Analítica (3), oct. 2023-sept. 2024, ISSN – L 2805 – 1815, pp. 10-38
ANALÍTICA
Revista de Filosofía
BERTRAND RUSSELL AND LUDWIG WITTGENSTEIN,
PERSONAL AND ACADEMIC RELATIONSHIP
BERTRAND RUSSELL Y LUDWIG WITTGENSTEIN,
RELACIÓN PERSONAL Y ACADÉMICA
Natalia Tomashpolskaia
Universidad de Málaga (UMA), España
natalia.tomashpolskaia@gmail.com
https://orcid.org/0000-0002-3017-4058
DOI https://doi.org/10.48204/2805-1815.4309
INFORMACIÓN
DEL ARTÍCULO ABSTRACT/RESUMEN
Recibido el: 1/08/2023
Aceptado el: 30/08/203
Keywords:
Russell, logical
atomism, Wittgenstein,
critique,
analytic philosophy,
logic
Palabras clave:
Russell, atomismo
lógico, Wittgenstein
crítica,
filosofía analítica,
lógica
:
Abstract:
In this article, the author analyses the relationship between two prominent
philosophers of the 20th century in Europe and Great Britain—Ludwig
Wittgenstein and Bertrand Russell. According to a lot of correspondence
available nowadays we can reconstruct not only the environment of thought in
Cambridge in the beginning and the first half of the 20th century but to find out
some very personal, subjective grounds for the changes of relationship
between thinkers, misunderstandings between them. Such a kind of
biographical-historical reconstruction does not interfere but helps to
understand better the origin, development, and criticism of philosophical ideas
and theories. In this context, the personal relationship between Russell and
Wittgenstein, their friendship for more than 30 years, and mutual assistance,
both intellectual and business, played a big role in the development and
formation of both philosophers as philosophers. Even mutual disagreements
and criticism of ideas over time helped them to see the shortcomings and
sometimes even complete failure of their theses and statements. First, the
author describes in detail the role of Russell in Wittgenstein’s life: first meeting
and inspiration to do philosophy, support in studies, assistance in the
publication of Wittgenstein’s first book, support, and facilitation in returning to
Cambridge in 1929, obtaining PhD degree and receiving Trinity College grant.
Second, the author considers the fundamental points of philosophical
disagreements between the two philosophers and Wittgenstein’s critique of
Russell’s ideas.
Resumen:
En este artículo, el autor analiza la relación entre dos destacados filósofos del
siglo XX en Europa y Gran Bretaña: Ludwig Wittgenstein y Bertrand Russell.
De acuerdo con una gran cantidad de correspondencia disponible hoy en día,
11 Bertrand Russell y Ludwig Wittenstein
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
podemos reconstruir no solo el entorno de pensamiento en Cambridge a
principios y la primera mitad del siglo XX, sino también encontrar motivos
subjetivos y personales para los cambios de relación entre pensadores,
malentendidos entre a ellos. Tal tipo de reconstrucción biográfico-histórica no
interfiere, sino que ayuda a comprender el origen, desarrollo y crítica de las
ideas y teorías filosóficas. En este contexto, la relación personal entre Russell
y Wittgenstein, su amistad durante más de 30 años y la ayuda mutua, tanto
intelectual como empresarial, jugaron un papel importante en el desarrollo y
formación de ambos filósofos como filósofos. Incluso los desacuerdos mutuos
y la crítica de ideas a lo largo del tiempo les ayudaron a ver las deficiencias y,
a veces, incluso el fracaso total de sus tesis y declaraciones. Primero, el autor
describe en detalle el papel de Russell en la vida de Wittgenstein: primer
encuentro e inspiración para hacer filosofía, apoyo en los estudios, asistencia
en la publicación del primer libro de Wittgenstein, apoyo y facilitación para
regresar a Cambridge en 1929, obtener el doctorado y recibiendo la beca del
Trinity College. En segundo lugar, el autor considera los puntos básicos y
fundamentales de los desacuerdos filosóficos entre dos filósofos y la crítica
de Wittgenstein a las ideas de Russell.
Introduction
In 1908 young Ludwig Wittgenstein, on his father’s advice, went to England to study
engineering. Earlier in 1906 after finishing school and getting his matriculation, he decided
to study engineering in Berlin at the Technische Hochschule in Charlottenburg after
reading Franz Reuleaux’s ‘Theoretische Kinematik’ (1875). However, he was not satisfied
with studying in Berlin, so he was looking for alternatives. In 1908 he enrolled at the
College of Technology in Manchester. In the autumn of this year, he started his studying
and practice at Manchester University as a research student in the Department of
Engineering, working on the development of a ‘motorless’ aeroengine. While developing
the propeller, Wittgenstein faced mathematical problems. And it piqued his interest more
than the technical development of motors. Wittgenstein discussed mathematical
problems with his colleagues in the engineering laboratory. Much later, one of
Wittgenstein’s pupils, remembering his teachings, suggested that Wittgenstein was
seeking the truth all his life, “He sought the truth at first in engineering, then in
mathematical logic”. (Hijab, 2001)
According to von Wright (1955), Wittgenstein asked someone for advice about
literature on the foundations of mathematics and was advised to read Bertrand Russell’s
The Principles of Mathematics, first published in 1903, after reading this book
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
podemos reconstruir no solo el entorno de pensamiento en Cambridge a
principios y la primera mitad del siglo XX, sino también encontrar motivos
subjetivos y personales para los cambios de relación entre pensadores,
malentendidos entre a ellos. Tal tipo de reconstrucción biográfico-histórica no
interfiere, sino que ayuda a comprender el origen, desarrollo y crítica de las
ideas y teorías filosóficas. En este contexto, la relación personal entre Russell
y Wittgenstein, su amistad durante más de 30 años y la ayuda mutua, tanto
intelectual como empresarial, jugaron un papel importante en el desarrollo y
formación de ambos filósofos como filósofos. Incluso los desacuerdos mutuos
y la crítica de ideas a lo largo del tiempo les ayudaron a ver las deficiencias y,
a veces, incluso el fracaso total de sus tesis y declaraciones. Primero, el autor
describe en detalle el papel de Russell en la vida de Wittgenstein: primer
encuentro e inspiración para hacer filosofía, apoyo en los estudios, asistencia
en la publicación del primer libro de Wittgenstein, apoyo y facilitación para
regresar a Cambridge en 1929, obtener el doctorado y recibiendo la beca del
Trinity College. En segundo lugar, el autor considera los puntos básicos y
fundamentales de los desacuerdos filosóficos entre dos filósofos y la crítica
de Wittgenstein a las ideas de Russell.
Introduction
In 1908 young Ludwig Wittgenstein, on his father’s advice, went to England to study
engineering. Earlier in 1906 after finishing school and getting his matriculation, he decided
to study engineering in Berlin at the Technische Hochschule in Charlottenburg after
reading Franz Reuleaux’s ‘Theoretische Kinematik’ (1875). However, he was not satisfied
with studying in Berlin, so he was looking for alternatives. In 1908 he enrolled at the
College of Technology in Manchester. In the autumn of this year, he started his studying
and practice at Manchester University as a research student in the Department of
Engineering, working on the development of a ‘motorless’ aeroengine. While developing
the propeller, Wittgenstein faced mathematical problems. And it piqued his interest more
than the technical development of motors. Wittgenstein discussed mathematical
problems with his colleagues in the engineering laboratory. Much later, one of
Wittgenstein’s pupils, remembering his teachings, suggested that Wittgenstein was
seeking the truth all his life, “He sought the truth at first in engineering, then in
mathematical logic”. (Hijab, 2001)
According to von Wright (1955), Wittgenstein asked someone for advice about
literature on the foundations of mathematics and was advised to read Bertrand Russell’s
The Principles of Mathematics, first published in 1903, after reading this book
Natalia Tomashpolskaia 12
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
Wittgenstein decided to write to Russell. Von Wright claims that Wittgenstein was
influenced by Russell’s study, and that let him apply to Frege’s works. In von Wright’s
words, “It was probably it which led him to study the works of Frege. The ‘new’ logic,
which in Frege and Russell had two of its most brilliant representatives, became the
gateway through which Wittgenstein entered philosophy”. (1955, p. 530) However,
Russell was wrong, when he wrote that Wittgenstein did not know Frege before he came
to Cambridge. (Russell, 1951) According to Hermine’s notes, it was Frege who advised
Wittgenstein to go to Cambridge and study with Russell. Wittgenstein himself told von
Wright, that after he had decided to give up on studying engineering, he first went to Jena
to meet Frege and discuss his subsequent plans with him (von Wright, 1955). Hermine,
Ludwig’s sister wrote in her memoir that her brother was working on a philosophical work,
and he wanted to present it to Frege. It had happened in summer when Wittgenstein
stopped in Jena on his way from Vienna to England. Frege endorsed Wittgenstein’s
philosophical thoughts and, also, advised him to continue his studies under Russell in
Cambridge. In the preface to Tractatus, Wittgenstein (1922) wrote, “I will only mention
that to the great works of Frege and the writings of my friend Bertrand Russell I owe in
large measure the stimulation of my thoughts”. (p. 23)
The years before WWI were the years of intellectual activity in Cambridge,
especially in the field of logic and mathematics. G. E. Moore, one of the most influential
logicians and philosophers in Cambridge at that time, published in 1899 The Nature of
Judgement, in 1903 his famous Principia Ethica, the same year Review of Franz
Brentano’s ‘The Origin of the Knowledge of Right and Wrong’, and Refutation of Idealism,
in (1905-6) The Nature and Reality of the Objects of Perception. In 1903, G. Frege
published the second volume of Grundgesetze der Arithmetik. In 1910, B. Russell
published the first volume of Principia Mathematica written in collaboration with A. N.
Whitehead, (Whitehead & Russell, 1910). This was the intellectual atmosphere in
Cambridge in 1910 when Wittgenstein arrived. Wittgenstein took an interest in new logic
represented by Frege and Russell. Wittgenstein had a historical-philosophical
background. Earlier he had read Schopenhauer, Boltzmann, and philosophical aspects
of Reuleaux’s Kinematics of Machinery.
