. The concept is in the mind, like the perceptual awareness of an object. But its objective content, the category, is the product of the way we integrate existents with their specific identities into conceptual awareness, in accordance with the nature and operation of our conceptual capacity. By analogy with perception, the objective content—the category or property—is not in the mind apart from the existents “out there” in the world, nor is it in the world apart from the mind.

The separation of sense from reference in the representationalist model of concepts attempts to separate the contribution of reality from the contribution of mind to the content of concepts. On the Objectivist view, that dichotomy is invalid. As Rand put it, “Units do not exist [intrinsically] . . . , units are things viewed by a consciousness in certain existing relationships”—the relationships of similarities and differences involved in concept-formation, as described in Section 2.24

Those units, as existents, have the full identity they have. The category includes those existents, with all the properties they have. The concept of that category, for any person possessing it, can include only what he knows. But the concept is open not only to new instances as one encounters them but also to new properties as one learns about them. In terms of the measurement-omission view of concept-formation, we don’t omit measurements of dimensions we are not aware of, but the concept includes the policy of omitting the measurements of new dimensions as we become aware of them. A child’s concept DOG might include the properties of being furry, larger than a cat, and usually friendly and protective. An adult’s concept includes the knowledge that dogs are carnivores, were domesticated from wolves, etc. A veterinarian’s concept includes more extensive knowledge of dogs’ physiology and anatomy. But across that range, the category dog remains the same, including all dogs that have or will exist; and all the characteristics they have, not only the ones they have in common but also their differences. The view that the concept DOG has a sense that includes a few common properties, or even all the ones we know at present, would freeze the concept at the present state of knowledge and detach it from the category, which is not frozen or closed to inquiry but includes the units with all their characteristics.25

23 Rand, IOE, 54; Kelley, Evidence of the Senses, 36–42; Peikoff, Objectivism, 110–12.

24 Rand, IOE, 2.

25 Rand, IOE, chap. 7.

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The analysis I have offered of the ontological status of the elements in conceptual awareness can be summarized in a table:

Table A

Ontological status Perception Concepts

Cognitive state (in the mind) Perceptual experience Concept

Objective content (relational) Existent as perceived in a form = as it appears

Intrinsic content (mindindependent)

Existents: particular, concrete entities, characteristics, actions, relationships

On this basis, we can now deal with issues of propositions and truth.

V. Propositions and Reality: Truth

Existents grasped as units—as instances of categories or properties

Existents: particular, concrete entities, characteristics, actions, relationships

The basic idea behind correspondence theories of truth is that thoughts and statements are true in virtue of their relation to reality. The idea is captured by Aristotle’s famous statement: “To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true.”26 Later discussions of truth typically aim to specify three elements in the truth relationship: the truthbearer, the truth-maker, and the relationship between them. Aristotle specifies the truth-bearer: “To say,” which can be taken to mean assert.27 But he does not specify either the truth-maker or the relation. In particular, his phrases “what is” and “what is not” refer to reality without specifying what exactly in reality makes an assertion true or false. He leaves that question open. Correspondence theories often try to answer that question by saying that truth-makers are facts. A statement is true if it corresponds to a fact. But what sort of being is a fact? I will argue that facts are the objective contents of propositions, in contrast with correspondence theorists who hold that facts must be intrinsic if they are going to be the makers of truth.

26 Metaphysics, 1011b25. See also Plato, Cratylus, 385b2.

27 Mark R. Wheeler, Being Measured: Truth and Falsehood in Aristotle's Metaphysics, (2020), 72.

Why facts are not intrinsic

The fact that my car is white is not to be identified with the car itself, as an entity, nor with its color attribute. A fact, qua fact, cannot be identified with anything intrinsic. A fact is always a fact that x is P, or the fact of x's being P, not x by itself, and not the substantive kind or attribute, action, or relationship designated by "P". Concrete particulars always have a location in space and time, but facts do not. The fact that my car is white does not follow the car around spatially. And it will survive the car’s demise: years from now, long after the car itself has been flattened for scrap, it will still be a fact that this car was white. As Peter Strawson observed,

The only plausible candidate for the position of what (in the world) makes the statement true is the fact it states; but the fact it states is not something in the world. It is not an object; not even (as some have supposed) a complex object consisting of one or more particular elements (constituents, parts) and a universal element (constituent, part).28

The suspicion that facts are not to be found in the world is compounded when we consider that the term "correspondence" suggests a one-one relationship between propositions and facts: each true proposition has its own fact that makes it true. This implies that there is an abundance of facts surrounding each concrete particular, one for each distinct way of identifying that particular abstractly. Consider again the proposition that my car is white. I can specify the existent I am referring to by using a more abstract term (vehicle) or a less abstract one (sedan). And I can specify its color more abstractly (as light-colored) or less (slightly off-white with brown tones). With just these three variants for the subject term and three for the predicate, we could produce nine propositions distinct in meaning. Are there nine facts about the color of my car? Again, my car is not blue. Does that negative truth require a negative fact? If so, the number of facts is limitless, for negative statements about the car can be produced indefinitely: It has never been in Idaho, it is not made of plywood, it has never been driven by Tom Cruise. . . .

