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According to Bertrand Russell, the phrase “theory of knowledge” has two meanings. One kind of theory, the lesser, accepts whatever knowledge science presents and seeks to account for it. Russell’s concern is with the wider kind, which embraces all problems of establishing the nature and validity of all knowledge. Confining...

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According to Bertrand Russell, the phrase “theory of knowledge” has two meanings. One kind of theory, the lesser, accepts whatever knowledge science presents and seeks to account for it. Russell’s concern is with the wider kind, which embraces all problems of establishing the nature and validity of all knowledge. Confining his attention in this work to empirical knowledge, he undertakes to discover two things: (1) What is meant by “empirical evidence for the truth of a proposition”? (2) What can be inferred from the fact that there sometimes is such evidence?

Russell brings to the problem of a theory of empirical knowledge the full force of its counterpart, logical knowledge, to whose modern development he is a foremost contributor. He attacks the problems of his general task by translating their elements into formal logical symbols so as to achieve a precision lacking in the language in which the problems are usually couched. Yet the book does not consider problems of logic as such, except when they are relevant to epistemology.


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To talk about epistemological matters, Russell sets up a modern linguistic apparatus. He conceives a hierarchy of languages, at whose base is the object-language, or primary language. Terms in the object-language include subjects and predicates. While ordinary language may provide a beginning, every subject of the object-language should be transformed into a unique proper name, making use of coordinates in the visual field and of measures of time for discriminating the object named. The name will apply to a complex; and sometimes names must be given to complex wholes without knowing what their constituents are. People learn the names of things ostensively, and only of those things they actually perceive while hearing or coining their names. The names are employed as subjects in propositions of the simplest sort, called atomic propositions. Their predicates may be designated relations. Letting R stand for the relation “above,” the proposition “A R B” consists of the relation R and the names A and B, and asserts that A is above B. This is a dyadic relation. Predicates may take any number of terms. The predicate of a single name is a monadic relation: “f (A)” states that a characteristic f is an attribute of A.

The secondary language consists of statements about the primary language (and must include the primary language within it). Therefore all words for logical conceptions, such as “is true,” “is false,” “or,” “if,” belong to the secondary language. All logical truths, because they depend for their truth on rules of syntax, are at least on this level, if not higher. An important group of propositions of the secondary language are those stating propositional attitudes, such as “A believes proposition p.”


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The distinctive feature of empirical rather than logical truth is, of course, its basis in percepts, the sense images by which perception is possible. Russell adapts A. J. Ayer’s phrase “basic propositions” to designate those propositions arising as immediately as possible from percepts. A basic proposition “is a proposition which arises on occasion of a perception, which is the evidence for its truth, and it has a form such that no two propositions having this form can be mutually inconsistent if derived from different percepts.” Examples in ordinary language are “I am hot,” “That is red.” Many basic propositions may arise describing a single percept, for people perceive a sensory whole combining the entire fields of vision, touch, and so on; and within this field people identify smaller wholes of sensory complexes—the individual objects of the world. Basic propositions need not be atomic propositions. An important group includes some propositions stating propositional attitudes—”I believe proposition p”—and thus basic propositions may occur in the secondary language as well as in the primary.

Unlike most prior writers, Russell does not affirm that basic propositions are indubitably true. He is quite willing to doubt them, particularly those involving the memory of percepts. However, what distinguishes basic propositions from others is their immediacy, whereas other propositions rest to some degree on inference. The evidence for a basic proposition is the momentary percept that causes it, and nothing can ever make a percept more or less certain than it is at the moment of its occurrence. It is from basic propositions that Russell proceeds to erect the structure of empirical knowledge. Because basic propositions are based on the least questionable objects of experience, they are the most dependable propositions in empirical inquiry. Thus, empirical knowledge is founded on propositions of the utmost particularity. Russell criticizes other writers for failing to screen out all traces of inference in the propositions they have regarded as basic.

