The Rise of Analytic Philosophy, 1879–1930

From Frege to Ramsey

Michael Potter

• Publisher: Routledge
• Year: 2019
• ISBN:
  9781317689706
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

In this book Michael Potter offers a fresh and compelling portrait of the birth of modern analytic philosophy, viewed through the lens of a detailed study of the work of the four philosophers who contributed most to shaping it: Gottlob Frege, Bertrand Russell, Ludwig Wittgenstein, and Frank Ramsey. It covers the remarkable period of discovery that began with the publication of Frege's Begriffsschrift in 1879 and ended with Ramsey's death in 1930. Potter—one of the most influential scholars of this period in philosophy—presents a deep but accessible account of the break with absolute idealism and neo-Kantianism, and the emergence of approaches that exploited the newly discovered methods in logic. Like his subjects, Potter focusses principally on philosophical logic, philosophy of mathematics, and metaphysics, but he also discusses epistemology, meta-ethics, and the philosophy of language. The book is an essential starting point for any student attempting to understand the work of Frege, Russell, Wittgenstein, and Ramsey, as well as their interactions and their larger intellectual milieux. It will also be of interest to anyone who wants to cast light on current philosophical problems through a better understanding of their origins.

PART I
Frege

1
Biography

Gottlob Frege was born in 1848 in Wismar, a Baltic port in what was then Mecklenburg. His father, the headmaster of a girls’ secondary school, died when he was 18 and his mother ran the school for some years thereafter. He went to Jena for his undergraduate degree, seemingly at the encouragement of a young mathematics teacher called Leo Sachse who had studied there a few years earlier. Frege majored in mathematics, but also attended Kuno Fischer’s Kant course. He studied geometry as a doctoral student at Göttingen for two years (during which time he attended Lotze’s lectures on the philosophy of religion) before returning to Jena for the remainder of his professional career. Although many of his publications were in philosophy, his teaching appointment at Jena was in the mathematics department.

Frege’s first major publication, in 1879, was Begriffsschrift (‘concept-script’), the book which began the modern era in logic. Although its reviews were by no means uniformly negative, he was disappointed by its reception. By then he was writing another book which continued the formal project initiated in Begriffsschrift of establishing a logical basis for arithmetic, but he was advised by a friend to postpone its publication and focus instead on explaining the motivation. The result was his 1884 book Die Grundlagen der Arithmetik (‘The Foundations of Arithmetic’), in which he sought to make it plausible that arithmetic is derivable from logic. The book largely avoids the pedantic and uncharitable criticisms of others that mar his later work, and is one of the most readable of the classics of philosophy.

This was evidently a relatively happy time in Frege’s life: he was recently married and now had a secure (although not well paid) job at Jena. Although he published nothing between 1885 and 1891, he made significant changes to his semantic theory, resulting in three papers in 1891–2: ‘On sense and reference’, in particular, remains one of the most widely read papers in analytic philosophy. In 1893 there appeared the first volume of Grundgesetze der Arithmetik (‘Basic Laws of Arithmetic’), intended as the culmination of the Begriffsschrift project. Frege said there (I, ix) that the delay in its publication was due partly to these changes, which had led him to put aside an almost complete manuscript, but he also mentioned once again his disappointment at the failure of his earlier work to have the effect it merited.

In 1902, with the second volume of Grundgesetze already in press, Frege received a now famous letter from Russell informing him that the formal system on which his whole account of arithmetic was based contained a contradiction. He went ahead with publication, but added a short appendix proposing an amendment to Basic Law V (the axiom which gave rise to the contradiction). The second volume ends abruptly, and he evidently intended a third, which never appeared.

After this, Frege took sick leave with what was probably depression. Some have speculated that the reason was the discovery that his life’s work was flawed— he realized quite soon (certainly by 1906) that his amended system is insufficient to ground arithmetic—but it is at least as likely that the reason was the death of his wife, after a long illness, in 1904. Wittgenstein said much later that he thought they had had children who died in infancy, but the records do not confirm this. Soon after his wife’s death, however, Frege took in an orphan called Alfred, a distant relative, whom he eventually adopted as his son. (He also gave financial support to Alfred’s sister, Toni.)

After the collapse of his attempt to derive arithmetic from logic, Frege continued to offer a lecture course on his concept-script at Jena each year (generally to very small audiences), but since he now omitted any mention of value-ranges (the notion which, as we shall see, was responsible for the contradiction), the system he taught had no hope of grounding logicism. Carnap, who attended the course in 1910, recalled an extremely shy man who addressed his lectures almost entirely to the blackboard.

Between 1911 and 1913 Frege received annual visits from Wittgenstein. These visits were formative for the young man, who held Frege in reverence for the rest of his life. They continued to correspond until Wittgenstein had him sent a typescript of the Tractatus in December 1918: Frege’s lack of comprehension of it was a bitter disappointment to him.

After missing two semesters in 1913–14 and three in 1917–18 through further ill health, Frege retired from his university position in 1918 and, aided by a generous gift from Wittgenstein, moved to Bad Kleinen, close to his Mecklenburg birthplace. He had for many years been planning a book on the philosophy of logic—to be called Logische Untersuchungen (‘Logical Investigations’)— and in retirement he published several chapters of it. He also continued to look for an account of mathematical knowledge, but he now speculated that it has a geometrical rather than a logical source.

Frege had previously counted himself a liberal, but in the last year of his life he expressed in his diary both disenchantment with democracy and intolerance of various other groups such as Catholics, Jews and the French. Although he explicitly disapproved of Hitler’s recent failed coup, his desire for a leader with ‘youthful vigour to sweep away the people’ (Mendelsohn 1996, 324) makes for uncomfortable reading. These diary entries were omitted from the collected edition of his writings as not being philosophical in character. Dummett later expressed regret at their omission, saying that by reading them he had ‘learned something about human beings which I should be sorry not to know’ (1973, xii).