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
Wittgenstein decided to write to Russell. Von Wright claims that Wittgenstein was
influenced by Russell’s study, and that let him apply to Frege’s works. In von Wright’s
words, “It was probably it which led him to study the works of Frege. The ‘new’ logic,
which in Frege and Russell had two of its most brilliant representatives, became the
gateway through which Wittgenstein entered philosophy”. (1955, p. 530) However,
Russell was wrong, when he wrote that Wittgenstein did not know Frege before he came
to Cambridge. (Russell, 1951) According to Hermine’s notes, it was Frege who advised
Wittgenstein to go to Cambridge and study with Russell. Wittgenstein himself told von
Wright, that after he had decided to give up on studying engineering, he first went to Jena
to meet Frege and discuss his subsequent plans with him (von Wright, 1955). Hermine,
Ludwig’s sister wrote in her memoir that her brother was working on a philosophical work,
and he wanted to present it to Frege. It had happened in summer when Wittgenstein
stopped in Jena on his way from Vienna to England. Frege endorsed Wittgenstein’s
philosophical thoughts and, also, advised him to continue his studies under Russell in
Cambridge. In the preface to Tractatus, Wittgenstein (1922) wrote, “I will only mention
that to the great works of Frege and the writings of my friend Bertrand Russell I owe in
large measure the stimulation of my thoughts”. (p. 23)
The years before WWI were the years of intellectual activity in Cambridge,
especially in the field of logic and mathematics. G. E. Moore, one of the most influential
logicians and philosophers in Cambridge at that time, published in 1899 The Nature of
Judgement, in 1903 his famous Principia Ethica, the same year Review of Franz
Brentano’s ‘The Origin of the Knowledge of Right and Wrong’, and Refutation of Idealism,
in (1905-6) The Nature and Reality of the Objects of Perception. In 1903, G. Frege
published the second volume of Grundgesetze der Arithmetik. In 1910, B. Russell
published the first volume of Principia Mathematica written in collaboration with A. N.
Whitehead, (Whitehead & Russell, 1910). This was the intellectual atmosphere in
Cambridge in 1910 when Wittgenstein arrived. Wittgenstein took an interest in new logic
represented by Frege and Russell. Wittgenstein had a historical-philosophical
background. Earlier he had read Schopenhauer, Boltzmann, and philosophical aspects
of Reuleaux’s Kinematics of Machinery.
13 Bertrand Russell y Ludwig Wittenstein
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
In 1912 Wittgenstein still had doubts whether to continue his studies in aeronautics
and engineering or to switch completely to philosophy. Russell advised him to write an
essay on any subject. Russell was impressed by the very first sentence and asked him
to devote himself to philosophy. Russell wrote in a letter from October 18, 1911, to
Ottoline Morell about Wittgenstein. “He turned out to be a man who had learnt engineering
at Charlottenburg, but during his course had acquired, by himself, a passion for the
philosophy of math’s, and has now come to Cambridge on purpose to hear me” (Russell
cited in Nedo, 2011). At the beginning of June 1912 Wittgenstein was admitted by the
Degree Committee of the Special Board for Moral Science as Advanced Student to a
course of research at Trinity College and “Mr. Bertrand Russell” was asked to “be kind
enough to act as the Director and Supervisor of the Student”. (Keynes in Wittgenstein,
1974, p. 1) Wittgenstein studied Logic and the Foundations of Mathematics with Russell
and Psychology at Moore’s lectures. His tutors were, first, the mathematician J. W. L.
Glaisher, and later W. M. Fletcher. Wittgenstein developed friendships with Russell,
Whitehead, Moore, J. M. Keynes, and mathematician G. H. Hardy. Moore recalled this
story in a letter to F.A. Hayek. During his first stay in Cambridge (1911-1913) Wittgenstein
became acquainted and established connections with the most famous and influential
philosophers of that time, i.e., B. Russell, G. Moore, and J. M. Keynes, who were active
members of the Apostles.1 They put Wittgenstein in touch with the Bloomsbury younger
elite (Bloomsbury Circle) of Cambridge University. (Garver, 2010; McGuinness, 1998)
The Apostles were fascinated by him, and Bloomsbury handled him cautiously but with
interest. (Griffin, 1992) Russell wrote a letter to Keynes on 11 November 1912 on
Wittgenstein’s election to the Apostles. Russell persuaded Wittgenstein to come to the
first meeting to see ‘how he could stand it, because from Wittgenstein’s “point of view the
Society is a mere waste of time”. (Russell cited in Nedo, 2011, p. 15)
1 Apostles – was a ‘secret’ society, also known as The Society of the Cambridge Conversazione Society. It
was founded in 1820 by George Tomlinson. It was not originally a secret society, but it played a very
important role at the turn of the century because almost all the most influential intellectuals were members
of this society. They were later so-called – the Bloomsbury Generation. For instance, David Pinsent
(Wittgenstein’s close friend) was considered but then rejected for membership in the Apostles. (Griffin,
1992, p. 84)
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
In 1912 Wittgenstein still had doubts whether to continue his studies in aeronautics
and engineering or to switch completely to philosophy. Russell advised him to write an
essay on any subject. Russell was impressed by the very first sentence and asked him
to devote himself to philosophy. Russell wrote in a letter from October 18, 1911, to
Ottoline Morell about Wittgenstein. “He turned out to be a man who had learnt engineering
at Charlottenburg, but during his course had acquired, by himself, a passion for the
philosophy of math’s, and has now come to Cambridge on purpose to hear me” (Russell
cited in Nedo, 2011). At the beginning of June 1912 Wittgenstein was admitted by the
Degree Committee of the Special Board for Moral Science as Advanced Student to a
course of research at Trinity College and “Mr. Bertrand Russell” was asked to “be kind
enough to act as the Director and Supervisor of the Student”. (Keynes in Wittgenstein,
1974, p. 1) Wittgenstein studied Logic and the Foundations of Mathematics with Russell
and Psychology at Moore’s lectures. His tutors were, first, the mathematician J. W. L.
Glaisher, and later W. M. Fletcher. Wittgenstein developed friendships with Russell,
Whitehead, Moore, J. M. Keynes, and mathematician G. H. Hardy. Moore recalled this
story in a letter to F.A. Hayek. During his first stay in Cambridge (1911-1913) Wittgenstein
became acquainted and established connections with the most famous and influential
philosophers of that time, i.e., B. Russell, G. Moore, and J. M. Keynes, who were active
members of the Apostles.1 They put Wittgenstein in touch with the Bloomsbury younger
elite (Bloomsbury Circle) of Cambridge University. (Garver, 2010; McGuinness, 1998)
The Apostles were fascinated by him, and Bloomsbury handled him cautiously but with
interest. (Griffin, 1992) Russell wrote a letter to Keynes on 11 November 1912 on
Wittgenstein’s election to the Apostles. Russell persuaded Wittgenstein to come to the
first meeting to see ‘how he could stand it, because from Wittgenstein’s “point of view the
Society is a mere waste of time”. (Russell cited in Nedo, 2011, p. 15)
1 Apostles – was a ‘secret’ society, also known as The Society of the Cambridge Conversazione Society. It
was founded in 1820 by George Tomlinson. It was not originally a secret society, but it played a very
important role at the turn of the century because almost all the most influential intellectuals were members
of this society. They were later so-called – the Bloomsbury Generation. For instance, David Pinsent
(Wittgenstein’s close friend) was considered but then rejected for membership in the Apostles. (Griffin,
1992, p. 84)
Natalia Tomashpolskaia 14
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
In 1912 in the letter to Russell from 22.06, Wittgenstein emphasised that logic for
him was still in the ‘melting-pot’, however, there were some points that had become
clearer for him. Wittgenstein was in the process of building his own concept of logic.
The propositions of Logic contain ONLY APPARENT variables and whatever may
turn out to be the proper explanation of apparent variables, its consequence must
be that there are NO logical constants.
Logic must turn out to be of a TOTALITY different kind than any other science.
(Wittgenstein cited by McGuinness, 2001, p. 30; emphasis in the original).
In 1913 Wittgenstein finished Notes on Logic, where he for the first time discussed
the aim of philosophy, formed his view on the distinction between philosophy and science,
and criticised some of Russell’s and Frege’s ideas.2 Wittgenstein wrote there that
philosophy is purely descriptive, there can be no deductions in philosophy, and it is always
‘over and under’ but not beside natural science. “Philosophy gives no pictures of reality
and can neither confirm nor confute scientific investigations. It consists of logic and
metaphysics, the former its basis”. (Wittgenstein, 1961, p. 93) Regarding Russell’s and
Frege’s ideas, Wittgenstein remarked that both Frege and Russell are false in their
statements “propositions are names” and “propositions correspond to complexes”
accordingly. “Propositions are names of complexes” is “especially false” statement
according to Wittgenstein. Expressing ideas that would be further written in Tractatus,
Wittgenstein (1961) explained that “What corresponds in reality to a proposition depends
upon whether it is true or false” (p. 93). How can we understand a proposition without
knowing whether it is true or false? Wittgenstein replied, “we know what is the case if it is
true and what is the case if it is false” (p. 93). Later in Tractatus, he wrote,
4.024 To understand a proposition means to know what is the case (wissen was
der Fall ist), if it is true (wenn er wahr ist).
(One can therefore understand it without knowing whether it is true or not.)
One understands it if one understands its constituent parts. (Wittgenstein, 1922)
2 ‘Generally, Wittgenstein's earliest investigations were in the realm of the problems with which Frege and
Russell had dealt’. (Von Wright, 1955, p. 532)
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
In 1912 in the letter to Russell from 22.06, Wittgenstein emphasised that logic for
him was still in the ‘melting-pot’, however, there were some points that had become
clearer for him. Wittgenstein was in the process of building his own concept of logic.
The propositions of Logic contain ONLY APPARENT variables and whatever may
turn out to be the proper explanation of apparent variables, its consequence must
be that there are NO logical constants.
Logic must turn out to be of a TOTALITY different kind than any other science.
(Wittgenstein cited by McGuinness, 2001, p. 30; emphasis in the original).
