A Brief History of Analytic Philosophy

From Russell to Rawls

Stephen P. Schwartz

• Publisher: Wiley-Blackwell
• Year: 2012
• Print ISBN: 9780470672082, 9780470672075
• eBook ISBN: 9781118271728
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

A Brief History of Analytic Philosophy: From Russell to Rawls presents a comprehensive overview of the historical development of all major aspects of analytic philosophy, the dominant Anglo-American philosophical tradition in the twentieth century. 

• Features coverage of all the major subject areas and figures in analytic philosophy - including Wittgenstein, Bertrand Russell, G.E. Moore, Gottlob Frege, Carnap, Quine, Davidson, Kripke, Putnam, and many others
• Contains explanatory background material to help make clear technical philosophical concepts
• Includes listings of suggested further readings
• Written in a clear, direct style that presupposes little previous knowledge of philosophy

 

Chapter 1

Russell and Moore

The question which Kant put at the beginning of his philosophy, namely “How is pure mathematics possible?” is an interesting and difficult one, to which every philosophy which is not purely sceptical must find some answer. (Russell 1959a/1912, p. 84)

Empiricism, Mathematics, and Symbolic Logic

Bertrand Russell—aristocrat (3rd Earl Russell), anti-war activist, prolific writer, and brilliant philosopher and mathematician—is the father of Anglo-American analytic philosophy. Russell did the hard work of expounding and promulgating the new symbolic logic that was to revolutionize the method of philosophy. Equally important for analytic philosophy, he introduced others to the works of Gottlob Frege and Ludwig Wittgenstein, who might otherwise have languished unappreciated. Russell proposed and energetically pursued philosophical issues that were keenly examined by philosophers throughout the twentieth century. Without Bertrand Russell's work, especially the work he produced early in his career in logic and the philosophy of language, there would have been no Anglo-American analytic philosophy.

Russell says that Frege was the pioneer and no doubt this is true. “Many matters which, when I was young, baffled me by the vagueness of all that had been said about them, are now amenable to an exact technique, which makes possible the kind of progress that is customary in science.…[T]he pioneer was Frege, but he remained solitary until his old age”(Russell 1963/1944, p. 20).¹ Russell's optimism about philosophical progress may seem overstated, but not his judgment of Frege. Frege did revolutionary work on the foundations of mathematics and was the first to clarify and investigate issues in the philosophy of language that were central to twentieth-century philosophy and are still central today. Indeed Gottlob Frege was the pioneer of the techniques that gave life to analytic philosophy, but he would not have had an impact without Russell's influence. Frege would have remained solitary. Russell brought Frege to the attention of other philosophers and mathematicians, especially in the English-speaking world, and developed and improved Frege's pioneering ideas.

Russell's greatest contribution to logic, philosophy, and mathematics was his publication of Principia Mathematica with Alfred North Whitehead (published in three volumes, 1910–13). Based on ideas originally articulated by Frege in the late nineteenth century, Russell developed and founded the field of symbolic logic. Symbolic logic today is central not only to philosophy but to many other areas including mathematics and computer science.² In addition to Principia Mathematica (often referred to simply as PM), Russell expounded the ideas and methods of the new symbolic logic energetically in his Principles of Mathematics and many other influential publications early in the twentieth century. The influence, importance, and central role of PM cannot be overemphasized. For example, Kurt Gödel titled his historic paper “On formally undecidable propositions of Principia Mathematica and related systems.” (More on this influential mathematical paper below (see pp. 162–4).)

The methodology that gives analytic philosophy its strength and structure is the logic and philosophy of language generated by the original work of Frege, Russell, and Whitehead.

Their results in logic and the philosophy of language have also had major impacts in other areas of philosophy. The revolution in logic in the early years of the twentieth century gave analytic philosophers the tools to articulate and defend a sophisticated form of empiricism. [Background 1.1 —Epistemology: empiricism versus rationalism (The background snippets are found at the end of the chapter.)] With the new tools in logic and philosophy of language, philosophers were able to repair the flaws and gaps in thinking of the classical British empiricists. The major gap was the lack of an explanation of how pure mathematics is possible. Modern logic as developed by Frege, Russell, and Whitehead yielded definite results in the foundations of mathematics and the philosophy of language that, though technical and expounded in daunting detail, went to the heart of epistemological issues. Empiricists could claim to have solved the outstanding problems plaguing their theory—namely our knowledge of mathematics—by using the techniques of mathematical logic. (This is explained in the next section.)

