[3.] Bertrand Russell. 1

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1 [3.] Bertrand Russell. 1 [3.1.] Biographical Background. 1872: born in the city of Trellech, in the county of Monmouthshire, now part of Wales 2 One of his grandfathers was Lord John Russell, who twice served as Prime Minister of Britain. Upon Russell s birth, John Stuart Mill agreed to be his godfather, but Mill died only a year later, so Russell never knew him. Russell s parents died when he was very young and he was subsequently raised by his grandmother, a strict Presbyterian. His first encounter with philosophical problems came at the age of 11, when his older brother introduced him to Euclid: This was one of the great events of my life, as dazzling as first love [Russell] demanded to know what grounds there were for accepting Euclid s axioms, and received the unsatisfying reply, If you don t accept them, we cannot go on. The doubt as to the premises of mathematics which I felt at that moment remained with me, and determined the course of my subsequent work He even claims that only his desire to know more mathematics prevented him from committing suicide while a schoolboy 3 He began writing about religious and metaphysical questions in a journal at the age of 15, and he kept the journal secret from his relatives. In 1890, he went to Trinity College, Cambridge, to study mathematics, but soon changed to philosophy. He was associated for much of his life with Cambridge University, first as a student, then as an instructor (although he did teach in the United States for a brief period in the 1930s). He was an extremely prolific writer; published about 70 books, some dealing with harder, more technical areas (logic and mathematics, philosophy of science, metaphysics and epistemology) and others dealing with softer, more popular areas (social philosophy, ethics and religion). Some of the later books were written for a popular audience; some were about sex and marriage and were very controversial for their time. He was married four times. He ran for public office in England but was unsuccessful because he was an avowed agnostic (Russell authored Why I am Not a Christian). He became a pacifist in about 1901 and was briefly imprisoned in England during WWII for writings critical of the US Army. He won the Nobel Prize for literature in He was engaged in political activism in the 1950s and 60s, e.g., he was a member of the Campaign for Nuclear Disarmament and was arrested when he participated in one of their protests. He died in 1970, in Wales, at the age of For a good summary of various aspects of Russell s philosophy, see A. D. Irvine, Bertrand Russell, The Stanford Encyclopedia of Philosophy (Fall 2004 Edition), Edward N. Zalta (ed.), URL = < 2 Russell s hometown is now the site of an important archaeological discovery: the Lost City of Trellech. < 3 Mark Sainsbury, Russell, Routledge, 1979, p.1. Quotations from Russell are from his Autobiography (1967).

2 [3.2.] Philosophical Background: Idealism vs. Realism. At the time that Russell began his studies at Cambridge, the most influential philosophical movement in Britain was a form of idealism: idealism (df.): in some sense, the world, or reality, is dependent on, or not entirely separate from, the mind, or reason. [This is an extremely vague definition; different idealists, e.g., Berkeley, Kant and Hegel, take this core idea in very different ways.] Russell was trained by philosophers who themselves were idealists, so it is no surprise that in his early years he himself accepted this view. 4 But around 1898, Russell famously abandoned idealism and adopted a form of realism: realism (df.): in some sense, the world, or reality, exists separately from the mind. Both Russell and G. E. Moore, his friend and colleague at Cambridge, are famous for abandoning idealism around the same time. [3.3.] Philosophical Background: Logicism and Russell s Paradox. Like Frege, Russell (beginning in 1900) devoted much time to establishing the truth of logicism: logicism (df.): the truths of arithmetic can be derived from, or reduced to, truths of logic. [This is the version of logicism Frege defended; Russell believed that, not just arithmetic, but all of mathematics, is reducible to logic.] Russell had followed Frege s work and wrote to him to point out a serious error: an assumption Frege made which was essential for the success of his project (of showing that arithmetic can be reduced to logic) had to be false. It is now universally acknowledged that Frege did not achieve his goal of showing that the truths of arithmetic could be derived from (or reduced to) the truths of logic. Russell continued to try to show that logicism was true and that the logical foundations of mathematics could be formulated in such a way as to avoid the paradox. 4 For an introduction to British idealism, see the first chapter of W. J. Mander, British Idealism: A History, Oxford University Press, 2012, URL = < accessed July 14, 2014.