In 1913 Wittgenstein finished Notes on Logic, where he for the first time discussed
the aim of philosophy, formed his view on the distinction between philosophy and science,
and criticised some of Russell’s and Frege’s ideas.2 Wittgenstein wrote there that
philosophy is purely descriptive, there can be no deductions in philosophy, and it is always
‘over and under’ but not beside natural science. “Philosophy gives no pictures of reality
and can neither confirm nor confute scientific investigations. It consists of logic and
metaphysics, the former its basis”. (Wittgenstein, 1961, p. 93) Regarding Russell’s and
Frege’s ideas, Wittgenstein remarked that both Frege and Russell are false in their
statements “propositions are names” and “propositions correspond to complexes”
accordingly. “Propositions are names of complexes” is “especially false” statement
according to Wittgenstein. Expressing ideas that would be further written in Tractatus,
Wittgenstein (1961) explained that “What corresponds in reality to a proposition depends
upon whether it is true or false” (p. 93). How can we understand a proposition without
knowing whether it is true or false? Wittgenstein replied, “we know what is the case if it is
true and what is the case if it is false” (p. 93). Later in Tractatus, he wrote,
4.024 To understand a proposition means to know what is the case (wissen was
der Fall ist), if it is true (wenn er wahr ist).
(One can therefore understand it without knowing whether it is true or not.)
One understands it if one understands its constituent parts. (Wittgenstein, 1922)
2 ‘Generally, Wittgenstein's earliest investigations were in the realm of the problems with which Frege and
Russell had dealt’. (Von Wright, 1955, p. 532)
15 Bertrand Russell y Ludwig Wittenstein
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
Being influenced by Moore and Russell, young Wittgenstein believed that logical
analysis of language would disclose the logico-metaphysical forms of facts and of their
constituent objects – the substance of the world. He suggested that there is a pre-
established metaphysical harmony between language and reality, i.e., the logico-
syntactical forms of expressions are the forms of what they represent. In his later
reflections, Wittgenstein came up with the idea that he had not solved this problem in
Tractatus. Abstract true-false relations are not the final explanations of the process of
understanding the proposition and its relationship with reality. The ordinary (living)
language works in a much more complicated and intricate way than the formal logical
explanation of it.
Russell and Wittgenstein, personal misunderstandings
In a letter to Russell dated 13.3.1919 from Cassino prison camp, Wittgenstein for the first
time said to Russell about his new book—Tractatus Logico-Philosophicus.
I’ve written a book called ‘Logisch-Philosophische Abhandlung’ containing all my
work of the last six years. I believe I’ve solved our problems finally. This may sound
arrogant, but I can’t help believing it. I finished the book in August 1918 and two
months after was made Prigioniere. I’ve got the manuscript here with me. […]
In fact, you would not understand it without a previous explanation as it’s written in
quite short remarks. (This of course means that nobody will understand it; although
I believe, it’s all as clear as crystal. But it upsets all our theory of truth, of classes,
of numbers and all the rest.) (Wittgenstein, 1974, p. 68)
Also, in a letter to Russell dated 19.8.1919, Wittgenstein complained Frege did not
understand his ideas in Tractatus. “I also sent my M.S. to Frege. He wrote to me a week
ago and I gather that he doesn’t understand a word of it all”. (p. 71) And in the other letter
from 6.9.1919, he added, “I’m in correspondence with Frege. He doesn’t understand a
single word of my work and I’m thoroughly exhausted from giving what are purely and
simply explanations”. (p. 77) In a letter from 29.3.1924, Keynes wrote to Wittgenstein
about Tractatus, “I feel certain that it is a work of extraordinary importance and genius”
(p. 116). Tractatus was written as a reaction to the logic of Russell and Frege.
Wittgenstein (1922) mentioned in the Preface to the Tractatus that “to the great works of
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
Being influenced by Moore and Russell, young Wittgenstein believed that logical
analysis of language would disclose the logico-metaphysical forms of facts and of their
constituent objects – the substance of the world. He suggested that there is a pre-
established metaphysical harmony between language and reality, i.e., the logico-
syntactical forms of expressions are the forms of what they represent. In his later
reflections, Wittgenstein came up with the idea that he had not solved this problem in
Tractatus. Abstract true-false relations are not the final explanations of the process of
understanding the proposition and its relationship with reality. The ordinary (living)
language works in a much more complicated and intricate way than the formal logical
explanation of it.
Russell and Wittgenstein, personal misunderstandings
In a letter to Russell dated 13.3.1919 from Cassino prison camp, Wittgenstein for the first
time said to Russell about his new book—Tractatus Logico-Philosophicus.
I’ve written a book called ‘Logisch-Philosophische Abhandlung’ containing all my
work of the last six years. I believe I’ve solved our problems finally. This may sound
arrogant, but I can’t help believing it. I finished the book in August 1918 and two
months after was made Prigioniere. I’ve got the manuscript here with me. […]
In fact, you would not understand it without a previous explanation as it’s written in
quite short remarks. (This of course means that nobody will understand it; although
I believe, it’s all as clear as crystal. But it upsets all our theory of truth, of classes,
of numbers and all the rest.) (Wittgenstein, 1974, p. 68)
Also, in a letter to Russell dated 19.8.1919, Wittgenstein complained Frege did not
understand his ideas in Tractatus. “I also sent my M.S. to Frege. He wrote to me a week
ago and I gather that he doesn’t understand a word of it all”. (p. 71) And in the other letter
from 6.9.1919, he added, “I’m in correspondence with Frege. He doesn’t understand a
single word of my work and I’m thoroughly exhausted from giving what are purely and
simply explanations”. (p. 77) In a letter from 29.3.1924, Keynes wrote to Wittgenstein
about Tractatus, “I feel certain that it is a work of extraordinary importance and genius”
(p. 116). Tractatus was written as a reaction to the logic of Russell and Frege.
Wittgenstein (1922) mentioned in the Preface to the Tractatus that “to the great works of
Natalia Tomashpolskaia 16
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
Frege and the writings of my friend Bertrand Russell I owe in large measure the
stimulation of my thoughts” (p. 23). On the one hand, it is a true logical work (and it
influenced Vienna Circle logicians and many other personalities), but on the other hand,
this book is ethical. Young Wittgenstein tried to describe his version of reality, how the
world is, and to go further only on particular logical problems. As von Wright wrote in
Wittgenstein’s biography (1955, p. 533), Tractatus was a synthesis of the theory of truth-
functions and the idea of language as a picture of reality. McGuinness (1988) in his
Introduction to ‘Wittgenstein in Cambridge, Letters and Documents 1911-1951’ summed
up:
The original Abhandlung, whose completion he announced to Russell in 1915, was
the product of this Cambridge period, but the additions he made to it in 1916-18
(the passages on God, freedom, and the mystical) issued rather from the next two
phases in his life. Tolstoy’s religion had taken hold of him in the war and the circle
of young disciples of Kraus and Loos whom he met in Olmütz acted as midwives
to the utterance of what he had previously and, as he thought, necessarily left
unsaid. (p. 4)
In December 1919 Wittgenstein was happy to meet B. Russell at the Hague for the
first time after WWI. This meeting was not very warm, the first notes of alienation and
misunderstanding appeared between Russell and Wittgenstein. After their meeting,
Russell in a letter to Lady Ottoline Morell wrote a wide and detailed description of the
changes that had happened in Wittgenstein’s mind. And this letter is very important to
understand the crucial points of the turn of Wittgenstein’s thought. In Russell’s words, it
was a turn for mysticism, he listed several thinkers who influences Wittgenstein in this
way, Kierkegaard, Angelus Silesius, William James, Tolstoy, and Dostoevsky. (Russell in
Wittgenstein, 1974) On his return to England, Russell wrote an introduction to
Wittgenstein’s Tractatus Logico-Philosophicus, and then helped to publish it in Germany
and in English languages. In a letter from 9.4.1920, Wittgenstein wrote to Russell that he
received the manuscript with his introduction. He was not in agreement with Russell “both
where you’re critical of me and also where you’re simply trying to elucidate my point of
view.” However, “that doesn’t matter. The future will pass judgement on us […].”
Wittgenstein understood that the introduction was necessary for publication, especially
from such a prominent figure as Bertrand Russell. In a previous letter from 19.1.20, he
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
Frege and the writings of my friend Bertrand Russell I owe in large measure the
stimulation of my thoughts” (p. 23). On the one hand, it is a true logical work (and it
influenced Vienna Circle logicians and many other personalities), but on the other hand,
this book is ethical. Young Wittgenstein tried to describe his version of reality, how the
world is, and to go further only on particular logical problems. As von Wright wrote in
Wittgenstein’s biography (1955, p. 533), Tractatus was a synthesis of the theory of truth-
functions and the idea of language as a picture of reality. McGuinness (1988) in his
Introduction to ‘Wittgenstein in Cambridge, Letters and Documents 1911-1951’ summed
up:
The original Abhandlung, whose completion he announced to Russell in 1915, was
the product of this Cambridge period, but the additions he made to it in 1916-18
(the passages on God, freedom, and the mystical) issued rather from the next two
phases in his life. Tolstoy’s religion had taken hold of him in the war and the circle
of young disciples of Kraus and Loos whom he met in Olmütz acted as midwives
to the utterance of what he had previously and, as he thought, necessarily left
unsaid. (p. 4)
In December 1919 Wittgenstein was happy to meet B. Russell at the Hague for the
first time after WWI. This meeting was not very warm, the first notes of alienation and
misunderstanding appeared between Russell and Wittgenstein. After their meeting,
Russell in a letter to Lady Ottoline Morell wrote a wide and detailed description of the
changes that had happened in Wittgenstein’s mind. And this letter is very important to
understand the crucial points of the turn of Wittgenstein’s thought. In Russell’s words, it
was a turn for mysticism, he listed several thinkers who influences Wittgenstein in this
way, Kierkegaard, Angelus Silesius, William James, Tolstoy, and Dostoevsky. (Russell in
Wittgenstein, 1974) On his return to England, Russell wrote an introduction to
Wittgenstein’s Tractatus Logico-Philosophicus, and then helped to publish it in Germany
and in English languages. In a letter from 9.4.1920, Wittgenstein wrote to Russell that he
received the manuscript with his introduction. He was not in agreement with Russell “both
where you’re critical of me and also where you’re simply trying to elucidate my point of
view.” However, “that doesn’t matter. The future will pass judgement on us […].”