These reflections strongly suggest that facts are in some way relative to our thoughts. To quote Strawson again: “Of course, statements and facts fit. They were made for each other. If you prize the statements off the world, you prize the facts off it too; but the world would be none the poorer.”29 If facts are dependent on knowers in some way, however, then they do not seem qualified to serve as the independent determiner of the truth or falsity of our statements.

28 P. F. Strawson, “Truth,” in Michael P. Lynch et al (eds.), The Nature of Truth: Classic and Contemporary Perspectives, 2nd ed. (MIT Press, 2021), 452. See also Marian David, “Truth as Identity and Truth as Correspondence” (in same volume), 691.

29 Ibid, 453–54.

Why facts are objective

Facts, I would argue, have the status of being objective, not intrinsic—the same status in regard to propositions that categories and abstract attributes have in regard to concepts. There are two general arguments for attributing this status to them.

The first is that a fact includes universal, abstract categories and attributes, and so must have the same status. Consider the fact that all elk are herbivores. This is a universal fact, about elk as such, all of them. It cannot be reduced to a series of particular facts about this elk, that elk, the other elk and so on, without including in the list the non-particular fact that these are all the elks there are. We cannot eliminate universality in reference.

Nor can we eliminate abstractness in identification. When I describe a table as wooden, I am saying that in regard to material composition it falls within the range of the concept “wooden.” Having omitted its measurements, I am not saying anything different about this table from what I am saying about any other wooden object, despite the concrete differences among their material characteristics: one is made of pine, another of oak; one is brightly varnished, another scuffed and water-stained. Consider then the propositions a) that the table is wooden and b) that it is pine. These propositions are made true by the same concrete determinate attribute: the actual material composition of the table. I am simply describing that composition at two different levels of abstractness. Thus, if the fact that the table is wooden is a different fact from the fact that it is pine, we must acknowledge that it contains an abstract element and has the same objective status as the abstraction wooden. In this sense, we may say that facts inherit that status from their conceptual components.

The second reason for attributing this objective status to facts is their own internal structure qua facts. The fact that the table is wooden has an internal subject-predicate structure, with the “is” representing a relationship between the table and its attribute. But there is no intrinsic relationship here. A thing is its identity; its identity is not something separate that is related to it.

The copula, in other words, has the same status at the propositional level as abstractness and universality at the conceptual level. For the reasons outlined in Section 3, the explicit reunification of an existent with its identity is a requirement imposed by the differentiating and abstracting nature of concepts, but there is no bifurcation between existence and identity in the thing itself, and thus no actual, intrinsic relationship for the copula to capture. We cannot speak of a relationship unless there is some distinction between the relata, and if the distinction is objective rather than intrinsic—i.e., dependent on the knower's perspective—then so must be the relationship.

It might be argued that while an existent is its identity, it cannot be equated with any one aspect of its identity. In the judgment that my car is white, the color I attribute to my car is only one part of its identity; there is thus a part-whole relationship between that which I refer to and that which I attribute to it, a relationship that does exist intrinsically. It is certainly true that an existent is not identical with any one aspect of its identity, and that it is in some sense the “totality” of its aspects—the term “totality” suggesting a part-whole relationship. But the suggestion is misleading. A part can exist in isolation from the whole. A part of an entity, like a table's leg, can be physically detached. A part of an action, like the first step of a waltz, can occur without the whole if the action is interrupted. But an attribute, action, or relationship, as an aspect of the identity of some existent, cannot be separated.

Because a part is separable, there is an actual relationship—normally a spatiotemporal and/or causal relationship—that it bears to other parts and to the whole. But there is no relationship of inherence between a feature of an existent's identity and the existent itself; the identity of the feature as an existent in its own right includes its being a feature of the particular existent; the distinction between them is a conceptual one. This difference between parts and features is captured in the grammar of English by the fact that we can say, e.g., that the apple is red (a feature) but not that it is seeds, skin, or flesh. To predicate a part, we must say that the apple has or is composed of seeds, skin, or flesh; what we predicate is not the part per se but the relational feature of having parts.

