The origin of the RSDLP split was Lenin's support for a smaller
party of professional revolutionaries, as opposed to the Menshevik
desire for a broad party membership. The influence of the factions
fluctuated in the years up to 1912, when the RSDLP formally split in
two. The political philosophy of the Bolsheviks was based on the
Leninist principles of vanguardism and democratic centralism.
Lenin was also more willing to use illegal means such as robbery to
fund the party's activities. By 1917, influenced by the experiences of World War I,
he reached the conclusion that the chain of world capitalism could
"break at its weakest link" in Russia before it assumed the level of the
advanced countries, opposing theorists such as Georgi Plekhanov. Lenin had also come to view poorer peasants as potential allies of the relatively small Russian proletariat.
After the February Revolution of 1917, Lenin returned to Russia and issued his April Theses, which called for "no support for the Provisional Government" and "all power to the soviets." During the summer of 1917, which saw events including the July Days and Kornilov affair,
large numbers of radicalized workers joined the Bolsheviks, which
planned the October Revolution that overthrew the government. The
Bolsheviks initially governed in coalition with the Left Socialist-Revolutionaries, but increasingly centralized power and suppressed opposition during the Russian Civil War. After 1921, it became the sole legal party in Soviet Russia and the Soviet Union. Under Joseph Stalin's leadership, Bolshevism became linked to his policies of "socialism in one country," rapid industrialization, collectivized agriculture, and centralized state control.
Lenin's political pamphlet What Is to Be Done?, written in 1901, helped to precipitate the Bolsheviks' split from the Mensheviks. In Germany, the book was published in 1902, but in Russia, strict censorship outlawed its publication and distribution. One of the main points of Lenin's writing was that a revolution
can only be achieved by a strong, professional leadership with deep
dedication to Marxist theoretical principles and an organization that
spanned through the whole of Russia, abandoning what Lenin called
"artisanal work" towards a more organized revolutionary work. After the
proposed revolution had successfully overthrown the Russian autocracy,
this strong leadership would relinquish power and allow a socialist party to fully develop within the principles of democratic centralism. Lenin said that if professional revolutionaries
did not maintain influence over the fight of the workers, then that
fight would steer away from the party's objective and carry on under the
influence of opposing beliefs or even away from revolution entirely.
The pamphlet also showed that Lenin's view of a socialist intelligentsia was in line with Marxist theory. For example, Lenin agreed with the Marxist ideal of social classes ceasing to be and for the eventual "withering away of the state". Most party members considered unequal treatment of workers immoral and were loyal to the idea of a completely classless society. This pamphlet also showed that Lenin opposed another group of reformers, known as "Economists",
who were for economic reform while leaving the government relatively
unchanged and who, in Lenin's view, failed to recognize the importance
of uniting the working population behind the party's cause.
Second Party Congress
At the 2nd Congress of the RSDLP, which was held in Brussels and then London during August 1903, Lenin and Julius Martov disagreed over the party membership rules. Lenin, who was supported by Georgy Plekhanov,
wanted to limit membership to those who supported the party full-time
and worked in complete obedience to the elected party leadership. Martov
wanted to extend membership to anyone "who recognises the Party
Programme and supports it by material means and by regular personal
assistance under the direction of one of the party's organisations." Lenin believed his plan would develop a core group of professional
revolutionaries who would devote their full time and energy towards
developing the party into an organization capable of leading a
successful proletarian revolution against the Tsarist autocracy.
The base of active and experienced members would be the
recruiting ground for this professional core. Sympathizers would be left
outside and the party would be organised based on the concept of democratic centralism.
Martov, until then a close friend of Lenin, agreed with him that the
core of the party should consist of professional revolutionaries, but he
argued that party membership should be open to sympathizers,
revolutionary workers, and other fellow travellers. The two had
disagreed on the issue as early as March–May 1903, but it was not until
the Congress that their differences became irreconcilable and split the
party. At first, the disagreement appeared to be minor and inspired by
personal conflicts. For example, Lenin's insistence on dropping less
active editorial board members from Iskra
or Martov's support for the Organizing Committee of the Congress which
Lenin opposed. The differences grew and the split became irreparable.
Internal unrest also arose over the political structure that was best suited for Soviet power. As discussed in What Is To Be Done?,
Lenin firmly believed that a rigid political structure was needed to
effectively initiate a formal revolution. This idea was met with
opposition from once close allies, including Martov, Plekhanov, Vera Zasulich, Leon Trotsky, and Pavel Axelrod. Plekhanov and Lenin's major dispute arose addressing the topic of nationalizing land or leaving it for private use. Lenin wanted to nationalize to aid in collectivization, whereas Plekhanov
thought worker motivation would remain higher if individuals were able
to maintain their own property. Those who opposed Lenin and wanted to
continue on the socialist mode of production path towards complete socialism
and disagreed with his strict party membership guidelines became known
as "softs" while Lenin supporters became known as "hards".
Some of the factionalism could be attributed to Lenin's steadfast
belief in his own opinion and what was described by Plekhanov as
Lenin's inability to "bear opinions which were contrary to his own" and
loyalty to his own self-envisioned utopia. Lenin was seen even by fellow party members as being so narrow-minded
and unable to accept criticism that he believed that anyone who did not
follow him was his enemy. Trotsky, one of Lenin's fellow revolutionaries, compared Lenin in 1904 to the French revolutionary Maximilien Robespierre.
Etymology of Bolshevik and Menshevik
The two factions of the Russian Social Democratic Labour Party (RSDLP) were originally known as hard (Lenin supporters) and soft (Martov supporters). In the 2nd Congress vote, Lenin's faction won votes on the majority of important issues, and soon came to be known as Bolsheviks, from the Russian bolshinstvo, 'majority'. Likewise, Martov's group came to be known as Mensheviks, from menshinstvo, 'minority'. However, Martov's supporters won the vote concerning the question of
party membership, and neither Lenin nor Martov had a firm majority
throughout the Congress as delegates left or switched sides. In the end,
the Congress was evenly split between the two factions.
Starting in 1907, English-language articles sometimes used the term Maximalist for "Bolshevik" and Minimalist for "Menshevik", which proved to be confusing as there was also a "Maximalist" faction within the Russian Socialist Revolutionary Party in 1904–1906 (which, after 1906, formed a separate Union of Socialists-Revolutionaries Maximalists) and then again after 1917.
The average party member was very young: in 1907, 22% of Bolsheviks
were under 20 years of age; 37% were 20–24 years of age; and 16% were
25–29 years of age. By 1905, 62% of the members were industrial workers (3% of the population in 1897). Twenty-two percent of Bolsheviks were gentry (1.7% of the total population) and 38% were uprooted peasants; compared with 19% and 26% for the Mensheviks. In 1907, 78% of the Bolsheviks were Russian and 10% were Jewish;
compared to 34% and 20% for the Mensheviks. Total Bolshevik membership
was 8,400 in 1905, 13,000 in 1906, and 46,100 by 1907; compared to
8,400, 18,000 and 38,200 for the Mensheviks. By 1910, both factions
together had fewer than 100,000 members.
Beginning of the 1905 Revolution (1903–05)
Between 1903 and 1904, the two factions were in a state of flux, with
many members changing sides. Plekhanov, the founder of Russian Marxism,
who at first allied himself with Lenin and the Bolsheviks, had parted
ways with them by 1904. Trotsky at first supported the Mensheviks, but
left them in September 1904 over their insistence on an alliance with
Russian liberals and their opposition to a reconciliation with Lenin and
the Bolsheviks. He remained a self-described "non-factional social democrat" until August 1917, when he joined Lenin and the Bolsheviks, as their positions resembled
his and he came to believe that Lenin was correct on the issue of the
party.
All but one member of the RSDLP Central Committee were arrested
in Moscow in early 1905. The remaining member, with the power of
appointing a new committee, was won over by the Bolsheviks. The lines between the Bolsheviks and the Mensheviks hardened in April
1905 when the Bolsheviks held a Bolsheviks-only meeting in London, which
they called the 3rd Party Congress. The Mensheviks organised a rival conference and the split was thus finalized.
The Bolsheviks played a relatively minor role in the 1905 Revolution and were a minority in the Saint Petersburg Soviet of Workers' Deputies led by Trotsky. However, the less significant Moscow Soviet was dominated by the Bolsheviks. These Soviets became the model for those formed in 1917.