When Frege died in 1925, he left his unpublished papers to his son, telling him that ‘even if all is not gold, there is gold in them’ (PW, ix). Alfred deposited the material at the University of Münster in 1935, but it was apparently destroyed in its entirety by an allied bombing raid in March 1945: although it matters little now, the raid was carried out not by the Americans, as Dummett (1973, 662) asserted, but by 175 aircraft of RAF Bomber Command. Fortunately for posterity, much of the content survives in copies which the editors of the Nachlass had made before the war.

References

Frege’s main works will be referred to here by the following abbreviations:

Bs	Begriffsschrift (1879)
Gl	Die Grundlagen der Arithmetik (1884)
Gg	Grundgesetze der Arithmetik (2 vols, 1893–1903)

His other surviving writings are translated in the following volumes:

CN	Conceptual Notation and Related Articles
CP	Collected Papers
PMC	Philosophical and Mathematical Correspondence
PW	Posthumous Writings
L13	Lectures on Logic

Further reading

Kreiser’s (2001) biography contains a great deal of circumstantial information but little insight. The fate of Frege’s Nachlass at Münster is described by Wehmeier & am Busch (2005). Of the single-volume introductions to his philosophy Kenny (1995) is the best for beginners; Kanterian (2012) focuses mainly on Begriffsschrift, Noonan (2001) on his later semantics. For an overview of Frege’s logic see Kneale & Kneale (1962, ch. 8).

2
Logic Before 1879

‘Logic is an old subject, and since 1879 it has been a great one.’ (Quine 1952, vii) That the publication of Begriffsschrift was a key moment in the history of logic can hardly be denied, but if we are to appreciate Frege’s achievement, we need to survey previous developments. Modern logic is so much in his shadow, indeed, that it is something of a challenge to present these as more than a series of missed opportunities to grasp Fregean insights.

Stoic logic

There were ancient traditions of Indian, Arabic and Chinese logic; but, for better or worse, these other traditions had rather little influence on European logic, which emerged from two distinct (and competing) schools in ancient Greece. The first of these schools, which was founded by Euclid of Megara (who studied under Socrates and was active in the early 4th century BC) before being continued by the Stoics, focused on propositional logic. Philo of Megara introduced the material conditional, nowadays written as p ⊃ q, around 300BC, and came tantalizingly close to the modern truth-table for it when he observed that there are three ways that it can be true and one that it can be false (Sextus Empiricus 2005, bk 2, §113). He argued against the attempt by his teacher, Diodorus Cronus, to treat the conditional as a tensed generalization—one that ‘neither could nor can begin with a truth and end with a falsehood’. Later Chrysippus recommended something closer to what we now call the strict conditional □(p ⊃ q).

Philo may have been an inch away from the modern conception of a truth-function, but his successors showed little recognition of its significance. Although Chrysippus distinguished between atomic and molecular propositions and included among the logical connectives the material conditional, conjunction and (exclusive) disjunction (which are truth-functions), he also included causation (which is not). Nonetheless, the Stoics did at least systematize the rules of inference (Modus Ponens, Modus Tollens, etc.) now familiar in introductory courses on propositional logic. Later logicians called propositions formed by means of the connectives just mentioned ‘hypothetical propositions’, and the inferences which they license ‘hypothetical syllogisms’. The details of the Stoic theory are somewhat obscured, however, by the paucity of the available texts. Only fragments of Chrysippus’s logical writings survive, and he is nowadays famous for little more than having died laughing at one of his own jokes.

Aristotelian logic

A second strand of logic began in the 4th century BC with Aristotle’s Prior Analytics, which studied the logical relationships between four kinds of proposition known as ‘categorical’.

• (A) Every Φ is a ψ
• (E) No Φ is a ψ
• (I) Some Φ is a ψ
• (O) Some Φ is not a ψ

It was Aristotle who initiated the use of a letter of the (Greek) alphabet ‘schematically’, i.e. to stand for an unspecified piece of language of some appropriate grammatical type.

We can treat the four Aristotelian forms as binary operators, written A(Φ, ψ), E(Φ, ψ), I(Φ, ψ) and O(Φ, ψ) respectively. So, for instance, the argument

	No ψ is a Φ
	Some X is a ψ)
∴	Some X is not a Φ

would be formalized as

	E(ψ, Φ)	(major premiss)
	I(X, ψ)	(minor premiss)
∴	O(X, ψ)	(conclusion)

Aristotle classified the various syllogisms and showed that all the valid ones follow from a small number of syllogisms and other rules.

From the outset Aristotelian logic was seen more as a competitor than as a supplement to Stoic logic, and there emerged among the peripatetics an ambition—towards which, however, they made little progress—of assimilating the latter to the former. Because of this failure, logic continued right up to the modern era to be seen as the study of two distinct kinds of syllogism, hypothetical and categorical, neither of which could capture all the complexity of actual arguments in fields such as mathematics.

In the following centuries the pace of development of Aristotle’s logic was slow. When the study of logic resumed in Europe after the Dark Ages, progress was further hampered by the fact that the Prior Analytics had been lost: its rediscovery in the 12th century marked the transition from what came to be known as the ‘old’ to the ‘new’ logic.

One purely notational device introduced in the Middle Ages was the labelling of the four forms A, E, I and O. The valid syllogisms were then given names which encoded (by means of the vowels) which forms they contained and (by means of the consonants) how they could be ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Acknowledgments
• Introduction
• Part I Frege
• Part II Russell
• Part III Wittgenstein
• Part IV Ramsey
• Bibliography
• Index