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| Philosophy Pages
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| History | Timeline | Philosophers | Locke | |||
Russell Life and Works . . Mathematics . . Descriptions . . Logical Atomism . . Social Concerns Bibliography Internet Sources |
Such optimism naturally depended upon a vigorous sense of the value of logic itself. Neither the simplistic treatment of predicates in the Aristotelian logic of the scholastics nor the crypto-metaphysical account of internal relations in the Hegelian dialectic of the Absolute idealists provides an adequate foundation for philosophy, Russell supposed, and the inductive reasoning of Bacon, Hume, and Mill offers grounds only for tentative empirical generalizations. Russell's hopes rested instead on a modern notion of the logical enterprise, in which inferential relations depend solely upon the logical form of individual propositions that can be shown to be tautologous.
One advantage of this notion is that it promised to establish formally the essential unity of logic and mathematics. As Russell and Cambridge mathematician Alfred North Whitehead demonstrated in Principia Mathematica (1910-13), it is possible to begin with a restricted set of logical symbols and, using only simple inferential techniques, prove the truth of the Peano axioms for basic arithmetic. Although its ultimate success was significantly undermined by Gödel's proof that some propositions necessarily remained undecidable, the construction of this formal system was an intellectual achievment of the first order.
Moreover, the logicization of arithmetic required attention to significant philosophical issues.
Russell and Whitehead used the principle of abstraction to eliminate properties from their logical system entirely, instead using
classes of objects, defined entirely by their
extension.
(Thus, for example, the number "5" is nothing other than the class of all classes that have quintuple membership.)
But this technique gave rise to
a significant paradox.
Since there can be classes of classes, it must be possible to offer extensional definitions of classes that have themselves as members.
But then consider "the class of all classes that are not members of themselves."
If this class is included within its own extension, then by definition, it should not be; but if it is not included, then it should be.
This appears to establish the formal
inconsistency of the entire system.
Russell's solution to the difficulty was a theory of types, according to which classes are arrayed hierarchically: although each class may have as members classes of lower orders, no class can contain any class of its own order (including itself).
Even if this solution worked for the technical apparatus of logic, we may still be faced with similar, less formal
difficulties with self-referential statements.
From his work on the logical foundations of mathematics, Russell derived an enormous confidence in the possibility of resolving philosophical problems by offering careful analyses of the logical structure (rather than the grammatical form) of what we say. The most clearly successful application of this technique is the "theory of descriptions" Russell expounded in On Denoting (1905).
We certainly make frequent use of "denoting phrases" in ordinary language, but if we uncritically accept their substantive use in grammar, we'll be inclined to suppose that they represent objects in the same way that proper names do. This gives rise to difficulties of three sorts:
Russell attacked these problems by emphasizing that descriptions signify differently than do logically proper names.
A name denotes its referent directly, carrying its own
existential import; but a description denotes only indirectly and must be regarded in a different way.
In fact, Russell held that denoting phrases cannot be correctly understood in isolation (since that invariably makes names of them).
In order to see how a denoting phrase refers, we must analyze the whoe proposition of which it is a part.
A statement that incorporates an indefinite description, such as "John met a person," should be analyzed as, "There is something that is a person and John met it."
In symbolic notation,
(∃x)(Px • Mjx)
An assertion that includes a definite description, such as "The author of Waverly was Scotch," should be analyzed as, "At least one person wrote Waverly; at most one person wrote Waverly; and whoever wrote Waverly was Scotch."
In symbolic notation,
(∃x){[Wx • (y)(Wy ⊃ y=x)] • Sx}
Notice that what seem to be simple statements in ordinary language turn out, on logical analysis, to involve two or three distinct assertions, all of which must be true if the statement as a whole is true.
This, Russell maintained, resolves problems of all three sorts:
Decades later, Strawson criticized Russell's treatment of descriptions by insisting that ordinary language be taken more seriously as it is.
On the other hand, relying upon Russell's suggestion that even proper names can be treated as definite descriptions,
Quine eliminated the presumed ontological implications of their use.
Despite these later developments, Russell's treatment of descriptions stands as a notable example of the potential benefits of philosophical analysis.
Russell himself went on to apply analytic methods to discussion of basic epistemological and metaphysical issues. In "On the Relations of Universals and Particulars" (1911), for example, Russell used logical arguments to resolve the ancient problem of universals. Ordinary language certainly permits the attribution of a common predicate to more than one subject: " a is P " and " b is P " may both be true. If only particular things exist, then a and b would be distinct, featureless beings whose likeness with respect to P could only be understood as a shared—and hence universal—property. If only universal things exist, then P would exist in two places at once, which would fail to account for the distinctness of a and b. Thus, Russell argued, both universals and bare particulars exist; only a robust realism can explain both the sameness and the diversity that we observe in ordinary experience.
More generally, Russell's lectures on Our Knowledge of the External World (1914) and Logical Atomism (1918) offered a comprehensive view of reality and our knowledge of it. As an empiricist, Russell assumed that all human knowledge must begin with sensory experience. Sense-data provide the primitive content of our experience, and for Russell (unlike the phenomenalists) these sense-data are not merely mental events, but rather the physical effects caused in us by external objects. Although each occurs immediately within the private space of an individual perceiver, he argued, classes of similar sense-data in various perceivers constitute a public space from which even unperceived (though in principle perceivable) sensibilia may be said to occur. Thus, the contents of sensory experience are both public and objective.
From this beginning, according to Russell, all else follows by logical analysis. Simple observations involving sense-data, such as "This patch is now green," are the atomic facts upon which all human knowledge is grounded. What we ordinarily call physical objects are definite descriptions constructed logically out of just such epistemic atoms. As Russell claimed in the fifth chapter of The Problems of Philosophy (1912),
Every proposition which we can understand must be composed wholly of constituents with which we are acquainted.Careful application of this principle, together with the techniques of logical analysis, accounts for everything we can know either by acquaintance or by description.
Some cases do call for special treatment.
Russell feared that some "negative facts" might require lengthy analysis in order to establish their ground without presuming acquaintance with non-existence objects.
"General facts" certainly do presume something more than a collection of atomic facts.
The truth of "All dogs are mammals," for example, depends not only on the truth of many propositions—"Houston is a mammal," "Chloë is a mammal," etc.—about individual dogs, but also on the further assertion that these individuals constitute the entire extension of the term "dog."
Suitably analyzed, however, all of human knowledge can be seen to rest solely upon the collective content of human experience.
Abstract philosophical matters were not all that Russell cared about. As he noted in the prologue to his Autobiography (1967), pity for human suffering (along with love and knowledge) was among his deepest concerns. At the height of his career, Russell spent years in jail as a conscientious objector to British involvement in the First World War, and this vocal pacifism resulted in the termination of his professorship at Cambridge. Although he came to regard the threat of Fascism as great enough to warrant the Second World War, Russell was profoundly concerned about the invention of atomic weapons with the capacity to destroy human civilization on an unprecedented scale. The warnings contained in his "The Bomb and Civilization" (1945) were expressed repeatedly throughout his life.
Russell's efforts to secure an academic career in the United States were thwarted by conservative opponents who drew attention to his unconventional opinions regarding sexual morality and organized religion.
In the notorious lecture entitled
"Why I Am Not a Christian" (1927)
Russell pointed out the inadequacy of traditional efforts to demonstrate
existence of god,
offered a balanced evaluation of the teachings of Jesus, and decried the harmful moral and social consequences of adherence to Christian religion.
Agnosticism was no more popular in America than divorce, and Russell's uncompromising honesty about these issues contributed greatly to his public reputation.
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