Mensheviks (1906–07)
As the Russian Revolution of 1905 progressed, Bolsheviks, Mensheviks,
and smaller non-Russian social democratic parties operating within the Russian Empire attempted to reunify at the 4th Congress of the RSDLP held in April 1906 at Folkets hus, Norra Bantorget, in Stockholm. When the Mensheviks made an alliance with the Jewish Bund, the Bolsheviks found themselves in a minority.
However, all factions retained their respective factional structure and the Bolsheviks formed the Bolshevik Centre, the de facto governing body of the Bolshevik faction within the RSDLP. At the 5th Congress
held in London in May 1907, the Bolsheviks were in the majority, but
the two factions continued functioning mostly independently of each
other.
Split between Lenin and Bogdanov (1908–10)
Tensions had existed between Lenin and Alexander Bogdanov from as early as 1904. Lenin had fallen out with Nikolai Valentinov after Valentinov had introduced him to Ernst Mach's Empiriocriticism, a viewpoint that Bogdanov had been exploring and developing as Empiriomonism. Having worked as co-editor with Plekhanov, on Zarya, Lenin had come to agree with the Valentinov's rejection of Bogdanov's Empiriomonism.
With the defeat of the revolution in mid-1907 and the adoption of
a new, highly restrictive election law, the Bolsheviks began debating
whether to boycott the new parliament known as the Third Duma. Lenin, Grigory Zinoviev, Lev Kamenev, and others argued for participating in the Duma while Bogdanov, Anatoly Lunacharsky, Mikhail Pokrovsky, and others argued that the social democratic faction in the Duma should be recalled. The latter became known as "recallists" (Russian: otzovists).
A smaller group within the Bolshevik faction demanded that the RSDLP
Central Committee should give its sometimes unruly Duma faction an
ultimatum, demanding complete subordination to all party decisions. This
group became known as "ultimatists" and was generally allied with the recallists.
With most Bolshevik leaders either supporting Bogdanov or
undecided by mid-1908 when the differences became irreconcilable, Lenin
concentrated on undermining Bogdanov's reputation as a philosopher. In
1909, he published a scathing book of criticism entitled Materialism and Empirio-criticism (1909), assaulting Bogdanov's position and accusing him of philosophical idealism. In June 1909, Bogdanov proposed the formation of Party Schools as
Proletarian Universities at a Bolshevik mini-conference in Paris
organised by the editorial board of the Bolshevik magazine Proletary. However, this proposal was not adopted and Lenin tried to expel Bogdanov from the Bolshevik faction. Bogdanov was then involved with setting up Vpered, which ran the Capri Party School from August to December 1909.
Final attempt at party unity (1910)
With both Bolsheviks and Mensheviks weakened by splits within their
ranks and by Tsarist repression, the two factions were tempted to try to
reunite the party. In January 1910, Leninists, recallists, and various
Menshevik factions held a meeting of the party's Central Committee in
Paris. Kamenev and Zinoviev were dubious about the idea; but under
pressure from conciliatory Bolsheviks like Victor Nogin, they were willing to give it a try.
One of the underlying reasons that prevented any reunification of
the party was the Russian police. The police were able to infiltrate
both parties' inner circles by sending in spies who then reported on the
opposing party's intentions and hostilities. This allowed the tensions to remain high between the Bolsheviks and Mensheviks and helped prevent their uniting.
Lenin was firmly opposed to any reunification but was outvoted
within the Bolshevik leadership. The meeting reached a tentative
agreement, and one of its provisions was to make Trotsky's Vienna-based Pravda,
a party-financed central organ. Kamenev, Trotsky's brother-in-law who
was with the Bolsheviks, was added to the editorial board; but the
unification attempts failed in August 1910 when Kamenev resigned from
the board amid mutual recriminations.
The factions permanently broke relations in January 1912 after the Bolsheviks organised a Bolsheviks-only Prague Party Conference
and formally expelled Mensheviks and recallists from the party. As a
result, they ceased to be a faction in the RSDLP and instead declared
themselves an independent party, called Russian Social Democratic Labour Party (Bolsheviks)
– or RSDLP(b). Unofficially, the party has been referred to as the
Bolshevik Party. Throughout the 20th century, the party adopted a number
of different names. In 1918, RSDLP(b) became All-Russian Communist
Party (Bolsheviks) and remained so until 1925. From 1925 to 1952, the
name was All-Union Communist Party (Bolsheviks) and from 1952 to 1991,
the Communist Party of the Soviet Union.
As the party split became permanent, further divisions became
evident. One of the most notable differences was how each faction
decided to fund its revolution. The Mensheviks decided to fund their
revolution through membership dues while Lenin often resorted to more
drastic measures since he required a higher budget. One of the common methods the Bolsheviks used was committing bank
robberies, one of which, in 1907, resulted in the party getting over
250,000 roubles, which is the equivalent of about $125,000. Bolsheviks were in constant need of money because Lenin practised his
beliefs, expressed in his writings, that revolutions must be led by
individuals who devote their entire lives to the cause. As compensation,
he rewarded them with salaries for their sacrifice and dedication. This
measure was taken to help ensure that the revolutionaries stayed
focused on their duties and motivated them to perform their jobs. Lenin
also used the party money to print and copy pamphlets which were
distributed in cities and at political rallies in an attempt to expand
their operations. Both factions received funds through donations from
wealthy supporters.
The elections to the Russian Constituent Assembly
took place in November 1917 in which the Bolsheviks came second with
23.9% of the vote and dissolved the Assembly in January 1918
Further differences in party agendas became evident as the beginning of World War I loomed near. Joseph Stalin was especially eager for the start of the war, hoping that it would turn into a war between classes or essentially a Russian Civil War. This desire for war was fuelled by Lenin's vision that the workers and
peasants would resist joining the war effort and therefore be more
compelled to join the socialist movement. Through the increase in
support, Russia would then be forced to withdraw from the Allied powers
in order to resolve her internal conflict. Unfortunately for the
Bolsheviks, Lenin's assumptions were incorrect. Despite his and the
party's attempts to push for a civil war through involvement in two
conferences in 1915 and 1916 in Switzerland, the Bolsheviks were in the
minority in calling for a ceasefire by the Imperial Russian Army in World War I.
Although the Bolshevik leadership had decided to form a separate
party, convincing pro-Bolshevik workers within Russia to follow suit
proved difficult. When the first meeting of the Fourth Duma was convened
in late 1912, only one out of six Bolshevik deputies, Matvei Muranov (another one, Roman Malinovsky, was later exposed as an Okhrana agent), voted on 15 December 1912 to break from the Menshevik faction within the Duma. The Bolshevik leadership eventually prevailed, and the Bolsheviks formed their own Duma faction in September 1913.
One final difference between the Bolsheviks and Mensheviks was
how ferocious and tenacious the Bolshevik party was in order to achieve
its goals, although Lenin was open minded to retreating from political
ideals if he saw the guarantee of long-term gains benefiting the party.
This practice was seen in the party's trying to recruit peasants and
uneducated workers by promising them how glorious life would be after
the revolution and granting them temporary concessions.
Bolshevik figures such as Anatoly Lunacharsky, Moisei Uritsky and Dmitry Manuilsky
considered that Lenin's influence on the Bolshevik party was decisive
but the October insurrection was carried out according to Trotsky's, not
to Lenin's plan.
In 1918, the party renamed itself the Russian Communist Party
(Bolsheviks) at Lenin's suggestion. In 1925, this was changed to
All-Union Communist Party (Bolsheviks). At the 19th Party Congress in 1952 the Party was renamed the Communist Party of the Soviet Union at Stalin's suggestion.
Non-Russian / Soviet political groups having used the name "Bolshevik"
During the Cold War in the United Kingdom, trade union leaders and other leftists were sometimes derisively described as Bolshies. The usage is roughly equivalent to the term "commie", "Red", or "pinko" in the United States during the same period. The term Bolshie later became a slang term for anyone who was rebellious, aggressive, or truculent.