Although Russell was uneasy with empiricism, his sympathy was with the classical British empiricists. Virtually all analytic philosophers have shared this sympathy while at the same time becoming increasingly uneasy with the details and presuppositions of classical empiricism. Russell could not accept “pure empiricism”—the view that all knowledge is derived from immediate sensory experience—but sought to move only as far from it as was absolutely necessary. Speaking of his very early views Russell says: “it seemed to me that pure empiricism (which I was disposed to accept) must lead to skepticism…”(Russell 1959b/1924, p. 31). Even worse than skepticism, Russell came to believe that pure empiricism led to solipsism and could not account for our knowledge of scientific laws or our beliefs about the future. Still, Russell always seemed to feel that these were problems for empiricism, not reasons to discard it outright.

Despite his sympathy with empiricism, in places Russell sounds like an unabashed rationalist: “It is, then, possible to make assertions, not only about cases which we have been able to observe, but about all actual or possible cases. The existence of assertions of this kind and their necessity for almost all pieces of knowledge which are said to be founded on experience shows that traditional empiricism is in error and that there is a priori and universal knowledge” (Russell 1973, p. 292. From a lecture given in 1911). [Background 1.2 —A priori, analytic, necessary]

Despite his wavering philosophical sympathies, Russell's mathematical logic gave later empiricists the tools to respond to the troubling difficulties with their position that Russell was pointing out. Mathematics is a priori and universal, so how can it be empirical? Twentieth-century analytic philosophy got its first shot of energy from a plausible answer to this question—an answer offered by the logical investigations of Frege and Russell.³

Frege and Russell were able to use symbolic logic to reconceptualize the very nature of mathematics and our mathematical knowledge (Figure 1.1). I must emphasize that symbolic logic as developed in PM was not just the use of symbols—so that for example we use “∨” instead of the word “or” and “(∃x)” for “some.” That would be impressive perhaps and simplifying in some ways, but not revolutionary. The revolution in logic, pioneered by Frege, and expounded by PM was based on the concept of treating logic mathematically, and then treating mathematics as a form of logic. This is Frege's and Russell's logicism.⁴ [Background 1.3 —Mathematical logic of PM versus traditional Aristotelian logic and a note on symbolism]

Figure 1.1 This is a page chosen at random from Principia Mathematica. PM is extremely daunting and is today studied only by specialists, although it has an accessible introduction that is a brief overview of symbolic logic.

Symbolic logic is not only of technical interest for those concerned about the foundations of mathematics. Virtually every philosophy major in every college and university in the United States and elsewhere is required to pass a course in symbolic logic. Not only philosophy majors, but other students as well—computer science majors, mathematics majors, not to mention English majors—take symbolic logic courses. Symbolic logic has also been central to the development of computers, and it is now a branch of mathematics, and is an indispensable tool for theoretical linguistics and virtually anyone working in technical areas of the study of language.

Symbolic logic has been the central motivating force for much of analytic philosophy. Besides giving philosophers the tools to solve problems that have concerned thinkers since the Greeks, the notion that mathematics is logic points to an answer to the question posed by Kant in the quote that opens this chapter. “How is pure mathematics possible?” This is an answer that removes mathematics as an obstacle to empiricism. Mathematics is possible because it is analytic.

Logicism

Whitehead and Russell's PM was an elaborate argument for logicism, which in turn was based on earlier work by Frege. The logicist program is succinctly stated by Russell and attributed to Frege: “Frege showed in detail how arithmetic can be deduced from pure logic, without the need of any fresh ideas or axioms, thus disproving Kant's assertion that ‘7 + 5 = 12’ is synthetic” (Russell 1959b, p. 32).