To summarize the account so far: Every mode of cognition has an identity due to the nature and operation of the cognitive faculty involved, at both the perceptual and the conceptual levels of awareness. As explained previously, the essential identity of concepts is their universality and abstractness, so that conceptual awareness of things takes the form of grasping them as members of universal categories and instances of abstract properties, with their specific measurements omitted. For propositions, the essential nature is identifying existents, as subjects, by using a copula to predicate of them some element in their identity. Categories and properties are the objective content of conceptual awareness. Facts have the same ontological status for propositional judgments.

True propositions, in other words, have facts as objective contents. As with the objective contents of percepts and concepts, facts are not some new entity existing in the mind, or in the world, or in some Platonic realm. What exists in the mind is the integrative cognitive action and its product, the judgment, retained as a belief; what exists in the world apart from the mind is the intrinsic content. The objective content is not an internal representation standing between the mind and reality, any more than the comparable item in perception—the entity-in-a-form—is an internal image or sense-datum.

This analysis can be summarized in an expansion of the previous table.

Table B

Ontological status

Cognitive state (in the mind)

Objective content (relational)

Perception

Perceptual experience

Existent as perceived in a form = as it appears

Intrinsic content (mindindependent)

Existents: particular, concrete entities, characteristics, actions, relationships

Concepts

Concept

Existents grasped as units—as instances of categories or properties

Existents: particular, concrete entities, characteristics, actions, relationships

Propositions

Judgment, belief

Facts: Identification of existents by predicating of them a feature(s) of their identities

Existents: particular, concrete entities, characteristics, actions, relationships

I have been describing facts as the objective contents of propositions. I spelled this out in the table to make it clear what I mean by “fact.” That’s important in part because the term is used in many ways in ordinary language. The word is often limited to fairly concrete, easily verified claims, not complex propositions. Is the 1st law of thermodynamics—that energy can be converted from one form to another, but cannot be created or destroyed—a fact? Yes, but it would be odd to describe it that way. Again, facts are often contrasted with opinions, though I would say that opinions can be true or false.30 In any case, “fact” is the term used in philosophy to mean truth-makers for any kind of proposition, and I will continue to do likewise.

False propositions

But the analysis so far holds only for true propositions. What about false ones? Surely they are of or about something. A false proposition can make a distinctive claim; the proposition that water runs uphill is distinct from the proposition that water cannot freeze. And what we showed about the unity of propositions (Section 3) holds for false as well as true ones: false propositions are complete thoughts, expressed in complete sentences; and can be premises or conclusions in an inference.

As stated in Section 1 above, the function of cognition is to identify things in reality. But the conceptual level is fallible: identification fails in the case of errors. And this cognitive level is open to entertaining

30 See David Kelley and Debby Hutchins, “Fact and Opinion,” Informal Logic, Vol. 43, No. 3 (2023).

hypotheses not yet proven. To say that x is P is a fact is to say x really is P—that it is not an error, not a speculation, not anything other than “what is” (to use Aristotle’s formulation). So false propositions cannot have facts as their contents.

This is a classic problem for the correspondence theory. Marion David describes it by contrasting two possible “truth-makers” for propositions, 1) facts and 2) states of affairs:

The difference is that (2) allows an explanation of the content of false propositions:

If the primary truth-bearers are sentences or mental states, then states of affairs could be their meanings or contents, and the correspondence relation in (2) could be understood accordingly, as the relation of representation, signification, meaning, or having-as-content. Facts, on the other hand, cannot be identified with the meanings or contents of sentences or mental states, on pain of the absurd consequence that false sentences and beliefs have no meaning or content. 31

The implication is that there are states of affairs that do not obtain. That may be a useful metaphor to emphasize that false propositions do have content. Taken literally, however, there’s a problem with such states of affairs. They are nonfactual, i.e. are nonexistent. But if false propositions have no link to objects or to facts or to states of affairs, how can they have meaning or content? The problem arises from the underlying assumption: the dichotomy between objective and subjective that we examined in the previous section. And our critique of that dichotomy leads to the solution.