3 [3.3.1] Russell s Paradox. 5 Russell discovered that a contradiction can be derived from the axioms of Frege s system of logic. Frege s axioms implied that there is such a thing as the set of all sets that are not members of themselves. But in fact, there cannot be such a set. To see this, consider the question: is that set (the set of all sets that are not members of themselves) a member of itself? If it is a member of itself, then it is not a member of itself (because the only members of the set are sets that are not members of themselves). But this is contradictory. If it is not a member of itself, then it is a member of itself (because it has as members all sets that are not members of themselves). But this is contradictory, too. So no matter which is the case, there is a contradiction. So it is impossible for there to be a set of all sets that are not members of themselves. Sometimes, this paradox is explained using the following analogy: Suppose that there is a town in which every man keeps himself clean-shaven, either by shaving himself or by going to the town s only barber. It seems possible that the barber shaves all and only men who do not shave themselves. But the paradox becomes apparent when we ask: does the barber shave himself? If he does shave himself, then he does not shave himself (since he shaves only men who do not shave themselves). But this is contradictory. If he does not shave himself, then he does shave himself (since he shaves all men who do not shave themselves. But this is contradictory. So no matter which is the case, there is a contradiction. So it is impossible for there to be a barber who shaves all and only men who shave themselves. Russell famously wrote Frege a letter in which he detailed the problem with his (Frege s system) and how it could give rise to contradictions. Frege saw that if Russell were right, his entire project was threatened. But rather than ignore Russell s letter, Frege tried to meet Russell s objection. Just before Frege s Basic Laws of Arithmetic v.2 was to be printed, Frege added an appendix commenting on this problem and on possible ways to avoid it. But Frege eventually came to agree that the problem identified by Russell was fatal to his project. He never finished the projected third volume of Basic Laws; he spent his remaining years working on other projects. 5 For more on this subject, see A. D. Irvine, Russell s Paradox, The Stanford Encyclopedia of Philosophy (Summer 2004 Edition), Edward N. Zalta (ed.), URL = < Generally, a paradox is a statement claiming something which goes beyond (or even against) common opinion (what is usually believed or held). (Andrea Cantini, Paradoxes and Contemporary Logic, The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.), URL = < The word pardox derives from the Greek for beyond ( para ) opinion ( doxa ).

4 [3.4.] Russell s Theory of Descriptions. Russell put forward this theory in his 1905 article On Denoting. [3.4.1.] Denoting Phrases. Russell intended his theory to explain the meaning of denoting phrases. Denotation usually means the same thing as reference (which is the word that is usually used to translate Frege s term Bedeutung ) so presumably, Russell wanted the theory to explain the meaning of phrases that refer. But it seems that he did not have all referring phrases in mind: By a denoting phrase I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the centre of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. (35, emphasis added) That last sentence isn t very helpful. Russell is better at giving examples of denoting phrases than he is at giving a general definition. (Also notice that Russell is not using quotation marks to distinguish when he is using words and when he is merely mentioning them. Bad Russell!) But from what he tells us here, Russell takes denoting phrases to include: definite descriptions and phrases of the form all (and their synonyms) and of the form some (and their synonyms). But what about proper names, like Venus (and Bertrand Russell, and Gottlob Frege )? In a later work 6, Russell maintains that proper names are usually really descriptions (193), i.e., definite descriptions. So they get included in Russell s theory as well. [3.4.2.] Why Denoting Phrases are Important. According to Russell, denoting phrases are very important for human knowledge. This is because there are some things we are capable of knowing only by way of denotation. He gives as an example: we know that the centre of mass of the solar system at a definite instant is some definite point, and we can affirm a number of propositions about it. (35) So this is something that we can have knowledge of: the center of mass of the solar system at a definite point in time. 6 Knowledge by Acquaintance and Knowledge by Description, 1917; in your textbook beginning at p.190. Russell distinguished between ordinary proper names (e.g., Venus, Barack Obama, the Eiffel Tower ) and logically proper names. The former are usually equivalent to descriptions, while the latter are the only names that refer directly to the things they denote. In English, there are only three logically proper names: this, that and I and the first two can refer only to sense data with which the speaker is directly acquainted. One s own name can also serve as a logically proper name if it is used by oneself to refer to oneself.