Empirical Knowledge

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A pure empiricism, depending only upon percepts for validation, would be self-refuting. It must contain some general proposition, which cannot be a basic proposition, about the dependence of knowledge upon experience; and the consequence is that such a proposition could not itself be known. Empirical knowledge requires certain additional elements besides basic propositions. These include provisions for making general statements and for stating logical relationships. Empirical knowledge, in other words, needs some epistemological premises as well as factual premises. Modes of inference are also required. These modes include the usual logical operations of deduction. More important in empirical knowledge, however, are nonlogical patterns of inference, namely, reasoning by analogy and by induction. For example, Russell throughout assumes that things perceived cause perceptions, and that perceptions cause propositions. His notion of cause is that it is a convenient device for collecting together propositions of certain percepts; it is something that one can arrive at inductively from appropriate combinations of percepts. Without some such organizing scheme for relating percepts, one would have nothing resembling empirical science. Yet neither causality nor induction is perceived, nor are they validated by logical syntax.

An innovation, no doubt startling to logicians, that Russell finds necessary to epistemology is to supply substantial meaning rather than merely formal meaning to logical terms. He finds these in psychological fact. “Or” rises from a hesitation, a conflict between two motor impulses when the organism is suspended between two courses of action. “Not” expresses a state of mind in which an impulse to action exists but is inhibited. “True” has its psychological ground in an expectation that is fulfilled; “false” in the surprise when an expectation is defeated. Such interpretations as these become possible when one accepts into epistemology not only logic but psychology and physical science, as one must in order to account for empirical rather than purely logical knowledge.

A Theory of Significance

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Russell is now able to develop a theory of significance. Regarded epistemologically, a proposition has two sides, objective and subjective. The objective side is what it indicates factually. The subjective side is what it expresses about the state of mind of its originator; this is called its significance. What it expresses may be belief, denial, or doubt. These distinctions, not needed in logic, solve many puzzles of epistemology. The points concerning significance are independent of truth or falsity of the proposition; truth and falsity come into the relation of the proposition to what it indicates. A proposition does not necessarily consist of words; it is psychological, of the stuff of belief, not language. However, words may always be found to state the belief that, as a proposition, may underlie the many possible ways of saying it, in one or in various languages. Russell provides a sample language to show that the psychological conditions of significance can be translated into precise syntactical rules.

Logical sentence patterns can start from particular propositions recording percepts and extend one’s thought over material that one has not experienced, and in this way one can expand one’s body of statement. If one knows “Socrates is mortal,” one can think “Something is mortal,” or “Everything is mortal,” and so on. Then further inquiry so as to have new percepts may test whether the new statements should be added to belief. Simple statements of immediate percepts may be expressed with constants—particular names—and predicates. However, any statement covering a percept one has not actually had must contain a variable term in place of a constant, for one can neither give nor learn a name (in Russell’s sense) for an object one has not perceived. An epistemological language will need names, whereas a logical language does not deal with particulars and has no use for names. By the use of variables rather than names, it is possible to have propositions transcending one’s experience. This is in fact what happens whenever one receives information from another person.

Thus far Russell has investigated meaning. In effect, he has constructed an epistemological language so that one can know what kinds of sentences are possible as statements of percepts and their relationships. It remains to examine the relationship between meaning and truth, between language and the world.

A Theory of Truth

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Among the many possible theories of truth, Russell adheres firmly to a correspondence theory. Truth is defined by events, not percepts, although it becomes known by percepts. Truth is thus a broader concept than knowledge. The truth of a proposition is established by perception of its verifier. The sort of sentence that provides the model for truth is a spontaneous sentence that expresses what it indicates—that is, in which the subjective and the objective content coincide. Such a sentence is “I am hot!” Provided the sentence is stimulated by the immediate circumstances of the moment, there is no reason to doubt it. The verifier of a true sentence is what the sentence indicates; in other words, what makes that sentence true is that I was hot when I said it. Similarly, the verifier of a sentence about the future is the occurrence of what it indicates, and when that occurrence is perceived, the sentence is verified. A false sentence has no verifier, and it indicates nothing. Obviously, some verifiers may never be perceived, and there are some sentences whose truth or falsity is never known. Sentences are true if their verifiers occur, but when verifiers are not perceived, the sentences cannot be said to be known. The presence of an observer, Russell affirms, is no requisite of verifiers occurring.