Wittgenstein understood that the introduction was necessary for publication, especially
from such a prominent figure as Bertrand Russell. In a previous letter from 19.1.20, he
17 Bertrand Russell y Ludwig Wittenstein
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
affirmed that “the printing can’t begin without it (introduction – added by me)”.3
Nevertheless, Leipzig’s publisher Recalm finally did not accept his book (Wittgenstein,
1974). Wittgenstein did not like Russell’s introduction translated in German at all, he wrote
Russell, “All the refinement of your English style was, obviously, lost in translation and
what remind was superficiality and misunderstanding”. (p. 88) In 1922, Russell and
Wittgenstein met each other again in Austria, Innsbruck. They argued, Wittgenstein was
expressive and said unpleasant things to Russell. Since that meeting, their friendship has
never been restored to what it had been before. (von Wright, 1974)
However, as years passed, Wittgenstein returned to Cambridge University on 18
January 1929. Wittgenstein being a remarkable person, had become a legendary
Cambridge eccentric during his first stay at Cambridge, and he was still well-remembered.
According to McGuinness (2088),
He was to repair Russell’s logic; he was to deal with Keynes’s probability in two or
three paragraphs; he was to show that ethics, Moore’s field, did not consist of
propositions at all. And perhaps this is what they wanted from him, they ‘looked to
him for the next big step in philosophy’, as Russell told Wittgenstein’s sister; and
after the war they were happy (as C. D. Broad put it) ‘to dance to the highly
syncopated pipings of Herr Wittgenstein’s flute. (p. 4)
It was necessary to obtain a Ph.D. degree to continue a research and teaching
career in Cambridge. Russell offered Wittgenstein to use his work Tractatus Logico-
Philosophicus translated into English by Ramsey eight years earlier as a thesis, finally it
was accepted as his doctoral work. Frank Ramsey was formally appointed as his
supervisor and B. Russell and R. Moore were his examiners. Wittgenstein passed an oral
examination on June 6 and on June 18 he was awarded his PhD degree from the
University of Cambridge. To be honest, this procedure was purely formal (Monk, 1990,
271). Clark in The Life of Bertrand Russell described the process of examination.
Moore and Russell first chatted informally to Wittgenstein as old friends rather than
as examiners and examinees. Then Russell turned to Moore. ‘Go on’, he said,
‘you’ve got to ask him some questions – you’re the Professor’. There was a short
discussion. Russell made a brief attempt to argue that Wittgenstein was
inconsistent in stating that little could be said about philosophy and that it was
3 Letters from 9.4.20 and 19.1.20. (Wittgenstein, 1974, p. 84)
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
affirmed that “the printing can’t begin without it (introduction – added by me)”.3
Nevertheless, Leipzig’s publisher Recalm finally did not accept his book (Wittgenstein,
1974). Wittgenstein did not like Russell’s introduction translated in German at all, he wrote
Russell, “All the refinement of your English style was, obviously, lost in translation and
what remind was superficiality and misunderstanding”. (p. 88) In 1922, Russell and
Wittgenstein met each other again in Austria, Innsbruck. They argued, Wittgenstein was
expressive and said unpleasant things to Russell. Since that meeting, their friendship has
never been restored to what it had been before. (von Wright, 1974)
However, as years passed, Wittgenstein returned to Cambridge University on 18
January 1929. Wittgenstein being a remarkable person, had become a legendary
Cambridge eccentric during his first stay at Cambridge, and he was still well-remembered.
According to McGuinness (2088),
He was to repair Russell’s logic; he was to deal with Keynes’s probability in two or
three paragraphs; he was to show that ethics, Moore’s field, did not consist of
propositions at all. And perhaps this is what they wanted from him, they ‘looked to
him for the next big step in philosophy’, as Russell told Wittgenstein’s sister; and
after the war they were happy (as C. D. Broad put it) ‘to dance to the highly
syncopated pipings of Herr Wittgenstein’s flute. (p. 4)
It was necessary to obtain a Ph.D. degree to continue a research and teaching
career in Cambridge. Russell offered Wittgenstein to use his work Tractatus Logico-
Philosophicus translated into English by Ramsey eight years earlier as a thesis, finally it
was accepted as his doctoral work. Frank Ramsey was formally appointed as his
supervisor and B. Russell and R. Moore were his examiners. Wittgenstein passed an oral
examination on June 6 and on June 18 he was awarded his PhD degree from the
University of Cambridge. To be honest, this procedure was purely formal (Monk, 1990,
271). Clark in The Life of Bertrand Russell described the process of examination.
Moore and Russell first chatted informally to Wittgenstein as old friends rather than
as examiners and examinees. Then Russell turned to Moore. ‘Go on’, he said,
‘you’ve got to ask him some questions – you’re the Professor’. There was a short
discussion. Russell made a brief attempt to argue that Wittgenstein was
inconsistent in stating that little could be said about philosophy and that it was
3 Letters from 9.4.20 and 19.1.20. (Wittgenstein, 1974, p. 84)
Natalia Tomashpolskaia 18
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
possible to reach unassailable truth. Then the Viva ended unexpectedly with
Wittgenstein clapping each of his examiners on the shoulder and exclaiming, ‘Don’t
worry, I know you’ll never understand it’. (Clark cited by Nedo, 2011, p. 8)
Earlier this month on 2 February 1929 Wittgenstein had begun work on a series of
18 manuscript volumes, he had finished his work only until 1940. On 19 June,
Wittgenstein received a grant from Trinity College, arranged by Moore, Russell, and
Ramsey. This one-off payment allowed him to continue his research work in Cambridge.
Russell admitted in a letter to Moore from 9 March 1930,
The Council of Trinity made a grant to Wittgenstein last June to enable him to carry
on his researches on the foundations of Mathematics. There is now a question of
making him a further grant; and they wish, before they decide, to have expert
reports on the work he has done since the last grant was made. They have
authorised me to ask you to make such a report for them. (Russell cited in Nedo
2011, p. 9)
In March and April 1930 Wittgenstein worked on the synopsis of manuscripts –
later known as the Typescript 208. He discussed this text with Bertrand Russell in March,
visiting him, especially for this purpose. Then Wittgenstein prepared a revision of
Typescript 208 – TS 209, known as Philosophische Bemerkungen, and showed it again
to Russel at the end of April. With this work on Russell’s advice, Wittgenstein applied for
a Fellowship at Trinity College in Cambridge, where he was admitted after evaluation of
his work. Therefore, during the academic year 1929/1930 and Easter and summer
holidays, Wittgenstein produced, Typescript 208, its revision Typescript TS 209, which
were both published posthumously in 1964 in Oxford with the name Philosophical
Remarks, and TS 210, the synopsis of the first part of volume IV. For Wittgenstein’s
admission to Trinity College, his work had to be evaluated by Russell and two Cambridge
mathematicians J. E. Littlewood and G. H. Hardy. Russell reproduced his opinion,
presented it to Trinity College Committee in his autobiography,
The theories contained in the work of Wittgenstein are novel, very original and
indubitably important. Whether they are true, I do not know. As a logician who likes
simplicity, I should wish to think that they are not, but from what I have read of
them I am quite sure that he should have an opportunity to work them out, since
when completed they may easily prove to constitute a whole new philosophy.
(Russell, 1968, vol. II, p. 200).
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
possible to reach unassailable truth. Then the Viva ended unexpectedly with
Wittgenstein clapping each of his examiners on the shoulder and exclaiming, ‘Don’t
worry, I know you’ll never understand it’. (Clark cited by Nedo, 2011, p. 8)
Earlier this month on 2 February 1929 Wittgenstein had begun work on a series of
18 manuscript volumes, he had finished his work only until 1940. On 19 June,
Wittgenstein received a grant from Trinity College, arranged by Moore, Russell, and
Ramsey. This one-off payment allowed him to continue his research work in Cambridge.
Russell admitted in a letter to Moore from 9 March 1930,
The Council of Trinity made a grant to Wittgenstein last June to enable him to carry
on his researches on the foundations of Mathematics. There is now a question of
making him a further grant; and they wish, before they decide, to have expert
reports on the work he has done since the last grant was made. They have
authorised me to ask you to make such a report for them. (Russell cited in Nedo
2011, p. 9)
In March and April 1930 Wittgenstein worked on the synopsis of manuscripts –
later known as the Typescript 208. He discussed this text with Bertrand Russell in March,
visiting him, especially for this purpose. Then Wittgenstein prepared a revision of
Typescript 208 – TS 209, known as Philosophische Bemerkungen, and showed it again
to Russel at the end of April. With this work on Russell’s advice, Wittgenstein applied for
a Fellowship at Trinity College in Cambridge, where he was admitted after evaluation of
his work. Therefore, during the academic year 1929/1930 and Easter and summer
holidays, Wittgenstein produced, Typescript 208, its revision Typescript TS 209, which
were both published posthumously in 1964 in Oxford with the name Philosophical
Remarks, and TS 210, the synopsis of the first part of volume IV. For Wittgenstein’s
admission to Trinity College, his work had to be evaluated by Russell and two Cambridge
mathematicians J. E. Littlewood and G. H. Hardy. Russell reproduced his opinion,
presented it to Trinity College Committee in his autobiography,
The theories contained in the work of Wittgenstein are novel, very original and
indubitably important. Whether they are true, I do not know. As a logician who likes
simplicity, I should wish to think that they are not, but from what I have read of
them I am quite sure that he should have an opportunity to work them out, since
when completed they may easily prove to constitute a whole new philosophy.
(Russell, 1968, vol. II, p. 200).
19 Bertrand Russell y Ludwig Wittenstein
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
What Russell was really thinking about Wittgenstein, he left in his autobiography written
in 1959 after Wittgenstein’s death, “He was perhaps the most perfect example I have ever
known of genius as traditionally conceived, passionate, profound, intense, and
dominating”. (Russell cited in Nedo, 2011, p. 7) In a letter to Lady Ottoline Morell in 1916,
Russell admitted that Wittgenstein’s critique and ideas influenced and changed his views
on different philosophical problems.
Do you remember that at the time…I wrote a lot of stuff about Theory of
Knowledge, which Wittgenstein criticized with the greatest severity? His criticism…
was an event of first-rate importance in my life, and affected everything I have done
since. I saw he was right, and I saw that I could not hope ever again to do
fundamental work in philosophy. My impulse was shattered, like a wave dashed to
pieces against a breakwater. (Russell, 1968, Vol. II, p. 57)
Analysing the diaries of both Wittgenstein and Russell themselves and others, we
can reconstruct the course of philosophical disputes and contradictions between them. It
is interesting to trace the dynamics of changes in Russell’s attitude towards Wittgenstein.