The solution is the distinction we have drawn between objective and intrinsic as ontological levels. Every act and product of consciousness, true or false, has an intrinsic content. By the thesis of the primacy of existence, no cognitive state can have a content made up ex nihilo. There must be some relationship to reality, some input of perceptual data. The integrative processes of the mind can only separate or combine, integrate or differentiate, rearrange or distort, the material provided by the senses. This is true of imaginary objects (unicorns), counterfactual suppositions (What if I could fly like a bird?), etc. What happens in the case of false assertions is that the material is mis-integrated. Thus, the claim that water runs uphill integrates certain existents (those substances designated by “water”) with a concept incompatible with their actual identity; the same is true for the claim that water never freezes. Though the two claims are false, and neither claim has an objective content, each integrates an intrinsic content into a judgment. It is the differences in their respective intrinsic contents, along with the manner of integration, that explains why they make different claims about water—and why they are false.

31 Marian David, “The Correspondence Theory of Truth,” Stanford Encyclopedia of Philosophy, Summer 2022 Edition.

It may then be asked: What purpose does objective content serve? Why not just say that there are various existents in the world and various ways of integrating them cognitively, and that when we integrate properly the result is true, false when mis-integrated? The reason is that we do not integrate all the way down, so to speak, in one fell swoop.

Consider first a true assertion, that elk are herbivores. When we form this judgment, we already possess the concepts ELK and HERBIVORE as tools of cognition; what we are integrating is the category elk with the attribute herbivore. If we tried to formulate the full truth conditions of this judgment in terms of what exists intrinsically, we would have an unimaginably long list of items: every elk that exists, past, present, and future; the members of other species from which we contrasted elk in forming the concept, including carnivores as contrast objects; every act of eating by each of these elk during its entire life; and every plant that exists, past, present, and future (since “herbivore” means “plant-eating”). This list of the intrinsic existents involved could not possibly be held in mind simultaneously and subjected to a single complex act of integration.

We integrate in stages, forming a new objective content which is then available as input for a higher-order integration. We form concepts to reduce an aggregate of concretes to a category or abstract feature. We form higher-order concepts by “abstraction from abstractions.”32 These include generic concepts formed by integrating lower-order ones; ANIMAL is a generic concept abstracting from HUMAN, DOG, etc. We form narrower concepts by specifying further dimensions of identity; LAWYER designates a subcategory of humans distinguished by profession. By contrast with basic-level concepts formed directly from perception, the vast majority of concepts are higher-order, which means they rest on prior concepts we have formed— concepts closer to the perceptual level. In addition, propositions are grounded in reality through observation and chains of inference. Even relatively simple examples of propositions, like “elks are herbivores,” have complex relationships to intrinsic elements in reality. Other propositions have much more complex relationships.

Consider now a false statement: “Lawyers in the U.S. earn less than bricklayers.” This is not a specialized or technical statement; any educated English-speaker can understand it, and most understand that it is false. But consider the prior integrations involved in that understanding. To mention only a few:

 Lawyers and bricklayers are professions. To understand the concept PROFESSION one must have the prior concept of WORK; among professions one must have the concepts LAWYER and BRICKLAYER. The concept LAWYER presupposes the concept LAW, and its presupposition

32 Rand, IOE, chap. 3.

GOVERNMENT.

BRICKLAYER presupposes the prior concepts BRICK and CONSTRUCTION (among others).

 To understand the (alleged) difference in compensation, one must understand the prior concepts of COMPENSATION (SALARY, etc.), and the concept MONEY. One must understand NUMBER well enough to compare numerical differences in monetary compensation.

The point is not that these integrations take an immense amount of effort. Once acquired, concepts and their linguistic expressions as words become automated; they are a repertoire we tap to form and understand propositions. The point is that the propositions that employ such higher-order concepts are true or false by virtue an immense number of intrinsic existents in reality.

The same is true of antecedent propositions from which a given proposition is derived. Each of the prior concepts is the locus for antecedent propositional knowledge: That laws are rules set by government, that people work for a living, that they typically work in specific trades or professions, that they are compensated for their work, and so on down to basic observations about people and social reality. These propositions are part of the content of the concepts involved, on the model of concepts as file folders for accumulated knowledge about their referents. We could also invoke the model of concepts as nodes in networks, linking concepts with other concepts in propositions. The file folder and network models, however, are metaphors. The point is that concepts and propositions are intimate partners in conceptual cognition. Even a false proposition like our example rests on those prior concepts and propositions. Even false propositions are based on extended sequences of information processing, including inductive and deductive inferences, acquired knowledge from study or observation, and on and on.