The verifier of a basic proposition is a single occurrence at a moment of time. As to sentences containing variables, there is (usually) not just one but a collection of verifiers for them. The actual verification of such sentences depends on what is said. “All men are mortal” says “For any x, if x is a man, then x is mortal.” This can never be verified by empirical knowledge because it would be impossible to examine all values of the variable—all men. “Some men live in Los Angeles” says “There is an x such that x is a man and x lives in Los Angeles.” This can be verified by one of a very large number of verifiers, since any individual man living in Los Angeles can be the assigned value of the variable. In this fashion, propositions that are not basic, but that, rather, by the use of variables indicate occurrences beyond the speaker’s experience, may be verified. One can give in advance a description of the occurrence that would make the proposition true, but one cannot name the occurrence. The relation between a sentence and its verifier is often much more remote than the explanation of simple cases would suggest.

Russell denies that either the verification or the verifier of a sentence constitutes its meaning. The verifier, as what the sentence indicates, relates to its truth; but one must know what the proposition means before one can know either its significance or its verifier; that is, before one can know either what it expresses or what it indicates. This knowledge is based ultimately on ostensive learning of object-words.

Known error arises in the experience of surprise upon a disappointed expectation. Its simplest case requires a combination of expectation, perception, and memory, in which either the expectation or perception must be negative, the others being positive. This combination accounts for perceptions that seem to be negative perceptions, such as in “There is no cheese in this cupboard.” We examine every object in the cupboard having a size that might result in a percept of cheese, but in every such case, the expectation is disappointed.

The relation of empirical knowledge to experience is explained by Russell as follows: I must depend completely upon my own experience for all beliefs whose verbal expression has no variables; these include only basic propositions of immediate experience and memory. Though not indubitable, they are highly trustworthy. All my knowledge of what transcends my experience, including everything I learn from others, includes variables. When someone tells me, “A is red,” using a proper name for something I have not experienced, if I believe him, what I believe is not “A is red” because I am not immediately acquainted with A, but “There is an x such that x is red.” (Future experience giving me a percept of A together with a percept of the name “A” may later entitle me to believe “A is red.”) Such a view of the nature of empirical knowledge would commit us either to depleting the body of knowledge to an intolerably small set of beliefs or else to relaxing our insistence that only the belief in true statements may be called knowledge. In order to admit the statements we believe on testimony, statements of things ever experienced anywhere by other human beings, and statements assumed in physical science, we should have to do the latter. In fact, upon examining the limitations of pure empiricism, Russell concludes there are no true empiricists.

Logical Difficulties

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Certain principles of logic present difficulties in epistemological language when one attempts to apply nonsyntactic criteria of truth. They are the principles of extensionality and atomicity. Loosely, the principle of extensionality allows one to insert any atomic proposition in the place of a given atomic proposition in a sentence in the secondary language. However, this will obviously not do for sentences stating propositional attitudes. “A believes p” should not entitle one to say, by substitution, that A believes any or all propositions whatever. The principle of atomicity in effect requires one to reduce the complex parts of any proposition on a higher language level to their components on the atomic level, then be governed in assessing the truth of the whole by the relationships thus exhibited. Difficulties that these two principles raise in logic were attacked by Ludwig Wittgenstein and other philosophers by distinguishing between the assertion of a proposition and the mere consideration of a proposition. Russell affirmed, however, that the appropriate distinction to be made is between indication and significance.

The principle of extensionality will be found to apply to all occurrences of a proposition within a larger proposition when its indication is what is relevant, but not when only its significance is relevant, as is the case with sentences of propositional attitudes. Russell is less sure whether atomicity must be accepted or denied; upon considering the immediacy of perception and, in contrast, the elaborateness of inference involved in applying the principle of atomicity, he is inclined to believe that its application is irrelevant to the theoretical construction of empirical knowledge.

Another matter arising in logic is the challenge to the law of the excluded middle (which says that a proposition must be either true or false, not a third thing). It has been suggested that sentences as yet unverified should not be called either true of false. However, Russell clings to a realism, and a correspondence theory of truth, declaring that a sentence is true if its verifier occurs, even though its perception may not be part of anyone’s experience. This outlook is extremely helpful in framing hypotheses, he says, and one should not attempt to do without it.