In the letters from 1911, he left very different descriptions of Wittgenstein’s behaviour and
his character in general:
19 October 1911
My German friend threatens to be an infliction, he came back with me after my
lecture and argued till dinner-time – obstinate and perverse, but I think not stupid.
1 November 1911
My German engineer is very argumentative and tiresome.
2 November 1911
My German engineer, I think is a fool. He thinks nothing empirical is knowable – I
asked him to admit that there was not a rhinoceros in the room, but he wouldn’t.
13 November 1911
[M]y German ex-engineer, as usual, maintained his thesis that there is nothing in
the world except asserted propositions, but at last I told him it was too large a
theme […]
16 November 1911
My ferocious German came and argued at me after my lecture, […] He is armour-
plated against all assaults of reasoning – it is really rather a waste of time talking
with him.
29 November 1911
I am getting to like him, he is literary, very musical, pleasant-mannered (being an
Austrian) and I think really intelligent. (Russell cited by Nedo, 2011, no page)
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
What Russell was really thinking about Wittgenstein, he left in his autobiography written
in 1959 after Wittgenstein’s death, “He was perhaps the most perfect example I have ever
known of genius as traditionally conceived, passionate, profound, intense, and
dominating”. (Russell cited in Nedo, 2011, p. 7) In a letter to Lady Ottoline Morell in 1916,
Russell admitted that Wittgenstein’s critique and ideas influenced and changed his views
on different philosophical problems.
Do you remember that at the time…I wrote a lot of stuff about Theory of
Knowledge, which Wittgenstein criticized with the greatest severity? His criticism…
was an event of first-rate importance in my life, and affected everything I have done
since. I saw he was right, and I saw that I could not hope ever again to do
fundamental work in philosophy. My impulse was shattered, like a wave dashed to
pieces against a breakwater. (Russell, 1968, Vol. II, p. 57)
Analysing the diaries of both Wittgenstein and Russell themselves and others, we
can reconstruct the course of philosophical disputes and contradictions between them. It
is interesting to trace the dynamics of changes in Russell’s attitude towards Wittgenstein.
In the letters from 1911, he left very different descriptions of Wittgenstein’s behaviour and
his character in general:
19 October 1911
My German friend threatens to be an infliction, he came back with me after my
lecture and argued till dinner-time – obstinate and perverse, but I think not stupid.
1 November 1911
My German engineer is very argumentative and tiresome.
2 November 1911
My German engineer, I think is a fool. He thinks nothing empirical is knowable – I
asked him to admit that there was not a rhinoceros in the room, but he wouldn’t.
13 November 1911
[M]y German ex-engineer, as usual, maintained his thesis that there is nothing in
the world except asserted propositions, but at last I told him it was too large a
theme […]
16 November 1911
My ferocious German came and argued at me after my lecture, […] He is armour-
plated against all assaults of reasoning – it is really rather a waste of time talking
with him.
29 November 1911
I am getting to like him, he is literary, very musical, pleasant-mannered (being an
Austrian) and I think really intelligent. (Russell cited by Nedo, 2011, no page)
Natalia Tomashpolskaia 20
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
Also, for instance, we come across interesting passages about Wittgenstein's
attitude to Russell’s ideas. In October 1912, Pinsent wrote about Wittgenstein’s new
solution to a problem in mathematical logic, “which should revolutionise lots of Symbolic
Logic ... the most masterly and convincing solution too’ and ‘Russell…thinks…is sound”.
(Pinsent, 1990, p. 37) The next year in 1913 he wrote more in detail about this situation
concerning symbolic logic.
Of course [Wittgenstein] has upset a lot of Russell's work-but Russell would be the
last to resent that, and really the greatness of his work suffers little thereby - as it
is obvious that Wittgenstein is one of Russell's disciples and owes enormously to
him. But Wittgenstein's work is really amazing - and I really believe that the mucky
morass of Philosophy is at last crystallizing about a rigid theory of Logic - the only
portion of Philosophy about which there is any possibility of man knowing anything
Metaphysics etc. are hampered by total lack of data. It is like the transition from
Alchemy to Chemistry. (Pinsent,1990, p. 59)
In a letter sent by Ramsey to his mother in September 1923, after a meeting with
Wittgenstein, he wrote that Wittgenstein was a ‘little annoyed’ that Russell was doing a
new edition of Principia Mathematica because “he thought he had shown R [Russell] that
it was so wrong that a new edition would be futile. It must be done altogether afresh”
(Ramsey in Nedo 2011, p. 21). Russell, on the other hand, did not understand
Wittgenstein’s Tractatus. Janik (2001) assumed that the real reason for this
misunderstanding was in absolutely different approaches. Russell, at that time, advocated
logical positivism, while Wittgenstein’s early ideas were based on a “Hertzian perspective
on philosophy.” In 1930 Wittgenstein said to his friend Maurice O’C Drury (Drury, 1984)
his opinion on Russell’s books, they “should be bound in two colours, those dealing with
mathematical logic in red – and all students of philosophy should read them; those dealing
with ethics and politics in blue – and no one should be allowed to read them” (p. 112). In
the notes from 1937, published in CV, Wittgenstein remembered how during their
conversations with Russell, the latter often exclaimed “Logic’s hell!” Here he explained
the nature of the difficulties when they both tried to resolve logical problems which were
inextricably connected with the peculiarities of the language. According to Wittgenstein,
this phrase in the best way expresses the feeling that they had when they were thinking
about the problems of logic. It expresses the “immense difficulty” of the problems of logic,
“their hard and slippery texture”. (Wittgenstein,1980, p. 30e)
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
Also, for instance, we come across interesting passages about Wittgenstein's
attitude to Russell’s ideas. In October 1912, Pinsent wrote about Wittgenstein’s new
solution to a problem in mathematical logic, “which should revolutionise lots of Symbolic
Logic ... the most masterly and convincing solution too’ and ‘Russell…thinks…is sound”.
(Pinsent, 1990, p. 37) The next year in 1913 he wrote more in detail about this situation
concerning symbolic logic.
Of course [Wittgenstein] has upset a lot of Russell's work-but Russell would be the
last to resent that, and really the greatness of his work suffers little thereby - as it
is obvious that Wittgenstein is one of Russell's disciples and owes enormously to
him. But Wittgenstein's work is really amazing - and I really believe that the mucky
morass of Philosophy is at last crystallizing about a rigid theory of Logic - the only
portion of Philosophy about which there is any possibility of man knowing anything
Metaphysics etc. are hampered by total lack of data. It is like the transition from
Alchemy to Chemistry. (Pinsent,1990, p. 59)
In a letter sent by Ramsey to his mother in September 1923, after a meeting with
Wittgenstein, he wrote that Wittgenstein was a ‘little annoyed’ that Russell was doing a
new edition of Principia Mathematica because “he thought he had shown R [Russell] that
it was so wrong that a new edition would be futile. It must be done altogether afresh”
(Ramsey in Nedo 2011, p. 21). Russell, on the other hand, did not understand
Wittgenstein’s Tractatus. Janik (2001) assumed that the real reason for this
misunderstanding was in absolutely different approaches. Russell, at that time, advocated
logical positivism, while Wittgenstein’s early ideas were based on a “Hertzian perspective
on philosophy.” In 1930 Wittgenstein said to his friend Maurice O’C Drury (Drury, 1984)
his opinion on Russell’s books, they “should be bound in two colours, those dealing with
mathematical logic in red – and all students of philosophy should read them; those dealing
with ethics and politics in blue – and no one should be allowed to read them” (p. 112). In
the notes from 1937, published in CV, Wittgenstein remembered how during their
conversations with Russell, the latter often exclaimed “Logic’s hell!” Here he explained
the nature of the difficulties when they both tried to resolve logical problems which were
inextricably connected with the peculiarities of the language. According to Wittgenstein,
this phrase in the best way expresses the feeling that they had when they were thinking
about the problems of logic. It expresses the “immense difficulty” of the problems of logic,
“their hard and slippery texture”. (Wittgenstein,1980, p. 30e)
21 Bertrand Russell y Ludwig Wittenstein
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
I believe our main reason for feeling like this was the following fact, that every time
some new linguistic phenomenon occurred to us, it could retrospectively show that
our previous explanation was unworkable. (We felt that language could always
make new, and impossible, demands; and that this made all explanation futile.) (p.
30e)
Wittgenstein blamed Russell for the lack of depth and insufficient attention to the
so-called ordinary life and its problems. In Zettel Wittgenstein (1967) wrote,
Some philosophers (or whatever you like to call them) suffer from what may be
called “loss of problems”. Then everything seems quite simple to them, no deep
problems seem to exist any more, the world becomes broad and flat and loses all
depth, and what they write becomes immeasurably shallow and trivial. Russell and
H. G. Wells suffer from this. (p. 82e)
In the lectures recorded by Moore (Wittgenstein & Moore, 2016) we meet:
“Russell’s view of structure of propositions was far too simple. Grammar of different kinds
of words is much more different than you would expect”. (p. 253)
Wittgenstein’s critique of Bertrand Russell’s basic ideas
Russell in the first decade of the 20th century tried to develop Gottlob Frege’s logical and
mathematical ideas, among them, predicate calculus. He sought to realize the leading
idea of Frege’s research—to reduce all mathematics to logic and, thus, to build a reliable
and obvious foundation for it, as well as to answer philosophical questions about the
nature of mathematics and the source of the irrefutability of its truths.
Russell had already been able to recognize the difficulties and problems that
Frege's approach ran into. Russell formulated the paradox that shook the system of
logical foundations of mathematics built by Frege. Russell’s paradox, like several other
paradoxes, is based on the fact that an expression is applied to itself (or, equivalently, a
certain property is asked whether it characterises itself). When an expression is applied
to itself, it is said to be used self-referentially. Self-referentiality is fraught with paradoxes
(e.g., the ‘Liar paradox’).4 Another significant difficulty that Frege's approach (Frege
4 Liar paradox is the statement of a liar, that he is lying, ‘I am lying’. If the liar is lying, then the liar is telling
the truth. But if the liar is telling the truth, it means that he lied. Here we face a contradiction trying to assign
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
I believe our main reason for feeling like this was the following fact, that every time
some new linguistic phenomenon occurred to us, it could retrospectively show that
our previous explanation was unworkable. (We felt that language could always
make new, and impossible, demands; and that this made all explanation futile.) (p.