5 But we have no acquaintance with it; we do not have presentations of it: it is not an object of perception, i.e., we do not perceive it with the senses; nor is it one of those objects with a more abstract logical character that we are acquainted with by way of thought (e.g., a number). The only way that we can reach this object is by means of denoting phrases. Without denoting phrases, we would be incapable of having knowledge of those things with which we are not acquainted. Russell gives an additional example: there seems no reason to believe that we are ever acquainted with other people s minds, seeing that these are not directly perceived; hence what we know about them is obtained through denoting. (33) [Unfortunately, Russell does not give an example of the sort of denoting phrase someone might use to refer to another person s mind or mental states. Frege s mind and Russell s pain don t seem to be denoting phrases as defined by Russell. Perhaps he has in mind something like the mental state currently being experienced by Frege. ] [3.4.3.] The Theory Itself. Unlike Frege s account of referring terms (like the Evening Star and the Morning Star ), Russell s theory of descriptions does not involve a distinction between sense and reference. Russell wants to operate with a simpler notion of meaning than Frege s. The following four points summarize Russell s theory of descriptions. 1. Denoting phrases have meaning only within the context of a sentence. Phrases like a woman, some man, all persons, the father of Charles II, the morning star, the evening star, etc., have no meaning when they occur by themselves. [D]enoting phrases never have any meaning in themselves every proposition in whose verbal expression they occur has a meaning. The difficulties concerning denoting are, I believe, all the result of a wrong analysis of propositions whose verbal expressions contain denoting phrases. (36) 2. The meaning of a denoting phrase in the context of a sentence is not what it appears to be. In The father of Charles II was executed, the denoting phrase The father of Charles II does not mean Charles I (even though Charles I of England was the father of Charles II of England). 3. The real meaning of a sentence containing a denoting phrase is given by the following sort of translation: I met a man means: I met x, and x is human is not always false. (36) Or, less formally than Russell himself puts it: There is an x such that x is human and I met x.

6 In these translations, x is a variable a letter that stands for some unspecified thing (as a variable in algebra stands for some unspecified number). Russell says that he take[s] the notion of the variable to be fundamental (36). This translation reveals that the original sentence, which is grammatically a subject-predicate sentence, is, from the point of view of logic, an existential sentence, i.e., a sentence asserting that something exists. 4. The real meaning of a sentence containing a definite description (and thus a proper name) includes: a. an existence claim (there is an x); b. a predication of a property (x has property F); c. a uniqueness claim (for all y, if y has F, then y=x). The sentence The father of Charles II was executed really means: It is not always false of x that x begat Charles II and that x was executed and that if y begat Charles II, y is identical with x is always true of y. (37) Less formally than Russell himself puts it: There is an x such that x begat Charles II, and for all y, if y begat Charles II, then y=x, and x was executed. This includes the following three elements: There is an x... [the existence claim] that begat Charles II [the predication of a property] and for all y, if y begat Charles II, y=x [the uniqueness claim] and x was executed. The definite description ( the father of Charles II ) has disappeared from this translation. (The phrase that begat Charles II is not the same as the definite description the father of Charles II.) Here is a different example that will soon be shown to be very important to Russell: The present king of France is a definite description. The sentence The present king of France is bald really means: There is an x... [the existence claim] that is presently King of France [the predication of a property] and for all y, if y is presently King of France, then y=x... [the uniqueness claim] and x is bald. And again, the definite description the present King of France has disappeared from this translation. (The phrase is presently King of France is not the same as the definite description the present king of France.)

7 ***These four claims do not constitute an argument for the theory; they simply summarize the theory itself. Regarding why we should believe the theory, Russell writes: The evidence for the above theory is derived from the difficulties which seem unavoidable if we regard denoting phrases as standing for genuine constituents of the propositions in whose verbal expressions they occur. (37) 7 In other words, other theories that attempt to explain the meaning of denoting terms have troublesome implications that Russell s theory does not have. Stopping point for Monday September 22. For next time, finish reading Russell s On Denoting, pp Come to class prepared to discuss these questions: 1. What are the three puzzles that Russell believes his theory of denoting will solve? 2. How does he think his theory will solve those puzzles? 7 This indicates that Russell understood a proposition to be (not an abstract object a thought or sense like Frege held it to be, but rather) something like the fact represented by a sentence.