At each stage, it is possible to integrate improperly and thus fail to produce a new objective content—the awareness of a fact. In most cases, we just have to go a few steps back, undoing the mis-integration, to find truths. It’s false that lawyers make less than bricklayers, but it’s true that people in each category are compensated for their work, that laws are applied to cases and that many structures are built with bricks, etc. A falsehood may perpetuate itself if the improper integration is incorporated in some further claim, as happens, for example, in complex pseudo-theories such as the flat-Earth theory. At some point we reach the question whether a proposition detached from reality is meaningful and false, or meaningless and thus neither true nor false. It is clear that we cannot evaluate a proposition as true or false unless it makes a definite claim, and this in turn requires that it specify one or more existents and that it specify one or more aspects of identity. But evaluating specific cases depends on a fuller analysis of meaning than I can offer here. Nevertheless, as explained previously, understanding conceptual-propositional awareness starts with true propositions, and their conditions of meaningfulness set the terms for all other propositions—false

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claims, speculations, etc. Meaningful propositions are not a genus with true and false propositions as species. That’s a representationalist view.

In light of the foregoing, we can see that the standard criticisms of the correspondence theory of truth have a point. It’s not that the theory is false, but that it is superficial and incomplete. The theory says that a proposition is true if it corresponds to a fact. But this is a tautology. That the proposition is true and that it has a fact as its content are joint consequences of an integrative act that results in an objective content.

This does not mean that a true proposition just is a fact, as identity theories of truth hold. “According to the identity theory of truth,” Marian David explains, true propositions do not correspond to facts, they are facts: the true proposition that snow is white = the fact that snow is white. This non-traditional competitor of the correspondence theory threatens to collapse the correspondence relation into identity.33

But the identity claim does not follow from the identical “that” clauses that characterize true propositions and facts. There is an ontological difference: A proposition is the content of a judgment or belief, which are subjective in status—on the knower’s side of the subject-object distinction. Facts are on the object side. As objective in status, they do not exist intrinsically. They are relational; they are the way in which conceptual knowers can identify existents in intrinsic reality.34 Consider an example.35 Someone rolls a coin under the table I’m sitting at. The coin is showing either heads or tails, but I don’t which it is, so I can’t affirm either proposition. But suppose it’s heads. Is that a fact? Yes. Any conceptual knower who sees the coin— including me if I looked—would recognize that it’s heads. Facts are aspects of reality. There are many facts I don’t know, many that no one knows. To call them facts is simply to indicate the form in which a conceptual knower might come to know these aspects of reality.

Unit-economy

In IOE, Rand says,

I would ask you all to keep in mind that a very important part of my entire theory is what I call uniteconomy: the substitution of one mental unit for an indefinite number of concretes of a certain kind.

33 David, “The Correspondence Theory of Truth.” David goes on to offer arguments against the identity theory.

34 I think that Rand is making the same, or at least a related, point in IOE (241–3). She says the concept of “fact” is needed 1) to distinguish true claims that identify reality from false ones; and 2) that we grasp information about the world “bit by bit,” not all at once in a cognitive smorgasbord.

35 I am indebted to Alexander Cohen for this example.

That is the essence of why we need concepts—that is the essence of what concepts do for us. Therefore, the substitution of one unit which refers to x number of possible units is the essence of concept-formation. The process is not complete without that substitution.36

Rand’s point about unit-economy as the essential function of concepts extends to propositions as well.

To see why, let’s begin by clarifying the difference between unity and unit-economy. They are closely related concepts, but they are not identical. Unity is an internal feature of a cognitive element; unit-economy is the relational function of such elements in integrating their referents in reality or in previously formed elements.

Consider unity first. In Section 3, I discussed the unity of subject and predicate in propositions, by analogy with chemical compounds as opposed to mixtures. That unity applies as well to percepts and concepts. Both of them are not mere lists but integrations of what gives rise to them. A percept is a unitary awareness of the environment—through vision, hearing, etc.—that is caused by but not reducible to the sum of neural inputs and processing involved. We form a concept by integrating similar units into a new mental unit that is retained for further use. The unity of a concept as a cognitive element is reflected in its nature as universal and abstract, properties not found in its concrete units.

In other words, a percept, a concept, and a proposition are all unified states of awareness. That’s what makes them cognitive units.

Unit-economy, on the other hand, is a relational feature of cognitive units—a one-to-many relationship. Percepts do not have that feature. In perceptual awareness, a percept has a one-to-one relation to its object. Of course, our perceptual awareness at any moment may take in many things. I look out my window and see trees, cars, people, buildings. But my awareness is of these concrete particulars only; it is limited to things that are in my current visual field and stimulating my receptors. The next time I look, I will see a different set of particular things. Some of the objects may stay the same, like the trees, but the set will be different, as will my experience of the scene.