30e)
Wittgenstein blamed Russell for the lack of depth and insufficient attention to the
so-called ordinary life and its problems. In Zettel Wittgenstein (1967) wrote,
Some philosophers (or whatever you like to call them) suffer from what may be
called “loss of problems”. Then everything seems quite simple to them, no deep
problems seem to exist any more, the world becomes broad and flat and loses all
depth, and what they write becomes immeasurably shallow and trivial. Russell and
H. G. Wells suffer from this. (p. 82e)
In the lectures recorded by Moore (Wittgenstein & Moore, 2016) we meet:
“Russell’s view of structure of propositions was far too simple. Grammar of different kinds
of words is much more different than you would expect”. (p. 253)
Wittgenstein’s critique of Bertrand Russell’s basic ideas
Russell in the first decade of the 20th century tried to develop Gottlob Frege’s logical and
mathematical ideas, among them, predicate calculus. He sought to realize the leading
idea of Frege’s research—to reduce all mathematics to logic and, thus, to build a reliable
and obvious foundation for it, as well as to answer philosophical questions about the
nature of mathematics and the source of the irrefutability of its truths.
Russell had already been able to recognize the difficulties and problems that
Frege's approach ran into. Russell formulated the paradox that shook the system of
logical foundations of mathematics built by Frege. Russell’s paradox, like several other
paradoxes, is based on the fact that an expression is applied to itself (or, equivalently, a
certain property is asked whether it characterises itself). When an expression is applied
to itself, it is said to be used self-referentially. Self-referentiality is fraught with paradoxes
(e.g., the ‘Liar paradox’).4 Another significant difficulty that Frege's approach (Frege
4 Liar paradox is the statement of a liar, that he is lying, ‘I am lying’. If the liar is lying, then the liar is telling
the truth. But if the liar is telling the truth, it means that he lied. Here we face a contradiction trying to assign
Natalia Tomashpolskaia 22
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
1892a, pp. 41-42; 1893, pp. 19-20) encountered (Beaney 1997, pp. 384-5) was the
problem of “empty names” (or definite description), that is, names that make sense but
have no meaning (they do not refer to anything). The difficulty was in fact that no logical
criteria in Frege's system could distinguish empty names from names that have meaning,
for this was a matter of information. This circumstance created great inconvenience in the
implementation of logical conclusions. Realising this difficulty, Frege put forward the
requirement that there should be no empty names in a logically correct language - they
should have been eliminated in advance. Russell (1905) remarked that Frege's approach
was “plainly artificial”.
Russell, on the other hand, took a different path, resulting in a completely different
concept of language meaning expressions. Russell was not only a mathematician but
also a philosopher, so the context of his thoughts and the range of problems he discussed
were much wider than that of Frege. As a young man, Russell was influenced by the
philosophy of British neo-Hegelianism, or absolute idealism. (See Griffin, 1992; Baker &
Hacker, 1980a, 1980b) According to absolute idealism, the world appears as an
indivisible and unified whole. No fact or element is self-sufficient. Therefore, any attempt
to consider the elements of the whole in isolation leads to distortion and delusion. Only a
complete and holistic consideration can claim the truth. All reasoning about the absolute
must be a priori because experience is limited to serve as a basis for it. Relationships
within the whole were seen as internal and necessary. Here, external, and accidental
relations were not recognized.
Studying Leibniz (see Griffin, 1992; Russell, 1900), Russell became aware of the
importance of relations, in particular ordering relations were essential for mathematics.
Neo-Hegelians rejected relations or insisted that any relations are internal. Russell
understood that his analysis of mathematics is impossible without relations, and he broke
with neo-Hegelianism. Instead, he had adopted a position that could be called “absolute
realism”, the type of ontology that includes everything that could be thought of or
to this statement a classical binary truth-value. If ‘this sentence is false’ is True, then it is False. However,
the statement says that it is false, and if it is False, it must be True.
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
1892a, pp. 41-42; 1893, pp. 19-20) encountered (Beaney 1997, pp. 384-5) was the
problem of “empty names” (or definite description), that is, names that make sense but
have no meaning (they do not refer to anything). The difficulty was in fact that no logical
criteria in Frege's system could distinguish empty names from names that have meaning,
for this was a matter of information. This circumstance created great inconvenience in the
implementation of logical conclusions. Realising this difficulty, Frege put forward the
requirement that there should be no empty names in a logically correct language - they
should have been eliminated in advance. Russell (1905) remarked that Frege's approach
was “plainly artificial”.
Russell, on the other hand, took a different path, resulting in a completely different
concept of language meaning expressions. Russell was not only a mathematician but
also a philosopher, so the context of his thoughts and the range of problems he discussed
were much wider than that of Frege. As a young man, Russell was influenced by the
philosophy of British neo-Hegelianism, or absolute idealism. (See Griffin, 1992; Baker &
Hacker, 1980a, 1980b) According to absolute idealism, the world appears as an
indivisible and unified whole. No fact or element is self-sufficient. Therefore, any attempt
to consider the elements of the whole in isolation leads to distortion and delusion. Only a
complete and holistic consideration can claim the truth. All reasoning about the absolute
must be a priori because experience is limited to serve as a basis for it. Relationships
within the whole were seen as internal and necessary. Here, external, and accidental
relations were not recognized.
Studying Leibniz (see Griffin, 1992; Russell, 1900), Russell became aware of the
importance of relations, in particular ordering relations were essential for mathematics.
Neo-Hegelians rejected relations or insisted that any relations are internal. Russell
understood that his analysis of mathematics is impossible without relations, and he broke
with neo-Hegelianism. Instead, he had adopted a position that could be called “absolute
realism”, the type of ontology that includes everything that could be thought of or
to this statement a classical binary truth-value. If ‘this sentence is false’ is True, then it is False. However,
the statement says that it is false, and if it is False, it must be True.
23 Bertrand Russell y Ludwig Wittenstein
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
mentioned. “The logic which I shall advocate is atomistic, as opposed to the monistic logic
of the people who more or less follow Hegel”. (Russell, 1918, p. 495).
In 1900, Russell discovered Peano’s method of symbolic logic. This year he
finished the draft of his The Principles of Mathematics. (Russell, 1903) Continuing
analysis of principles of mathematics, in 1901 Russell came up with his famous class
paradox (also known as a Russell-Zermelo5 paradox. He discovered that a class of all
classes which are not members of themselves both was and was not a member of itself
(according to set-theoretical principles current at his time), or, in other interpretations, the
set of all sets that are not members of themselves will be a member of itself if and only if
it is not a member of itself.
The axiom that all referents with respect to a given relation form a class seems,
however, to require some limitation, and that for the following reason. We saw that
some predicates can be predicated of themselves. Consider now those … of which
this is not the case. … [T]here is no predicate which attaches to all of them and to
no other terms. For this predicate will either be predicable or not predicable of itself.
If it is predicable of itself, it is one of those referents by relation to which it was
defined, and therefore, in virtue of their definition, it is not predicable of itself.
Conversely, if it is not predicable of itself, then again it is one of the said referents,
of all of which (by hypothesis) it is predicable, and therefore again it is predicable
of itself. This is a contradiction. (Russell, 1986, Vol. 3, p. 195)
This significant paradox was unresolved in classical logic, all sentences were
entailed by a contradiction. Propositional functions – “’x is a set’ cannot be applied to
themselves because self-application leads to a vicious circle”. (Russell, 1963, Vol. I., p.
67; see Poincaré, 1905, p. 307) Trying to solve this problem Russell developed his theory
of types during 1903-1908 (arranging all sentences into a hierarchy of levels). (Russell,
1908)
First, in 1903, he introduced the ‘simple’ version of this theory, and in 1908 the
‘ramified theory’. He was concerned about this theory because he realised that there
could not be a single solution. Together with Whitehead, Russell suggested applying the
axiom of reducibility to resolve some most worrisome aspects of their theory of types.
5 Zermelo noticed the similar contradiction in about 1897-1902, anticipating Russell. See Ebbinghaus &
Peckhaus (2007, pp. 43-38).
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
mentioned. “The logic which I shall advocate is atomistic, as opposed to the monistic logic
of the people who more or less follow Hegel”. (Russell, 1918, p. 495).
In 1900, Russell discovered Peano’s method of symbolic logic. This year he
finished the draft of his The Principles of Mathematics. (Russell, 1903) Continuing
analysis of principles of mathematics, in 1901 Russell came up with his famous class
paradox (also known as a Russell-Zermelo5 paradox. He discovered that a class of all
classes which are not members of themselves both was and was not a member of itself
(according to set-theoretical principles current at his time), or, in other interpretations, the
set of all sets that are not members of themselves will be a member of itself if and only if
it is not a member of itself.
The axiom that all referents with respect to a given relation form a class seems,
however, to require some limitation, and that for the following reason. We saw that
some predicates can be predicated of themselves. Consider now those … of which
this is not the case. … [T]here is no predicate which attaches to all of them and to
no other terms. For this predicate will either be predicable or not predicable of itself.
If it is predicable of itself, it is one of those referents by relation to which it was
defined, and therefore, in virtue of their definition, it is not predicable of itself.
Conversely, if it is not predicable of itself, then again it is one of the said referents,
of all of which (by hypothesis) it is predicable, and therefore again it is predicable
of itself. This is a contradiction. (Russell, 1986, Vol. 3, p. 195)
This significant paradox was unresolved in classical logic, all sentences were
entailed by a contradiction. Propositional functions – “’x is a set’ cannot be applied to
themselves because self-application leads to a vicious circle”. (Russell, 1963, Vol. I., p.
67; see Poincaré, 1905, p. 307) Trying to solve this problem Russell developed his theory
of types during 1903-1908 (arranging all sentences into a hierarchy of levels). (Russell,
1908)
First, in 1903, he introduced the ‘simple’ version of this theory, and in 1908 the
‘ramified theory’. He was concerned about this theory because he realised that there
could not be a single solution. Together with Whitehead, Russell suggested applying the
axiom of reducibility to resolve some most worrisome aspects of their theory of types.
5 Zermelo noticed the similar contradiction in about 1897-1902, anticipating Russell. See Ebbinghaus &
Peckhaus (2007, pp. 43-38).