According to the unrestricted comprehension principle, for any sufficiently well-defined property, there is the set of all and only the objects that have that property. Let R be the set of all sets that are not members of themselves (sometimes called "the Russell set"). If R
is not a member of itself, then its definition entails that it is a
member of itself; yet, if it is a member of itself, then it is not a
member of itself, since it is the set of all sets that are not members
of themselves. The resulting contradiction is Russell's paradox. In
symbols:
Let Then
Russell also showed that a version of the paradox could be derived in the axiomatic system constructed by the German philosopher and mathematician Gottlob Frege, hence undermining Frege's attempt to reduce mathematics to logic and calling into question the logicist programme. Two influential ways of avoiding the paradox were both proposed in 1908: Russell's own type theory and the Zermelo set theory. In particular, Zermelo's axioms restricted the unlimited comprehension principle. With the additional contributions of Abraham Fraenkel, Zermelo set theory developed into the standard Zermelo–Fraenkel set theory (commonly known as ZFC when including the axiom of choice).
The main difference between Russell's and Zermelo's solution to the
paradox is that Zermelo modified the axioms of set theory while
maintaining a standard logical language, while Russell modified the
logical language itself. The language of ZFC, with the help of Thoralf Skolem, turned out to be that of first-order logic.
The paradox had already been discovered independently in 1899 by the German mathematician Ernst Zermelo. However, Zermelo did not publish the idea, which remained known only to David Hilbert, Edmund Husserl, and other academics at the University of Göttingen. At the end of the 1890s, Georg Cantor
– considered the founder of modern set theory – had already realized
that his theory would lead to a contradiction, as he told Hilbert and Richard Dedekind by letter.
Informal presentation
Most sets commonly encountered are not members of themselves. Call a
set "normal" if it is not a member of itself, and "abnormal" if it is a
member of itself. Clearly every set must be either normal or abnormal.
For example, consider the set of all squares in a plane.
This set is not itself a square in the plane, thus it is not a member
of itself and is therefore normal. In contrast, the complementary set
that contains everything which is not a square in the plane is itself not a square in the plane, and so it is one of its own members and is therefore abnormal.
Consider the set of all normal sets, R, and try to determine whether R is normal or abnormal. If R were normal, it would be contained in the set of all normal sets (itself), and therefore be abnormal; on the other hand if R
were abnormal, it would not be contained in the set of all normal sets
(itself), and therefore be normal. This leads to the conclusion that R is neither normal nor abnormal: Russell's paradox.
a contradiction. Therefore, this naive set theory is inconsistent.
Philosophical implications
Prior to Russell's paradox (and to other similar paradoxes discovered around the time, such as the Burali-Forti paradox), a common conception of the idea of set was the "extensional concept of set", as recounted by von Neumann and Morgenstern:
A set is an arbitrary collection of
objects, absolutely no restriction being placed on the nature and
number of these objects, the elements of the set in question. The
elements constitute and determine the set as such, without any ordering
or relationship of any kind between them.
In particular, there was no distinction between sets and proper
classes as collections of objects. Additionally, the existence of each
of the elements of a collection was seen as sufficient for the existence
of the set of said elements. However, paradoxes such as Russell's and
Burali-Forti's showed the impossibility of this conception of a set, by
examples of collections of objects that do not form sets, despite all
said objects being existent.
Set-theoretic responses
From the principle of explosion of classical logic, any proposition can be proved from a contradiction.
Therefore, the presence of contradictions like Russell's paradox in an
axiomatic set theory is disastrous; since if any formula can be proved
true it destroys the conventional meaning of truth and falsity.
Further, since set theory was seen as the basis for an axiomatic
development of all other branches of mathematics, Russell's paradox
threatened the foundations of mathematics as a whole. This motivated a
great deal of research around the turn of the 20th century to develop a
consistent (contradiction-free) set theory.
In 1908, Ernst Zermelo proposed an axiomatization
of set theory that avoided the paradoxes of naive set theory by
replacing arbitrary set comprehension with weaker existence axioms, such
as his axiom of separation (Aussonderung). (Avoiding paradox was not Zermelo's original intention, but instead to document which assumptions he used in proving the well-ordering theorem.) Modifications to this axiomatic theory proposed in the 1920s by Abraham Fraenkel, Thoralf Skolem, and by Zermelo himself resulted in the axiomatic set theory called ZFC. This theory became widely accepted once Zermelo's axiom of choice ceased to be controversial, and ZFC has remained the canonical axiomatic set theory down to the modern day.
ZFC does not assume that, for every property, there is a set of
all things satisfying that property. Rather, it asserts that given any
set X, any subset of X definable using first-order logic exists. The object R defined by Russell's paradox above cannot be constructed as a subset of any set X, and is therefore not a set in ZFC. In some extensions of ZFC, like von Neumann–Bernays–Gödel set theory, objects like R are called proper classes.
ZFC is silent about types, although the cumulative hierarchy
has a notion of layers that resemble types. Zermelo himself never
accepted Skolem's formulation of ZFC using the language of first-order
logic. As José Ferreirós notes, Zermelo insisted instead that
"propositional functions (conditions or predicates) used for separating
off subsets, as well as the replacement functions, can be 'entirely arbitrary' [ganz beliebig]"; the modern interpretation given to this statement is that Zermelo wanted to include higher-order quantification in order to avoid Skolem's paradox. Around 1930, Zermelo also introduced (apparently independently of von Neumann), the axiom of foundation,
thus—as Ferreirós observes—"by forbidding 'circular' and 'ungrounded'
sets, it [ZFC] incorporated one of the crucial motivations of TT [type
theory]—the principle of the types of arguments". This 2nd order ZFC
preferred by Zermelo, including axiom of foundation, allowed a rich
cumulative hierarchy. Ferreirós writes that "Zermelo's 'layers' are
essentially the same as the types in the contemporary versions of simple
TT [type theory] offered by Gödel and Tarski. The cumulative hierarchy
into which Zermelo developed his models can be described as the universe
of a cumulative TT in which transfinite types are allowed. (Once an
impredicative standpoint is adopted, abandoning the idea that classes
are constructed, it is natural to accept transfinite types.) Thus,
simple TT and ZFC could be regarded as systems that 'talk' essentially
about the same intended objects. The main difference is that TT relies
on a strong higher-order logic, while Zermelo employed second-order
logic, and ZFC can also be given a first-order formulation. The
first-order 'description' of the cumulative hierarchy is much weaker, as
is shown by the existence of countable models (Skolem's paradox), but
it enjoys some important advantages."
In ZFC, given a set A, it is possible to define a set B that consists of exactly the sets in A that are not members of themselves. B cannot be in A by the same reasoning in Russell's Paradox. This variation of Russell's paradox shows that no set contains everything.
Through the work of Zermelo and others, especially John von Neumann,
the structure of what some see as the "natural" objects described by
ZFC eventually became clear: they are the elements of the von Neumann universe, V, built up from the empty set by transfinitely iterating the power set
operation. It is thus possible again to reason about sets in a
non-axiomatic fashion without running afoul of Russell's paradox, namely
by reasoning about the elements of V. Whether it is appropriate to think of sets in this way is a point of contention among the rival points of view on the philosophy of mathematics.
Russell discovered the paradox in May or June 1901. By his own account in his 1919 Introduction to Mathematical Philosophy, he "attempted to discover some flaw in Cantor's proof that there is no greatest cardinal". In a 1902 letter, he announced the discovery to Gottlob Frege of the paradox in Frege's 1879 Begriffsschrift and framed the problem in terms of both logic and set theory, and in particular in terms of Frege's definition of function:
There is just one point where I
have encountered a difficulty. You state (p. 17 [p. 23 above]) that a
function too, can act as the indeterminate element. This I formerly
believed, but now this view seems doubtful to me because of the
following contradiction. Let w be the predicate: to be a predicate that cannot be predicated of itself. Can w be predicated of itself? From each answer its opposite follows. Therefore we must conclude that w
is not a predicate. Likewise there is no class (as a totality) of those
classes which, each taken as a totality, do not belong to themselves.
From this I conclude that under certain circumstances a definable
collection [Menge] does not form a totality.
Russell would go on to cover it at length in his 1903 The Principles of Mathematics, where he repeated his first encounter with the paradox:
Before taking leave of fundamental
questions, it is necessary to examine more in detail the singular
contradiction, already mentioned, with regard to predicates not
predicable of themselves. ... I may mention that I was led to it in the
endeavour to reconcile Cantor's proof....
Russell wrote to Frege about the paradox just as Frege was preparing the second volume of his Grundgesetze der Arithmetik. Frege responded to Russell very quickly; his letter dated 22 June 1902
appeared, with van Heijenoort's commentary in Heijenoort 1967:126–127.