Unit-economy is a function solely of the conceptual level. A concept has a one-to-many relation to the units it integrates, as explained in Section II above. As Rand says that relationship is what gives concepts such enormous leverage in expanding our awareness of reality.

In what way, then, do propositions perform the same function? How do they exhibit unit-economy?

To begin with, a proposition inherits the unit-economy of its component concepts. To use a previous example, the proposition that elk are herbivores refers to all elk, abstracting from the concrete differences between this elk and that one. The predicate is also abstract. The amounts and type of plants that

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herbivores eat varies widely. Elk eat mainly grasses; beavers eat tree bark and aquatic plants; deer like tender twigs, shrubs, and flowers. The concept HERBIVORE abstracts from all these differences, but subsumes all of these dietary habits as units.

Definitions involve another type of unit-economy. Definitions are propositions that serve the purpose of clarifying concepts, by stating the essential characteristics of what the concept designates. Consider the traditional definition of humans as rational animals. The genus, animal, embraces all the attributes of animals that distinguish them from plants and inanimate objects. The differentia, rational, embraces all the traits that reason makes possible—from speech, to agreements and contracts, to the accumulation of knowledge over generations, among many others. In this way, both the genus and the differentia have a one-to-many function: one proposition stands for many features of a concept’s units. As Leonard Peikoff notes,

The principle of unit-economy has many further manifestations in the field of concept-formation. Proper definitions, I have said, are condensations, which enable us to retain in a single statement a complex set of the referents’ features. Thus definitions, too, are unit reducers. The concept condenses its referents, reduces them to a single mental unit; the definition then condenses their known characteristics; it reduces these to a single statement.

Like concepts, however, definitions are open to revision with new discoveries about their referents. At any time, we can base a definition only on what we know at that time about the referents. But the acquisition of new knowledge might imply that some other characteristic is more essential, and we would need to revise the definition accordingly.

Yet another form of unit-economy that propositions provide, and the most important, has to do with evidence. A distinctive feature of propositions is that, unlike percepts or concepts, they make a statement, and accordingly can be true or false. Knowledge of their truth or falsity is based on evidence. The thesis of empiricism implies that evidence must trace back to direct perceptual awareness of reality. But there are many routes to reality. There can be many lines of evidence for a given proposition.

Consider the proposition that George Washington was the first president of the United States. This is common knowledge among many people. No one today has directly seen Washington; acceptance of the proposition is based on testimony. But few of us can remember when or how we learned it. I assume I learned the fact in grade school, but I have no memory of the class or teacher. I have acquired further confirmation from extensive experience and reading, without ever encountering disconfirming evidence. My

37 Peikoff, OPAR, 108.

38 See Rand, IOE, chap. 5, “Definitions.”

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knowledge of the fact is based on and incorporates that evidence, but integrates it into a single propositional conclusion. And other people who know the same fact will have different evidential bases.

In this way, a proposition exhibits a form of one-to-many unit reduction. Just as we have the concept DOG without knowing most of its units, we know that dogs are four-legged without knowing most of the possible evidence supporting that proposition. Propositions are also like concepts in having a “some but any” feature. A concept integrates similar units along dimensions they share but in different measurements, on the principle that a unit must have some specific measurement but many have any (within a certain range). A proposition is established as true or false on the basis of some body of adequate evidence but may be established by any (within the various chains of evidence that are adequate by logical standards).

Conclusion

This completes my presentation of an Objectivist theory of propositions. The main points, to summarize, are:

 Primacy of existence: Concrete, particular existents—entities, properties, actions, and relationships— exist independently of the awareness of them. The function of cognition is to identify them.

 Concepts and propositions are derived from direct perceptual awareness of existents and subsequent processes of integration.

 Concepts are abstract and universal. They are formed by measurement-omission and exist in hierarchies of abstractions from abstractions. They serve the cognitive function of unit-economy.

 Propositions have an internal structure that essentially involves predicating an identity of a subject.

 The unity of propositions derives from the axiom that existence is identity.

 The categories and properties that concepts identify are objective in ontological status.

 Propositions, if true, identify facts of reality, which are objective in ontological status.

 Propositions, like concepts, serve the cognitive function of unit-economy.

What I have provided is a framework for understanding propositions, their internal structure and their truth or falsity. I have not addressed the many more specific issues required for a full theory. But I think they can be addressed within the framework outlined in the bullet points above.

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