Natalia Tomashpolskaia 24
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
However, critics claimed that this axiom was rather simple (Linsky, 1999, 2002; Wahl,
2011). Also, during this period Russell defended logicism, a theory according to which
mathematics is reducible to logic. Russell suggested two main theses in his programme
of logicism, (i) all mathematical truths can be translated into logical truths; (ii) all
mathematical proofs can be recast as logical proofs. “The fact that all Mathematics is
Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been
established, the remainder of the principles of mathematics consists in the analysis of
Symbolic Logic itself”. (Russell, 1903, p. 5) Russell tried to use logic to clarify not only the
issues of mathematics but also to clarify issues of philosophy.
Frank Ramsey, a mathematician and Wittgenstein’s friend, criticised Russell’s
Theory of Types. In a letter to Wittgenstein dated February 20, 1924, he wrote that he
“made out the proper solution rather in detail of some of the contradictions which made
Russell’s Theory of Types unnecessarily complicated.” For Ramsey this complicity “made
him [Russell] put in the Axiom of Reducibility.” Ramsey was reading the manuscript of the
new material Russell was putting into the Principia Mathematica. And he agreed with
Wittgenstein, that “it is of no importance.” All this new stuff “is a clever proof of
mathematical induction without using the axiom of reducibility.” And there were neither
new ideas nor fundamental changes. Russell accepted only one of Wittgenstein’s critical
remarks on “that it is nonsense to put an adjective where a substantive ought to be which
helps in his theory of types.” Moreover, Russell “indignantly denied ever having said that
vagueness is a characteristic of the physical world”. (Nedo, 2011, p. 20) In a letter to
Moore dated 6.2.1924 Ramsey described in detail his critique to Russell’s Theory of
Types, agreed with Wittgenstein, and mentioned his new project.
I am working based on Wittgenstein’s work, which seems to me to show that
Principia is wrong not merely in detail but fundamentally. I have got Russell’s
manuscript of the stuff he is inserting into the new edition and it seems to me to
take no account of Wittgenstein’s work at all. There is a new Theory of Types
without the axiom of reducibility, on which however Russell hasn’t succeeded
improving a lot of ordinary mathematics, whose truth, he concludes, remains
doubtful. But I have got on Wittgenstein’s principles a new theory of types without
any doubtful axioms, which gives all the results of Russell’s one and solves all the
contradictions.
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
However, critics claimed that this axiom was rather simple (Linsky, 1999, 2002; Wahl,
2011). Also, during this period Russell defended logicism, a theory according to which
mathematics is reducible to logic. Russell suggested two main theses in his programme
of logicism, (i) all mathematical truths can be translated into logical truths; (ii) all
mathematical proofs can be recast as logical proofs. “The fact that all Mathematics is
Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been
established, the remainder of the principles of mathematics consists in the analysis of
Symbolic Logic itself”. (Russell, 1903, p. 5) Russell tried to use logic to clarify not only the
issues of mathematics but also to clarify issues of philosophy.
Frank Ramsey, a mathematician and Wittgenstein’s friend, criticised Russell’s
Theory of Types. In a letter to Wittgenstein dated February 20, 1924, he wrote that he
“made out the proper solution rather in detail of some of the contradictions which made
Russell’s Theory of Types unnecessarily complicated.” For Ramsey this complicity “made
him [Russell] put in the Axiom of Reducibility.” Ramsey was reading the manuscript of the
new material Russell was putting into the Principia Mathematica. And he agreed with
Wittgenstein, that “it is of no importance.” All this new stuff “is a clever proof of
mathematical induction without using the axiom of reducibility.” And there were neither
new ideas nor fundamental changes. Russell accepted only one of Wittgenstein’s critical
remarks on “that it is nonsense to put an adjective where a substantive ought to be which
helps in his theory of types.” Moreover, Russell “indignantly denied ever having said that
vagueness is a characteristic of the physical world”. (Nedo, 2011, p. 20) In a letter to
Moore dated 6.2.1924 Ramsey described in detail his critique to Russell’s Theory of
Types, agreed with Wittgenstein, and mentioned his new project.
I am working based on Wittgenstein’s work, which seems to me to show that
Principia is wrong not merely in detail but fundamentally. I have got Russell’s
manuscript of the stuff he is inserting into the new edition and it seems to me to
take no account of Wittgenstein’s work at all. There is a new Theory of Types
without the axiom of reducibility, on which however Russell hasn’t succeeded
improving a lot of ordinary mathematics, whose truth, he concludes, remains
doubtful. But I have got on Wittgenstein’s principles a new theory of types without
any doubtful axioms, which gives all the results of Russell’s one and solves all the
contradictions.
25 Bertrand Russell y Ludwig Wittenstein
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
But Wittgenstein and I think it wrong to suppose with Russell that mathematics is
more complicated formal logic (tautologies) and I am trying to make definite the
vague idea Wittgenstein has of what it does consist of. If I am successful, I think it
will illuminate not only mathematics but physics also because a successful theory
of mathematics will help one to separate and give a true account of the a priori
element in physics. (This certainly exists for ‘this is not both red and blue’ is a
priori). (McGuinness, 2006, p. 21)
Wittgenstein in Zettel (1970) explained that the practical purpose of Russell’s Theory
of Types is, “Russell makes us realize that we must sometimes put restrictions on the
expression of generality in order to avoid having consequences drawn from it” (p. 120e).
In the notes of Wittgenstein’s (Wittgenstein & Moore, 2016) lectures recorded by Moore
we can find the following: “This explains what’s wrong with Russell’s theory of types: a
theory of types is a grammar, and must not mention meanings of words”. (p. 30) Since
about the end of 1929, Wittgenstein had been developing his new ‘later’ approach to
language, introducing consequently such terms as “language-games”, “family
resemblance”, “grammar”, “rules”, “forms of life”, making a transition from the logical point
of view on language to anthropological. Hence, in 1932 he denied the idea that
mathematics and logic are one building with logic as the foundation, that mathematics
derives from logic, and “Russell’s calculus is one calculus among the others. It is a bit of
mathematics”. (Wittgenstein, 2001, p. 13) In TBT Wittgenstein (2005) explained: “Through
Russell, but especially through Whitehead, there entered into philosophy a false
exactitude that is the worst enemy of real exactitude. At the bottom of this lies the
erroneous belief that a calculus could be the metamathematical foundation of
mathematics”. (p. 376e)
Logical atomism
In the first lecture of his lecture course16 entitled The Philosophy of Logical Atomism
(1918-1919), Russell (1918) wrote:
6 “The following articles are the lectures of a course of eight lectures delivered in London in the first months
of 1918, and are very largely concerned with explaining certain ideas which I learnt from my friend and
former pupil Ludwig Wittgenstein. I have had no opportunity of knowing his views since August, 1914, and
I do not even know whether he is alive or dead. He has therefore no responsibility for what is said in these
lectures beyond that of having originally supplied many of the theories contained in them.’ (Russell, 1928,
p. 495).
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
But Wittgenstein and I think it wrong to suppose with Russell that mathematics is
more complicated formal logic (tautologies) and I am trying to make definite the
vague idea Wittgenstein has of what it does consist of. If I am successful, I think it
will illuminate not only mathematics but physics also because a successful theory
of mathematics will help one to separate and give a true account of the a priori
element in physics. (This certainly exists for ‘this is not both red and blue’ is a
priori). (McGuinness, 2006, p. 21)
Wittgenstein in Zettel (1970) explained that the practical purpose of Russell’s Theory
of Types is, “Russell makes us realize that we must sometimes put restrictions on the
expression of generality in order to avoid having consequences drawn from it” (p. 120e).
In the notes of Wittgenstein’s (Wittgenstein & Moore, 2016) lectures recorded by Moore
we can find the following: “This explains what’s wrong with Russell’s theory of types: a
theory of types is a grammar, and must not mention meanings of words”. (p. 30) Since
about the end of 1929, Wittgenstein had been developing his new ‘later’ approach to
language, introducing consequently such terms as “language-games”, “family
resemblance”, “grammar”, “rules”, “forms of life”, making a transition from the logical point
of view on language to anthropological. Hence, in 1932 he denied the idea that
mathematics and logic are one building with logic as the foundation, that mathematics
derives from logic, and “Russell’s calculus is one calculus among the others. It is a bit of
mathematics”. (Wittgenstein, 2001, p. 13) In TBT Wittgenstein (2005) explained: “Through
Russell, but especially through Whitehead, there entered into philosophy a false
exactitude that is the worst enemy of real exactitude. At the bottom of this lies the
erroneous belief that a calculus could be the metamathematical foundation of
mathematics”. (p. 376e)
Logical atomism
In the first lecture of his lecture course16 entitled The Philosophy of Logical Atomism
(1918-1919), Russell (1918) wrote:
6 “The following articles are the lectures of a course of eight lectures delivered in London in the first months
of 1918, and are very largely concerned with explaining certain ideas which I learnt from my friend and
former pupil Ludwig Wittgenstein. I have had no opportunity of knowing his views since August, 1914, and
I do not even know whether he is alive or dead. He has therefore no responsibility for what is said in these
lectures beyond that of having originally supplied many of the theories contained in them.’ (Russell, 1928,
p. 495).
Natalia Tomashpolskaia 26
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
The kind of philosophy that I wish to advocate, which I call Logical Atomism, is one
which has forced itself upon me in the course of thinking about the philosophy of
mathematics, although I should find it hard to say exactly how far there is a definite
logical connection between the two. (p. 495)
“When I say that my logic is atomistic,” Russell continued, “I mean that I share the
common-sense belief that there are many separate things; I do not regard the apparent
multiplicity of the world as consisting merely in phases and unreal divisions of a single
indivisible Reality”. (p. 496) The concept is called logical atomism because the ‘atoms’,
according to Russell, that he wished “to arrive at as the sort of last residue in analysis are
logical atoms and not physical atoms.” (p. 496) This is the last given to which logical
analysis arrives, i.e., the elements that are no longer decomposable by logical analysis.