Frege then wrote an appendix admitting to the paradox, and proposed a solution that Russell would endorse in his Principles of Mathematics, but was later considered by some to be unsatisfactory. For his part, Russell had his work at the printers and he added an appendix on the doctrine of types.
Ernst Zermelo in his (1908) A new proof of the possibility of a well-ordering (published at the same time he published "the first axiomatic set theory") laid claim to prior discovery of the antinomy in Cantor's naive set theory. He states: "And yet, even the elementary form that Russell9
gave to the set-theoretic antinomies could have persuaded them [J.
König, Jourdain, F. Bernstein] that the solution of these difficulties
is not to be sought in the surrender of well-ordering but only in a
suitable restriction of the notion of set". Footnote 9 is where he stakes his claim:
91903, pp.
366–368. I had, however, discovered this antinomy myself, independently
of Russell, and had communicated it prior to 1903 to Professor Hilbert
among others.
Frege sent a copy of his Grundgesetze der Arithmetik to
Hilbert; as noted above, Frege's last volume mentioned the paradox that
Russell had communicated to Frege. After receiving Frege's last volume,
on 7 November 1903, Hilbert wrote a letter to Frege in which he said,
referring to Russell's paradox, "I believe Dr. Zermelo discovered it
three or four years ago". A written account of Zermelo's actual
argument was discovered in the Nachlass of Edmund Husserl.
In 1923, Ludwig Wittgenstein proposed to "dispose" of Russell's paradox as follows:
The reason why a function cannot be its own argument is that the sign
for a function already contains the prototype of its argument, and it
cannot contain itself. For let us suppose that the function F(fx) could
be its own argument: in that case there would be a proposition F(F(fx)), in which the outer function F and the inner function F must have different meanings, since the inner one has the form O(fx) and the outer one has the form Y(O(fx)).
Only the letter 'F' is common to the two functions, but the letter by
itself signifies nothing. This immediately becomes clear if instead of F(Fu) we write (do) : F(Ou) . Ou = Fu. That disposes of Russell's paradox. (Tractatus Logico-Philosophicus, 3.333)
Russell and Alfred North Whitehead wrote their three-volume Principia Mathematica hoping to achieve what Frege had been unable to do. They sought to banish the paradoxes of naive set theory
by employing a theory of types they devised for this purpose. While
they succeeded in grounding arithmetic in a fashion, it is not at all
evident that they did so by purely logical means. While Principia Mathematica avoided the known paradoxes and allows the derivation of a great deal of mathematics, its system gave rise to new problems.
In any case, Kurt Gödel in 1930–31 proved that while the logic of much of Principia Mathematica, later known as first-order logic, is complete, Peano arithmetic is necessarily incomplete if it is consistent. This is very widely—though not universally—regarded as having shown the logicist program of Frege to be impossible to complete.
In 2001, A Centenary International Conference celebrating the
first hundred years of Russell's paradox was held in Munich and its
proceedings have been published.
Applied versions
Some versions of this paradox are closer to real-life and may be easier to understand for non-logicians. For example, the barber paradox
supposes a male barber who shaves all men who do not shave themselves
and only men who do not shave themselves. When one thinks about whether
the barber shaves himself or not, a similar paradox begins to emerge.
An exception may be the Grelling–Nelson paradox,
in which words and meaning are the elements of the scenario rather than
people and hair-cutting. Though it is easy to refute the barber's
paradox by saying that such a barber does not (and cannot) exist, it is impossible to say something similar about a meaningfully defined word.
One way that the paradox has been dramatised is: suppose that
every public library has to compile a catalogue of all its books. Since
the catalogue is itself one of the library's books, some librarians
include it in the catalogue for completeness; while others leave it out
as it being one of the library's books is self evident. Next, imagine
that all these catalogues are sent to the national library. Some of them
include themselves in their listings, others do not. The national
librarian compiles two master catalogues—one of all the catalogues that
list themselves, and one of all those that do not.
The question is: should these master catalogues list themselves?
The 'catalogue of all catalogues that list themselves' is no problem. If
the librarian does not include it in its own listing, it remains a true
catalogue of those catalogues that do include themselves. If he does
include it, it remains a true catalogue of those that list themselves.
However, just as the librarian cannot go wrong with the first master
catalogue, he is doomed to fail with the second. When it comes to the
'catalogue of all catalogues that do not list themselves', the librarian
cannot include it in its own listing, because then it would include
itself, and so belong in the other catalogue, that of catalogues that do
include themselves. However, if the librarian leaves it out, the
catalogue is incomplete. Either way, it can never be a true master
catalogue of catalogues that do not list themselves.
Applications and related topics
Russell-like paradoxes
As illustrated above for the barber paradox, Russell's paradox is not hard to extend. Take:
The original Russell's paradox with "contain": The container (Set)
that contains all (containers) that do not contain themselves.
The Grelling–Nelson paradox with "describer": The describer (word) that describes all words, that do not describe themselves.
Richard's paradox
with "denote": The denoter (number) that denotes all denoters (numbers)
that do not denote themselves. (In this paradox, all descriptions of
numbers get an assigned number. The term "that denotes all denoters
(numbers) that do not denote themselves" is here called Richardian.)
In the 1970s and 1980s, Carl Sagan and Frank Drake, among others, argued that Earth is a typical rocky planet in a typical planetary system, located in a non-exceptional region of a common galaxy, now known to be a barred spiral galaxy. From the principle of mediocrity (extended from the Copernican principle),
they argued that the evolution of life on Earth, including human
beings, was also typical, and therefore that the universe teems with
complex life. In contrast, Ward and Brownlee argue that planets which
have all the requirements for complex life are not typical at all but
actually exceedingly rare.
There is no reliable or reproducible evidence that extraterrestrial organisms of any kind have visited Earth. No transmissions or evidence of intelligent life have been detected or observed anywhere other than Earth in the Universe.
This runs counter to the knowledge that the Universe is filled with a
very large number of planets, some of which likely hold the conditions
hospitable for life. Life typically expands until it fills all available
niches. These contradictory facts form the basis for the Fermi paradox, of which the Rare Earth hypothesis is one proposed solution.
In order for a small rocky planet to support complex life, Ward
and Brownlee argue, the values of several variables must fall within
narrow ranges. The universe
is so vast that it might still contain many Earth-like planets, but if
such planets exist, they are likely to be separated from each other by
many thousands of light-years.
Such distances may preclude communication among any intelligent species
that may evolve on such planets, which would solve the Fermi paradox which wonders: if extraterrestrial aliens are common, why aren't they obvious?
The right location in the right kind of galaxy
Rare Earth suggests that much of the known universe, including large
parts of the Milky Way galaxy, are "dead zones" unable to support
complex life. Those parts of a galaxy where complex life is possible
make up the galactic habitable zone, which is primarily characterized by distance from the Galactic Center.
As that distance increases, star metallicity declines. Metals (which in astronomy refers to all elements other than hydrogen and helium) are necessary for the formation of terrestrial planets.
The X-ray and gamma ray radiation from the black hole at the Galactic Center, and from nearby neutron stars,
becomes less intense as distance increases. Thus the early universe,
and present-day galactic regions where stellar density is high and supernovae are common, will be dead zones.
Gravitational perturbation of planets and planetesimals
by nearby stars becomes less likely as the density of stars decreases.
Hence the further a planet lies from the Galactic Center or a spiral
arm, the less likely it is to be struck by a large bolide which could extinguish all complex life on a planet.
Dense centers of galaxies such as NGC 7331 (often referred to as a "twin" of the Milky Way) have high radiation levels toxic to complex life.
According to Rare Earth, globular clusters are unlikely to support life.
Item #1 rules out the outermost reaches of a galaxy; #2 and #3 rule
out galactic inner regions. Hence a galaxy's habitable zone may be a
relatively narrow ring of adequate conditions sandwiched between its
uninhabitable center and outer reaches.
Also, a habitable planetary system must maintain its favorable location long enough for complex life to evolve. A star with an eccentric
(elliptical or hyperbolic) galactic orbit will pass through some spiral
arms, unfavorable regions of high star density; thus a life-bearing
star must have a galactic orbit that is nearly circular, with a close
synchronization between the orbital velocity of the star and of the
spiral arms. This further restricts the galactic habitable zone within a
fairly narrow range of distances from the Galactic Center. Lineweaver
et al. calculate this zone to be a ring 7 to 9 kiloparsecs in radius, including no more than 10% of the stars in the Milky Way, about 20 to 40 billion stars. Gonzalez et al. would halve these numbers; they estimate that at most 5% of stars in the Milky Way fall within the galactic habitable zone.