A continually recurring question in any investigation involving logical and nonlogical knowledge is whether anything about the structure of the world can be inferred from the structure of language. Because words are sensible objects, Russell believes that such inference is possible. While the investigation is confined to names and their objects, there is no reason to attempt such inference. However, on examining sentences, one discovers that those like “A is to the left of B” cannot be explained without raising the question of universals. There is no escape from admitting relations as part of the nonlinguistic constitution. A universal is the meaning of a relation-word. “Above” and “before,” just as truly as proper names, mean something in perception. Thus, in a logical language, there will be some distinctions of parts of speech that correspond to objective distinctions. Again, when one asks whether the word “similar” in recurring instances means the same thing or only similar things, there is no logical escape from granting that it means the same thing, thus establishing the universal “similar.” Russell concludes, although with admitted hesitation, that there are universals and not merely general words. Knowledge must then be not of words alone but of the nonlinguistic world also. One who denies this fact must deny that one even knows when one is using a word; a complete agnosticism is not compatible with the maintenance of linguistic propositions. Hence, Russell believes that the study of syntax can assist us to considerable knowledge of the structure of the world.

With this work, given as the William James Lectures at Harvard University in 1940, Russell performed at least three worthy services for modern epistemology. By asserting that more than one thing can be known from one experience, that there is more than a single kind of knowledge, and that the mind can attain negative knowledge through perception, he assigned to the mind a fuller role in shaping its life than that accorded it by positivists and reductionistic philosophers. He pointed out the necessity for a metaphysic, if only a very simple one, and in doing so gave strength to the counterclaim against logical positivism that logical positivism is itself a metaphysic. Most important, his penetrating criticism showed the importance of the limitations upon empirical knowledge that its advocates, in their consciousness of the limitations of other kinds of knowledge, are prone to overlook.


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Additional Reading

Dejnozka, Jan. Bertrand Russell on Modality and Logical Relevance. Avebury Series on Philosophy. Aldershot: Ashgate, 1999. This work presents a criticism and interpretation of modality and logical relevance in the work of Bertrand Russell. Includes index.

Grayling, A. C. Russell. Past Masters series. Oxford: Oxford University Press, 1996. This work, part of a series on great thinkers, covers the life and accomplishments of Russell. Includes an index.

Irvine, A. D., ed. Bertrand Russell: Critical Assessments. London: Routledge, 1999. This book critically examines the life and work of Russell, including his philosophy.

Landini, Gregory. Russell’s Hidden Substitutional Theory. New York: Oxford University Press, 1998. This work takes a closer look at one of Russell’s logical theories. Includes index.

Monk, Ray. Bertrand Russell: The Spirit of Solitude. London: J. Cape, 1996. This biography of Russell examines the philosopher’s life and works. Includes bibliographical references and index.

Monk, Ray. Bertrand Russell: The Ghost of Madness 1921-1970. London: Jonathon Cape, 2001. Volume 2 of Monk’s thorough biography, covering the troubled mature years of the philosopher.

Monk, Ray. Russell. New York: Routledge, 1999. An excellent biographical introduction to the thoughts of the philosopher, clearly presented and requiring no special background. Bibliography.

Monk, Ray, and Anthony Palmer, eds. Bertrand Russell and the Origins of Analytical Philosophy. Bristol, England: Thoemmes Press, 1996. This collection of essays looks at Bertrand Russell and analytical philosophy. Includes bibliographical references.

Pampapathy Rao, A. Understanding Principia and Tractatus: Russell and Wittgenstein Revisited. San Francisco: International Scholars Publications, 1998. This work compares the philosophies and beliefs of Ludwig Wittgenstein and Russell.

Roberts, George W., ed. Bertrand Russell Memorial Volume. Atlantic Highlands, N.J.: Humanities Press, 1979. Essays from notable scholars focusing on the philosophical achievements of Russell.

Saintsbury, Richard Mark. Russell. London: Routledge and Kegan Paul, 1979. This text serves a twofold purpose as an analysis of Russell’s ideas and as a critique of their adequacy.

Tait, Katharine. My Father, Bertrand Russell. New York: Harcourt Brace Jovanovich, 1975. Tait describes her father’s flaws as a parent. This text offers a sensitive angle on the intellectual life of Russell and brings his social and educational theories under the critical lens of practice.

Vellacott, Jo. Bertrand Russell and the Pacifists in the First World War. New York: St. Martin’s Press, 1981. This book documents the origins of the pacifist movement in Great Britain, focusing on its socialist and Quaker roots.

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