Logicism was one of several responses to difficulties that emerged in the foundations of mathematics toward the end of the nineteenth century. These difficulties perplexed Russell and many others. We can skip over the technicalities for now, and keep in mind that none of the difficulties that troubled Russell would matter for any practical applications of mathematics or arithmetic. You could still balance your checkbook even if the foundations of mathematics had not been put on a firm footing. Nevertheless, to a philosopher of Russell's uncompromising character these difficulties were intellectually troubling. The results of his investigations have thrilled and baffled philosophers ever since and tormented and fascinated (at least a few) students taking Symbolic Logic.

The nature of mathematics and arithmetic is a central problem for philosophers, especially in the area of epistemology. In the argument between the empiricists and rationalists, the question of our knowledge of mathematical facts plays a key role. Even an impure (i.e., moderate) empiricist must answer the question how we know that 7 + 5 = 12, that the interior angles of a triangle equal 180°, that there are infinitely many prime numbers, and so on. “Of course, we know them because we were told them in school and read them in the textbook.” This answer, while having an appealing simplicity, would disappoint both the rationalist and the empiricist and is abjectly unphilosophical. We know those mathematical facts because we can figure them out, “see the truth of them,” especially when we've been shown the proofs or done the calculations. [Background 1.4 —Proofs that the sum of the interior angles of a triangle is 180° and that there are infinitely many prime numbers] And the marvelous thing is, not only that we “see” the truths, but also understand that they must be so, could not be otherwise, and are necessary and absolute. No experience could impart such certainty. Mathematical knowledge dooms the empiricist claim that all knowledge is based on experience.

Russell's assertions about geometry in the following quote apply to all of mathematics. (When he uses the term “idealists” his description applies to rationalists.)

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Geometry, throughout the 17th and 18th centuries, remained, in the war against empiricism, an impregnable fortress of the idealists. Those who held—as was generally held on the Continent—that certain knowledge, independent of experience, was possible about the real world, had only to point to Geometry: none but a madman, they said, would throw doubt on its validity, and none but a fool would deny its objective reference. The English Empiricists, in this matter, had, therefore, a somewhat difficult task; either they had to ignore the problem, or if, like Hume and Mill, they ventured on the assault, they were driven into the apparently paradoxical assertion that Geometry, at bottom, had no certainty of a different kind from that of Mechanics…(Russell 1897, p. 1)⁵

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The problem that empiricism has with mathematics is worth pondering. Even if “7 + 5 = 12” and “the interior angles of a triangle equal 180°” are derived in some way from experiences of counting and measuring angles, it is impossible that, e.g., our knowledge of the infinitude of primes comes from experience. Although perhaps the idea could be led back by many steps to experiences with counting and dividing and so on, I do not see how any experience or observation (other than “seeing” the proof) could get one to know with certainty that there are infinitely many prime numbers. Using a computer to generate prime numbers wouldn't help. It would just keep calculating primes, but how could we know it would never get to the last one? There is no possible empirical test that would establish that there are infinitely many primes. Yet the proof is so simple and obvious that there can be no doubt. If you are troubled by the indirect nature of the proof, be assured there are direct proofs. In any case, Euclid's proof assures us there is a larger prime given any series of primes.

Empirical evidence and observations even if pervasive and universal cannot explain the certainty and necessity of mathematical propositions. In the case of a mathematical proposition such as “7 + 5 = 12,” empirical observations are not evidence or support. If a proposition is based on observational evidence, then there must be pos...

Table of contents

• Cover
• Title Page
• Copyright
• Dedication
• Preface
• Introduction
• Chapter 1: Russell and Moore
• Chapter 2: Wittgenstein, the Vienna Circle, and Logical Positivism
• Chapter 3: Responses to Logical Positivism: Quine, Kuhn, and American Pragmatism
• Chapter 4: Oxford Ordinary Language Philosophy and Later Wittgenstein
• Chapter 5: Responses to Ordinary Language Philosophy: Logic, Language, and Mind
• Chapter 6: The Rebirth of Metaphysics
• Chapter 7: Naming, Necessity, and Natural Kinds: Kripke, Putnam, and Donnellan
• Chapter 8: Ethics and Metaethics in the Analytic Tradition
• Chapter 9: Epilogue: Analytic Philosophy Today and Tomorrow
• References
• Index