Approximately 77% of observed galaxies are spiral, two-thirds of all spiral galaxies are barred, and more than half, like the Milky Way, exhibit multiple arms. According to Rare Earth, our own galaxy is unusually quiet and dim (see below), representing just 7% of its kind. Even so, this would still represent more than 200 billion galaxies in the known universe.
The Milky Way galaxy also appears unusually favorable in
suffering fewer collisions with other galaxies over the last 10 billion
years, which can cause more supernovae and other disturbances. Also, the Milky Way's central black hole seems to have neither too much nor too little activity.
The orbit of the Sun around the center of the Milky Way is indeed almost perfectly circular, with a period of 226 Ma
(million years), closely matching the rotational period of the galaxy.
However, the majority of stars in barred spiral galaxies populate the
spiral arms rather than the halo and tend to move in gravitationally aligned orbits,
so there is little that is unusual about the Sun's orbit. While the
Rare Earth hypothesis predicts that the Sun should rarely, if ever, have
passed through a spiral arm since its formation, astronomer Karen
Masters has calculated that the orbit of the Sun takes it through a
major spiral arm approximately every 100 million years. Some researchers have suggested that several mass extinctions do indeed correspond with previous crossings of the spiral arms.
The right orbital distance from the right type of star
According to the hypothesis, Earth has an improbable orbit in the very narrow habitable zone (dark green) around the Sun.
The terrestrial example suggests that complex life requires liquid
water, the maintenance of which requires an orbital distance neither too
close nor too far from the central star, another scale of habitable zone or Goldilocks principle. The habitable zone varies with the star's type and age.
For advanced life, the star must also be highly stable, which is
typical of middle star life, about 4.6 billion years old. Proper metallicity and size are also important to stability. The Sun has a low (0.1%) luminosity variation. To date, no solar twin
star, with an exact match of the Sun's luminosity variation, has been
found, though some come close. The star must also have no stellar
companions, as in binary systems, which would disrupt the orbits of any planets. Estimates suggest 50% or more of all star systems are binary. Stars gradually brighten over time and it takes hundreds of millions or
billions of years for animal life to evolve. The requirement for a
planet to remain in the habitable zone even as its boundaries move
outwards over time restricts the size of what Ward and Brownlee call the
"continuously habitable zone" for animals. They cite a calculation that
it is very narrow, within 0.95 and 1.15 astronomical units
(one AU is the distance between the Earth and the Sun), and argue that
even this may be too large because it is based on the whole zone within
which liquid water can exist, and water near boiling point may be much
too hot for animal life.
The liquid water and other gases available in the habitable zone bring the benefit of the greenhouse effect. Even though the Earth's atmosphere
contains a water vapor concentration from 0% (in arid regions) to 4%
(in rainforest and ocean regions) and – as of November 2022 – only 417.2
parts per million of CO2, these small amounts suffice to raise the average surface temperature by about 40 °C, with the dominant contribution being due to water vapor.
All known life requires the complex chemistry of metallic elements. The absorption spectrum
of a star reveals the presence of metals within, and studies of stellar
spectra reveal that many, perhaps most, stars are poor in metals.
Because heavy metals originate in supernova
explosions, metallicity increases in the universe over time. Low
metallicity characterizes the early universe: globular clusters and
other stars that formed when the universe was young, stars in most
galaxies other than large spirals,
and stars in the outer regions of all galaxies. Metal-rich central
stars capable of supporting complex life are therefore believed to be
most common in the less dense regions of the larger spiral
galaxies—where radiation also happens to be weak.
The right arrangement of planets around the star
Depiction
of the Sun and planets of the Solar System and the sequence of planets.
Rare Earth argues that without such an arrangement, in particular the
presence of the massive gas giant Jupiter (the fifth planet from the Sun
and the largest), complex life on Earth would not have arisen.
Rare Earth proponents argue that a planetary system capable of
sustaining complex life must be structured more or less like the Solar
System, with small, rocky inner planets and massive outer gas giants. Without the protection of such "celestial vacuum cleaner" planets, such
as Jupiter, with strong gravitational pulls, other planets would be
subject to more frequent catastrophic asteroid collisions. An asteroid
only twice the size of the one which caused the Cretaceous–Paleogene
extinction might have wiped out all complex life.
Observations of exoplanets have shown that arrangements of planets similar to the Solar System are rare. Most planetary systems
have super-Earths, several times larger than Earth, close to their
star, whereas the Solar System's inner region has only a few small rocky
planets and none inside Mercury's orbit. Only 10% of stars have giant
planets similar to Jupiter and Saturn, and those few rarely have stable,
nearly circular orbits distant from their star. Konstantin Batygin
and colleagues argue that these features can be explained if, early in
the history of the Solar System, Jupiter and Saturn drifted towards the
Sun, sending showers of planetesimals towards the super-Earths which
sent them spiralling into the Sun, and ferrying icy building blocks into
the terrestrial region of the Solar System which provided the building
blocks for the rocky planets. The two giant planets then drifted out
again to their present positions. In the view of Batygin and his
colleagues: "The concatenation of chance events required for this
delicate choreography suggest that small, Earth-like rocky planets – and
perhaps life itself – could be rare throughout the cosmos."
A continuously stable orbit
Rare Earth proponents argue that a gas giant also must not be too
close to a body where life is developing. Close placement of one or more
gas giants could disrupt the orbit of a potential life-bearing planet,
either directly or by drifting into the habitable zone.
The need for stable orbits rules out stars with planetary systems
that contain large planets with orbits close to the host star (called "hot Jupiters").
It is believed that hot Jupiters have migrated inwards to their current
orbits. In the process, they would have catastrophically disrupted the
orbits of any planets in the habitable zone. To exacerbate matters, hot Jupiters are much more common orbiting F and G class stars.
A terrestrial planet of the right size
Planets
of the Solar System, shown to scale. Rare Earth argues that complex
life cannot exist on large gaseous planets like Jupiter and Saturn (top
row) or Uranus and Neptune (top middle) or smaller planets such as Mars
and Mercury.
The Rare Earth hypothesis argues that life requires terrestrial planets like Earth, and since gas giants lack such a surface, that complex life cannot arise there.
A planet that is too small cannot maintain much atmosphere,
rendering its surface temperature low and variable and oceans
impossible. A small planet will also tend to have a rough surface, with
large mountains and deep canyons. The core will cool faster, and plate tectonics will be brief or entirely absent. On Earth heat loss is balanced by heat production from radioactive
decay, resulting in a thin crust and plate tectonics. On a significantly
larger planet, heat production would exceed heat loss and Earth would
probably not have developed an outer crust, making plate tectonics and
life impossible.
Plate tectonics
The Great American Interchange on Earth, approximately 3.5 to 3 Ma, an example of species competition, resulting from continental plate interactionAn artist's rendering of the structure of Earth's magnetic field-magnetosphere that protects Earth's life from solar radiation.
1) Bow shock. 2) Magnetosheath. 3) Magnetopause. 4) Magnetosphere.
5) Northern tail lobe. 6) Southern tail lobe. 7) Plasmasphere.
Plate tectonics depend on the right chemical composition and a long-lasting source of heat from radioactive decay. Continents must be made of less dense felsic rocks that "float" on underlying denser mafic rock. Taylor emphasizes that tectonic subduction zones require the lubrication of oceans of water. Plate tectonics also provide a means of biochemical cycling.
Plate tectonics and, as a result, continental drift and the creation of separate landmasses would create diversified ecosystems and biodiversity, one of the strongest defenses against extinction. An example of species diversification and later competition on Earth's continents is the Great American Interchange. North and Middle America drifted into South America at around 3.5 to 3 Ma. The fauna of South America had already evolved separately for about 30 million years, since Antarctica separated, but, after the merger, many species were wiped out, mainly in South America, by competing North American animals.
A large moon
Tide pools resulting from the tidal interactions of the Moon are said to have promoted the evolution of complex life.
The Moon is unusual because the other rocky planets in the Solar System either have no satellites (Mercury and Venus), or only relatively tiny satellites which are probably captured asteroids (Mars). After Charon,
the Moon is also the largest natural satellite in the Solar System
relative to the size of its parent body, being 27% the size of Earth.
The giant-impact theory hypothesizes that the Moon resulted from the impact of a roughly Mars-sized body, dubbed Theia, with the young Earth. This giant impact also gave the Earth its axial tilt (inclination) and velocity of rotation. Rapid rotation reduces the daily variation in temperature and makes photosynthesis viable. The Rare Earth hypothesis further argues that the axial tilt cannot be too large or too small (relative to the orbital plane).
A planet with a large tilt will experience extreme seasonal variations
in climate. A planet with little or no tilt will lack the stimulus to
evolution that climate variation provides. In this view, the Earth's tilt is "just right". The gravity of a large
satellite also stabilizes the planet's tilt; without this effect, the variation in tilt would be chaotic, probably making complex life forms on land impossible.
If the Earth had no Moon, the ocean tides resulting solely from the Sun's gravity would be only half that of the lunar tides. A large satellite gives rise to tidal pools, which may be essential for the formation of complex life, though this is far from certain.
A large satellite also increases the likelihood of plate tectonics through the effect of tidal forces on the planet's crust. The impact that formed the Moon may also have initiated plate tectonics, without which the continental crust would cover the entire planet, leaving no room for oceanic crust.It is possible that the large-scale mantle convection
needed to drive plate tectonics could not have emerged if the crust had
a uniform composition. A further theory indicates that such a large
moon may also contribute to maintaining a planet's magnetic shield by
continually acting upon a metallic planetary core as dynamo, thus
protecting the surface of the planet from charged particles and cosmic
rays, and helping to ensure the atmosphere is not stripped over time by
solar winds.
An atmosphere
Earth's atmosphere
A terrestrial planet must be the right size, like Earth and Venus, in
order to retain an atmosphere. On Earth, once the giant impact of Theia thinned Earth's atmosphere, other events were needed to make the atmosphere capable of sustaining life. The Late Heavy Bombardment reseeded Earth with water lost after the impact of Theia. The development of an ozone layer generated a protective shield against ultraviolet (UV) sunlight.Nitrogen and carbon dioxide are needed in a correct ratio for life to form. Lightning is needed for nitrogen fixation. The gaseous carbon dioxide needed for life comes from sources such as volcanoes and geysers. Carbon dioxide is preferably needed at relatively low levels (currently at approximately 400 ppm on Earth) because at high levels it is poisonous. Precipitation is needed to have a stable water cycle. A proper atmosphere must reduce diurnal temperature variation.
One or more evolutionary triggers for complex life
This diagram illustrates the twofold cost of sex. If each individual were to contribute to the same number of offspring (two), (a) the sexual population remains the same size each generation, whereas (b) the asexual population doubles in size each generation.
Regardless of whether planets with similar physical attributes to the
Earth are rare or not, some argue that life tends not to evolve into
anything more complex than simple bacteria without being provoked by
rare and specific circumstances. Biochemist Nick Lane argues that simple cells (prokaryotes)
emerged soon after Earth's formation, but since almost half the
planet's life had passed before they evolved into complex ones (eukaryotes), all of whom share a common ancestor, this event can only have happened once. According to some views, prokaryotes
lack the cellular architecture to evolve into eukaryotes because a
bacterium expanded up to eukaryotic proportions would have tens of
thousands of times less energy available to power its metabolism. Two
billion years ago, one simple cell incorporated itself into another,
multiplied, and evolved into mitochondria
that supplied the vast increase in available energy that enabled the
evolution of complex eukaryotic life. If this incorporation occurred
only once in four billion years or is otherwise unlikely, then life on
most planets remains simple. An alternative view is that the evolution of mitochondria was
environmentally triggered, and that mitochondria-containing organisms
appeared soon after the first traces of atmospheric oxygen.
The evolution and persistence of sexual reproduction is another mystery in biology. The purpose of sexual reproduction is unclear, as in many organisms it has a 50% cost (fitness disadvantage) in relation to asexual reproduction. Mating types (types of gametes, according to their compatibility) may have arisen as a result of anisogamy (gamete dimorphism), or the male and female sexes may have evolved before anisogamy. It is also unknown why most sexual organisms use a binary mating system, and why some organisms have gamete dimorphism. Charles Darwin was the first to suggest that sexual selection drives speciation; without it, complex life would probably not have evolved.
The right time in evolutionary history
Timeline of evolution; human writing exists for only 0.000218% of Earth's history.
While life on Earth is regarded to have spawned relatively early in
the planet's history, the evolution from multicellular to intelligent
organisms took around 800 million years. Civilizations on Earth have existed for about 12,000 years, and radio
communication reaching space has existed for little more than 100 years.
Relative to the age of the Solar System (~4.57 Ga) this is a short
time, in which extreme climatic variations, super volcanoes, and large
meteorite impacts were absent. These events would severely harm
intelligent life, as well as life in general. For example, the Permian-Triassic mass extinction,
caused by widespread and continuous volcanic eruptions in an area the
size of Western Europe, led to the extinction of 95% of known species
around 251.2 Ma ago. About 65 million years ago, the Chicxulub impact at the Cretaceous–Paleogene boundary (~65.5 Ma) on the Yucatán peninsula in Mexico led to a mass extinction.
Rare Earth equation
The following discussion is adapted from Cramer. The Rare Earth equation is Ward and Brownlee's riposte to the Drake equation. It calculates , the number of Earth-like planets in the Milky Way having complex life forms, as:
According to Rare Earth, the Cambrian explosion that saw extreme diversification of chordata from simple forms like Pikaia (pictured) was an improbable event.
where:
N* is the number of stars in the Milky Way.
This number is not well-estimated, because the Milky Way's mass is not
well estimated, with little information about the number of small stars.
N* is at least 100 billion, and may be as high as 500 billion, if there are many low visibility stars.
is the average number of planets in a star's habitable zone. This zone
is fairly narrow, being constrained by the requirement that the average
planetary temperature be consistent with water remaining liquid
throughout the time required for complex life to evolve. Thus, =1 is a likely upper bound.
We assume .
The Rare Earth hypothesis can then be viewed as asserting that the
product of the other nine Rare Earth equation factors listed below,
which are all fractions, is no greater than 10−10 and could plausibly be as small as 10−12. In the latter case, could be as small as 0 or 1. Ward and Brownlee do not actually calculate the value of ,
because the numerical values of quite a few of the factors below can
only be conjectured. They cannot be estimated simply because we have but one data point: the Earth, a rocky planet orbiting a G2 star in a quiet suburb of a large barred spiral galaxy, and the home of the only intelligent species we know; namely, ourselves.
is the fraction of stars in the galactic habitable zone (Ward, Brownlee, and Gonzalez estimate this factor as 0.1).
is the fraction of stars in the Milky Way with planets.
is the fraction of planets that are rocky ("metallic") rather than gaseous.
is the fraction of habitable planets where microbial life arises. Ward
and Brownlee believe this fraction is unlikely to be small.
is the fraction of planets where complex life evolves. For 80% of the
time since microbial life first appeared on the Earth, there was only
bacterial life. Hence Ward and Brownlee argue that this fraction may be
small.
is the fraction of the total lifespan of a planet during which complex
life is present. Complex life cannot endure indefinitely, because the
energy put out by the sort of star that allows complex life to emerge
gradually rises, and the central star eventually becomes a red giant,
engulfing all planets in the planetary habitable zone. Also, given
enough time, a catastrophic extinction of all complex life becomes ever
more likely.
is the fraction of habitable planets with a large moon. If the giant impact theory of the Moon's origin is correct, this fraction is small.
is the fraction of planetary systems with large Jovian planets. This fraction could be large.
is the fraction of planets with a sufficiently low number of extinction
events. Ward and Brownlee argue that the low number of such events the
Earth has experienced since the Cambrian explosion may be unusual, in which case this fraction would be small.
Lammer, Scherf et al. define Earth-like habitats (EHs) as rocky
exoplanets within the habitable zone of complex life (HZCL) on which
Earth-like N2-O2-dominated atmospheres with minor amounts of CO2 can exist. They estimate the maximum number of EHs in the Milky Way as , with the actual number of EHs being possibly much less than that. This would reduce the Rare Earth equation to:
The Rare Earth equation, unlike the Drake equation, does not factor the probability that complex life evolves into intelligent life
that discovers technology. Barrow and Tipler review the consensus among
such biologists that the evolutionary path from primitive Cambrian chordates, e.g., Pikaia to Homo sapiens, was a highly improbable event. For example, the large brains of humans have marked adaptive disadvantages, requiring as they do an expensive metabolism, a long gestation period, and a childhood lasting more than 25% of the average total life span. Other improbable features of humans include:
Being one of a handful of extant bipedal land (non-avian) vertebrate. Combined with an unusual eye–hand coordination, this permits dextrous manipulations of the physical environment with the hands;
A vocal apparatus far more expressive than that of any other mammal, enabling speech. Speech makes it possible for humans to interact cooperatively, to share knowledge, and to acquire a culture;
The capability of formulating abstractions to a degree permitting the invention of mathematics, and the discovery of science and technology. Only recently did humans acquire anything like their current scientific and technological sophistication.
Advocates
Writers who support the Rare Earth hypothesis:
Stuart Ross Taylor, a specialist on the Solar System, firmly believed in the hypothesis.
Taylor concluded that the Solar System is probably unusual, because it
resulted from so many chance factors and events.
Stephen Webb, a physicist, mainly presents and rejects candidate solutions for the Fermi paradox. The Rare Earth hypothesis emerges as one of the few solutions left standing by the end of his book Where is Everybody?
Simon Conway Morris, a paleontologist, endorses the Rare Earth hypothesis in chapter 5 of his Life's Solution: Inevitable Humans in a Lonely Universe, and cites Ward and Brownlee's book with approval.
John D. Barrow and Frank J. Tipler, cosmologists, vigorously defend the hypothesis that humans are likely to be the only intelligent life in the Milky Way, and perhaps the entire universe. But this hypothesis is not central to their book The Anthropic Cosmological Principle, a thorough study of the anthropic principle and of how the laws of physics are peculiarly suited to enable the emergence of complexity in nature.
Ray Kurzweil, a computer pioneer and self-proclaimed Singularitarian, argues in his 2005 book The Singularity Is Near that the coming Singularity
requires that Earth be the first planet on which sapient,
technology-using life evolved. Although other Earth-like planets could
exist, Earth must be the most evolutionarily advanced, because otherwise
we would have seen evidence that another culture had experienced the
Singularity and expanded to harness the full computational capacity of
the physical universe.
John Gribbin, a prolific science writer, defends the hypothesis in Alone in the Universe: Why our planet is unique (2011).
Marc J. Defant, professor of geochemistry and volcanology,
elaborated on several aspects of the rare Earth hypothesis in his TEDx
talk entitled: Why We are Alone in the Galaxy. He also wrote in his book in 1998: "I do not believe that we were the
destined outcome of evolution. In fact, we are probably the result of an
incredible number of chance circumstances (one example is the meteorite
impact at the end of the Cretaceous which probably destroyed the
dinosaurs and led to mammal domination). The coincidental nature of our
evolution should be clear from this book. I might even contend that so
many "coincidences" had to take place during the history of the
universe, that intelligent life on this planet may be the only life in
our universe. I do not mean to suggest that we must have been "created."
I mean to say that maybe there is not as much chance of finding life in
our galaxy or universe as some would have us believe. We may be it."
Brian Cox, physicist and popular science celebrity confesses his support for the hypothesis in his 2014 BBC production of the Human Universe.
Richard Dawkins, evolutionary biologist, notes the Fermi paradox in his book, The Greatest Show on Earth,
while discussing how life first evolved on Earth. Although we do not
yet know the precise process for how life first began on Earth,
Dawkins's view is that it is an implausible theory (i.e., improbable)
given we have not encountered any evidence for life existing elsewhere
in the universe. He concludes that life is probably very rare throughout
the universe.
Criticism
Cases against the Rare Earth hypothesis take various forms.
The hypothesis appears anthropocentric
The hypothesis concludes, more or less, that complex life is rare
because it can evolve only on the surface of an Earth-like planet or on a
suitable satellite of a planet. Some biologists, such as Jack Cohen, believe this assumption too restrictive and unimaginative; they see it as a form of circular reasoning.
According to David Darling, the Rare Earth hypothesis is neither hypothesis nor prediction, but merely a description of how life arose on Earth. In his view, Ward and Brownlee have done nothing more than select the factors that best suit their case.
What matters is not whether there's anything unusual about the Earth; there's going to be something idiosyncratic
about every planet in space. What matters is whether any of Earth's
circumstances are not only unusual but also essential for complex life.
So far we've seen nothing to suggest there is.
Critics also argue that there is a link between the Rare Earth hypothesis and the unscientific idea of intelligent design.
Exoplanets around main sequence stars are being discovered in large numbers
An increasing number of extrasolar planet discoveries are being made, with 6,128 planets in 4,584 planetary systems known as of 30 October 2025. Rare Earth proponents argue life cannot arise outside Sun-like systems, due to tidal locking and ionizing radiation outside the F7–K1 range. However, some exobiologists have suggested that stars outside this range may give rise to life
under the right circumstances; this possibility is a central point of
contention to the theory because these late-K and M category stars make
up about 82% of all hydrogen-burning stars.
Current technology limits the testing of important Rare Earth criteria: surface water, tectonic plates, a large moon and biosignatures
are currently undetectable. Though planets the size of Earth are
difficult to detect and classify, scientists now think that rocky
planets are common around Sun-like stars. The Earth Similarity Index (ESI) of mass, radius and temperature provides a means of measurement, but falls short of the full Rare Earth criteria.
Rocky planets orbiting within habitable zones may not be rare
Some argue that Rare Earth's estimates of rocky planets in habitable zones ( in the Rare Earth equation) are too restrictive. James Kasting cites the Titius–Bode law
to contend that it is a misnomer to describe habitable zones as narrow
when there is a 50% chance of at least one planet orbiting within one. In 2013, astronomers using the Kepler space telescope's data estimated that about one-fifth of G-type and K-type stars (sun-like stars and orange dwarfs) are expected to have an Earth-sized or super-Earth-sized planet (1–2Earths wide) close to an Earth-like orbit (0.25–4 F🜨), yielding about 8.8 billion of them for the entire Milky Way Galaxy.
Uncertainty over Jupiter's role
The requirement for a system to have a Jovian planet as protector (Rare Earth equation factor ) has been challenged, affecting the number of proposed extinction events (Rare Earth equation factor ). Kasting's 2001 review of Rare Earth questions whether a Jupiter protector has any bearing on the incidence of complex life. Computer modelling including the 2005 Nice model and 2007 Nice 2 model yield inconclusive results in relation to Jupiter's gravitational influence and impacts on the inner planets. A study by Horner and Jones (2008) using computer simulation found that
while the total effect on all orbital bodies within the Solar System is
unclear, Jupiter has caused more impacts on Earth than it has
prevented. Lexell's Comet,
a 1770 near miss that passed closer to Earth than any other comet in
recorded history, was known to be caused by the gravitational influence
of Jupiter.
Plate tectonics may not be unique to Earth or a requirement for complex life
Geological discoveries like the active features of Pluto's Tombaugh Regio appear to contradict the argument that geologically active worlds like Earth are rare.
Ward and Brownlee argue that for complex life to evolve (Rare Earth equation factor ), tectonics must be present to generate biogeochemical cycles,
and predicted that such geological features would not be found outside
of Earth, pointing to a lack of observable mountain ranges and subduction. There is, however, no scientific consensus on the evolution of plate
tectonics on Earth. Though it is believed that tectonic motion first
began around three billion years ago, by this time photosynthesis and oxygenation had already begun.
Furthermore, recent studies point to plate tectonics as an episodic
planetary phenomenon, and that life may evolve during periods of
"stagnant-lid" rather than plate tectonic states.
Recent evidence also points to similar activity either having occurred or continuing to occur elsewhere. The geology of Pluto, for example, described by Ward and Brownlee as "without mountains or volcanoes ... devoid of volcanic activity", has since been found to be quite the contrary, with a geologically active surface possessing organic molecules and mountain ranges like Tenzing Montes and Hillary Montes comparable in relative size to those of Earth, and observations suggest the involvement of endogenic processes. Plate tectonics has been suggested as a hypothesis for the Martian dichotomy, and in 2012 geologist An Yin put forward evidence for active plate tectonics on Mars. Europa has long been suspected to have plate tectonics and in 2014 NASA announced evidence of active subduction. Like Europa, analysis of the surface of Jupiter's largest moon Ganymede
strike-strip faulting and surface materials of possible endogenic
origin suggests that plate tectonics has also taken place there.In 2017, scientists studying the geology of Charon confirmed that icy plate tectonics also operated on Pluto's largest moon. Since 2017 several studies of the geodynamics of Venus
have also found that, contrary to the view that the lithosphere of
Venus is static, it is actually being deformed via active processes
similar to plate tectonics, though with less subduction, implying that
geodynamics are not a rare occurrence in Earth sized bodies.
Kasting suggests that there is nothing unusual about the
occurrence of plate tectonics in large rocky planets and liquid water on
the surface as most should generate internal heat even without the
assistance of radioactive elements. Studies by Valencia and Cowan suggest that plate tectonics may be inevitable for terrestrial planets Earth-sized or larger, that is, Super-Earths, which are now known to be more common in planetary systems.
Free oxygen may be neither rare nor a prerequisite for multicellular life
Animals in the genus Spinoloricus are thought to defy the paradigm that all animal life on Earth need oxygen.
The hypothesis that molecular oxygen, necessary for animal life, is rare and that a Great Oxygenation Event (Rare Earth equation factor ) could only have been triggered and sustained by tectonics, appears to have been invalidated by more recent discoveries.
Ward and Brownlee ask "whether oxygenation, and hence the rise of
animals, would ever have occurred on a world where there were no
continents to erode". Extraterrestrial free oxygen has recently been detected around other solid objects, including Mercury, Venus, Mars, Jupiter's four Galilean moons, Saturn's moons Enceladus, Dione and Rhea and even the atmosphere of a comet. This has led scientists to speculate whether processes other than
photosynthesis could be capable of generating an environment rich in
free oxygen. Wordsworth (2014) concludes that oxygen generated other
than through photodissociation may be likely on Earth-like exoplanets, and could actually lead to false positive detections of life. Narita (2015) suggests photocatalysis by titanium dioxide as a geochemical mechanism for producing oxygen atmospheres.
Since Ward & Brownlee's assertion that "there is irrefutable
evidence that oxygen is a necessary ingredient for animal life", anaerobicmetazoa have been found that indeed do metabolise without oxygen. Spinoloricus cinziae, for example, a species discovered in the hypersalineanoxicL'Atalante basin at the bottom of the Mediterranean Sea in 2010, appears to metabolise with hydrogen, lacking mitochondria and instead using hydrogenosomes. Studies since 2015 of the eukaryotic genus Monocercomonoides
that lack mitochondrial organelles are also significant as there are no
detectable signs that mitochondria are part of the organism. Since then further eukaryotes, particularly parasites, have been identified to be completely absent of mitochondrial genome, such as the 2020 discovery in Henneguya zschokkei. Further investigation into alternative metabolic pathways used by these
organisms appear to present further problems for the premise.
Stevenson (2015) has proposed other membrane alternatives for complex life in worlds without oxygen. In 2017, scientists from the NASA Astrobiology Institute discovered the necessary chemical preconditions for the formation of azotosomes on Saturn's moon Titan, a world that lacks atmospheric oxygen. Independent studies by Schirrmeister and by Mills concluded that
Earth's multicellular life existed prior to the Great Oxygenation Event,
not as a consequence of it.
NASA scientists Hartman and McKay argue that plate tectonics may
in fact slow the rise of oxygenation (and thus stymie complex life
rather than promote it). Computer modelling by Tilman Spohn in 2014 found that plate tectonics
on Earth may have arisen from the effects of complex life's emergence,
rather than the other way around as the Rare Earth might suggest. The
action of lichens on rock may have contributed to the formation of
subduction zones in the presence of water. Kasting argues that if oxygenation caused the Cambrian explosion then
any planet with oxygen producing photosynthesis should have complex
life.
A magnetosphere may not be rare or a requirement
The importance of Earth's magnetic field to the development of
complex life has been disputed. The origin of Earth's magnetic field
remains a mystery though the presence of a magnetosphere appears to be relatively common
for larger planetary mass objects as all Solar System planets larger
than Earth possess one. There is increasing evidence of present or past magnetic activity in
terrestrial bodies such as the Moon, Ganymede, Mercury and Mars. Without sufficient measurement present studies rely heavily on
modelling methods developed in 2006 by Olson & Christensen to
predict field strength. Using a sample of 496 planets such models predict Kepler-186f
to be one of few of Earth size that would support a magnetosphere
(though such a field around this planet has not currently been
confirmed). However current recent empirical evidence points to the occurrence of
much larger and more powerful fields than those found in the Solar
System, some of which cannot be explained by these models.
Kasting argues that the atmosphere provides sufficient protection
against cosmic rays even during times of magnetic pole reversal and
atmosphere loss by sputtering. Kasting also dismisses the role of the magnetic field in the evolution of eukaryotes, citing the age of the oldest known magnetofossils.
A large moon may be neither rare nor necessary
The requirement of a large moon (Rare Earth equation factor )
has also been challenged. Even if it were required, such an occurrence
may not be as unique as predicted by the Rare Earth Hypothesis. Work by Edward Belbruno and J. Richard Gott of Princeton University suggests that giant impactors such as those that may have formed the Moon can indeed form in planetary trojan points (L4 or L5Lagrangian point) which means that similar circumstances may occur in other planetary systems.
Collision between two planetary bodies (artist concept)
The assertion that the Moon's stabilization of Earth's obliquity and
spin is a requirement for complex life has been questioned. Kasting
argues that a moonless Earth would still possess habitats with climates
suitable for complex life and questions whether the spin rate of a
moonless Earth can be predicted. Although the giant impact theory
posits that the impact forming the Moon increased Earth's rotational
speed to make a day about 5 hours long, the Moon has slowly "stolen"
much of this speed to reduce Earth's solar day since then to about 24
hours and continues to do so: in 100 million years Earth's solar day
will be roughly 24 hours 38 minutes (the same as Mars's solar day); in 1
billion years, 30 hours 23 minutes. Larger secondary bodies would exert
proportionally larger tidal forces that would in turn decelerate their
primaries faster and potentially increase the solar day of a planet in
all other respects like Earth to over 120 hours within a few billion
years. This long solar day would make effective heat dissipation for
organisms in the tropics and subtropics extremely difficult in a similar
manner to tidal locking to a red dwarf star. Short days (high rotation
speed) cause high wind speeds at ground level. Long days (slow rotation
speed) cause the day and night temperatures to be too extreme.
Many Rare Earth proponents argue that the Earth's plate tectonics
would probably not exist if not for the tidal forces of the Moon or the
impact of Theia (prolonging mantle effects). The hypothesis that the Moon's tidal influence initiated or sustained
Earth's plate tectonics remains unproven, though at least one study
implies a temporal correlation to the formation of the Moon. Evidence for the past existence of plate tectonics on planets like Mars which may never have had a large moon would counter this argument,
although plate tectonics may fade anyway before a moon is relevant to
life.Kasting argues that a large moon is not required to initiate plate tectonics.
Rare Earth proponents argue that simple life may be common, though
complex life requires specific environmental conditions to arise.
Critics consider life could arise on a moon
of a gas giant, though this is less likely if life requires
volcanicity. The moon must have stresses to induce tidal heating, but
not so dramatic as seen on Jupiter's Io. However, the moon is within the
gas giant's intense radiation belts, sterilizing any biodiversity
before it can get established. Dirk Schulze-Makuch disputes this, hypothesizing alternative biochemistries for alien life. While Rare Earth proponents argue that only microbial extremophiles
could exist in subsurface habitats beyond Earth, some argue that complex
life can also arise in these environments. Examples of extremophile
animals such as the Hesiocaeca methanicola, an animal that inhabits ocean floor methane clathrates substances more commonly found in the outer Solar System, the tardigrades which can survive in the vacuum of space or Halicephalobus mephisto
which exists in crushing pressure, scorching temperatures and extremely
low oxygen levels 3.6 kilometres ( 2.2 miles) deep in the Earth's
crust, are sometimes cited by critics as complex life capable of thriving in "alien" environments. Jill Tarter
counters the classic counterargument that these species adapted to
these environments rather than arose in them, by suggesting that we
cannot assume conditions for life to emerge which are not actually
known. There are suggestions that complex life could arise in sub-surface
conditions which may be similar to those where life may have arisen on
Earth, such as the tidally heated subsurfaces of Europa or Enceladus. Ancient circumvental ecosystems such as these support complex life on Earth such as Riftia pachyptila that exist completely independent of the surface biosphere.
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