From Russell's point of view, ‘physical objects,’ ‘physical events,’ ‘matter,’ ‘space,’
‘consciousness,’ and ‘subject’ are all logical constructions built from ‘logical atoms,’ and
logical connectives according to the rules of logic. Therefore, they are decomposable by
logical analysis. What are ‘logical atoms?’ As we can see, Russell defines them by
pointing to their place in the procedure of logical analysis. How is a logical analysis
conducted? Russell defines it as a transition from something unclear, indefinite, or
imprecise (vagueness and inaccuracy are not commonly realised due to the habitual
expression) to clear precise and definite concepts. Russell considers as clear, precise,
and definite the concepts whose connection with the signified is clear and
understandable, so that there can be no misunderstanding about their meaning and
whether what they signify exists.
Russell proposes to proceed as a self-evident assumption that there are facts in
the world and that we form judgements about these facts and express them in sentences.
A fact is something that can be expressed by a sentence. It can also be said that a fact
is what makes a sentence true or false. The facts themselves are neither true nor false.
Logic distinguishes between private (‘Some flowers are red’) and general (‘All men are
mortal’) sentences, as well as positive (‘Man is a rational animal’) and negative (‘Socrates
is not Plato’s father’). Accordingly, Russell also classifies facts, they also turn out to be
particular and general, positive, and negative. Ergo, Russell describes reality through the
prism of logical concepts so that reality reflects the accepted method of logical analysis.
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
The kind of philosophy that I wish to advocate, which I call Logical Atomism, is one
which has forced itself upon me in the course of thinking about the philosophy of
mathematics, although I should find it hard to say exactly how far there is a definite
logical connection between the two. (p. 495)
“When I say that my logic is atomistic,” Russell continued, “I mean that I share the
common-sense belief that there are many separate things; I do not regard the apparent
multiplicity of the world as consisting merely in phases and unreal divisions of a single
indivisible Reality”. (p. 496) The concept is called logical atomism because the ‘atoms’,
according to Russell, that he wished “to arrive at as the sort of last residue in analysis are
logical atoms and not physical atoms.” (p. 496) This is the last given to which logical
analysis arrives, i.e., the elements that are no longer decomposable by logical analysis.
From Russell's point of view, ‘physical objects,’ ‘physical events,’ ‘matter,’ ‘space,’
‘consciousness,’ and ‘subject’ are all logical constructions built from ‘logical atoms,’ and
logical connectives according to the rules of logic. Therefore, they are decomposable by
logical analysis. What are ‘logical atoms?’ As we can see, Russell defines them by
pointing to their place in the procedure of logical analysis. How is a logical analysis
conducted? Russell defines it as a transition from something unclear, indefinite, or
imprecise (vagueness and inaccuracy are not commonly realised due to the habitual
expression) to clear precise and definite concepts. Russell considers as clear, precise,
and definite the concepts whose connection with the signified is clear and
understandable, so that there can be no misunderstanding about their meaning and
whether what they signify exists.
Russell proposes to proceed as a self-evident assumption that there are facts in
the world and that we form judgements about these facts and express them in sentences.
A fact is something that can be expressed by a sentence. It can also be said that a fact
is what makes a sentence true or false. The facts themselves are neither true nor false.
Logic distinguishes between private (‘Some flowers are red’) and general (‘All men are
mortal’) sentences, as well as positive (‘Man is a rational animal’) and negative (‘Socrates
is not Plato’s father’). Accordingly, Russell also classifies facts, they also turn out to be
particular and general, positive, and negative. Ergo, Russell describes reality through the
prism of logical concepts so that reality reflects the accepted method of logical analysis.
27 Bertrand Russell y Ludwig Wittenstein
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
The grammatical category of sentences is distinguished by the property that they can be
true or false. Thus, Russell argues, they cannot be considered as names, as Frege did.
Sentences are not names of facts, for if we recognized true sentences as names of facts,
then what would false sentences be called?
It is very important to realise such things, for instance, as that propositions are not
names for facts. It is quite obvious as soon as it is pointed out to you, but as a
matter of fact I never had realised it until it was pointed out to me by a former pupil
of mine, Wittgenstein. It is perfectly evident as soon as you think of it, that a
proposition is not a name for a fact, from the mere circumstance that there are two
propositions corresponding to each fact. (Russell, 1918, p. 507)
Russell assigns the central position to the category of the sentence and raises the
question of its understanding. A sentence is a complex symbol made up of other, simpler
symbols.
A proposition is just a symbol. It is a complex symbol in the sense that it has parts
which are also symbols, a symbol may be defined as complex when it has parts
that are symbols. In a sentence containing several words, the several words are
each symbol, and the sentence composing them is therefore a complex symbol in
that sense. (Russell, 1918, p. 507)
A sentence is understandable only if the simple symbols that form it are
understandable. In general, as Russell notes, symbols must be studied so as not to
confuse the properties of symbols and the properties of the things they denote. Because
of this confusion, all sorts of philosophical problems associated with ‘existence’ arise. Do
numbers, properties exist? Is there a set of all sets? A symbol, Russell explains, is all that
matters. Different types of symbols relate differently to what they signify. The value of a
complex symbol is determined by the values of its constituent simple ones (a symbol is
simple if its parts are not themselves a symbol).
There are different kinds of symbols, different kinds of relation between symbol
and what is symbolized, and very important fallacies arise from not realizing this.
The sort of contradictions about which I shall be speaking in connection with types
in a later lecture all arise from mistakes in symbolism, from putting one sort of
symbol in the place where another sort of symbol ought to be. (Russell, 1918, p.
508)
Speaking about symbolism, Russell explained,
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
The grammatical category of sentences is distinguished by the property that they can be
true or false. Thus, Russell argues, they cannot be considered as names, as Frege did.
Sentences are not names of facts, for if we recognized true sentences as names of facts,
then what would false sentences be called?
It is very important to realise such things, for instance, as that propositions are not
names for facts. It is quite obvious as soon as it is pointed out to you, but as a
matter of fact I never had realised it until it was pointed out to me by a former pupil
of mine, Wittgenstein. It is perfectly evident as soon as you think of it, that a
proposition is not a name for a fact, from the mere circumstance that there are two
propositions corresponding to each fact. (Russell, 1918, p. 507)
Russell assigns the central position to the category of the sentence and raises the
question of its understanding. A sentence is a complex symbol made up of other, simpler
symbols.
A proposition is just a symbol. It is a complex symbol in the sense that it has parts
which are also symbols, a symbol may be defined as complex when it has parts
that are symbols. In a sentence containing several words, the several words are
each symbol, and the sentence composing them is therefore a complex symbol in
that sense. (Russell, 1918, p. 507)
A sentence is understandable only if the simple symbols that form it are
understandable. In general, as Russell notes, symbols must be studied so as not to
confuse the properties of symbols and the properties of the things they denote. Because
of this confusion, all sorts of philosophical problems associated with ‘existence’ arise. Do
numbers, properties exist? Is there a set of all sets? A symbol, Russell explains, is all that
matters. Different types of symbols relate differently to what they signify. The value of a
complex symbol is determined by the values of its constituent simple ones (a symbol is
simple if its parts are not themselves a symbol).
There are different kinds of symbols, different kinds of relation between symbol
and what is symbolized, and very important fallacies arise from not realizing this.
The sort of contradictions about which I shall be speaking in connection with types
in a later lecture all arise from mistakes in symbolism, from putting one sort of
symbol in the place where another sort of symbol ought to be. (Russell, 1918, p.
508)
Speaking about symbolism, Russell explained,
Natalia Tomashpolskaia 28
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
I am using it in a sense to include all language of every sort and kind, so that every
word is a symbol, and every sentence, and so forth. When I speak of a symbol, I
simply mean something that ‘means’ something else, and as to what I mean by
‘meaning’ I am not prepared to tell you. (p. 508)
What is the meaning of a simple symbol? How can one understand it?
I think that the notion of meaning is always more or less psychological, and that it
is not possible to get a pure logical theory of meaning, nor therefore of symbolism.
I think that it is of the very essence of the explanation of what you mean by a
symbol to take account of such things as knowing, of cognitive relations, and
probably also of association. The theory of symbolism and the use of symbolism
is not a thing that can be explained in pure logic without taking account of the
various cognitive relations that you may have to things. (p. 508)
Russell answers that we can understand the meaning only through direct acquaintance
with the object denoted by this symbol. By direct acquaintance, he means the presence
of a given object in the subject's sensory experience of object symbols, each of which
corresponds to a component of the complex. Russell gave an illustration of what he
meant,
For instance, the word ‘Socrates,’ you will say, means a certain man; the word
‘mortal’ means a certain quality; and the sentence ‘Socrates is mortal’ means a
certain fact. But these three sorts of meaning are entirely distinct, and you will get
into the most hopeless contradictions if you think the word ‘meaning’ has the same
meaning in each of these three cases. It is very important not to suppose that there
is just one thing which is meant by ‘meaning,’ and that therefore there is just one
sort of relation of the symbol to what is symbolized. A name would be a proper
symbol to use for a person; a sentence (or a proposition) is the proper symbol for
a fact. (Russell, 1918, p. 509)
The concept of logical atomism is both logical and metaphysical at the same time.
As a logician, Russell considers the structure of an ideal language; as a metaphysician,
he claims that reality has the same structure. In the past metaphysical doctrines had often
based their general idea of the structure of reality on some scientific discipline. Thus, the
Pythagoreans asserted that reality has a mathematical essence, and used the language
of mathematics to describe it. In the 18th-19th century, Newtonian mechanics was applied
as a model for describing and explaining reality. Nowadays, evolutionary biology, systems
theory, or computer science often become the basis of philosophical reasoning about the
general nature of reality. For Russell, as we can see, logic played this role. He believed
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
I am using it in a sense to include all language of every sort and kind, so that every
word is a symbol, and every sentence, and so forth. When I speak of a symbol, I
simply mean something that ‘means’ something else, and as to what I mean by
‘meaning’ I am not prepared to tell you. (p. 508)
What is the meaning of a simple symbol? How can one understand it?
I think that the notion of meaning is always more or less psychological, and that it
is not possible to get a pure logical theory of meaning, nor therefore of symbolism.
I think that it is of the very essence of the explanation of what you mean by a
symbol to take account of such things as knowing, of cognitive relations, and
probably also of association. The theory of symbolism and the use of symbolism
is not a thing that can be explained in pure logic without taking account of the
various cognitive relations that you may have to things. (p. 508)
Russell answers that we can understand the meaning only through direct acquaintance
with the object denoted by this symbol. By direct acquaintance, he means the presence
of a given object in the subject's sensory experience of object symbols, each of which
corresponds to a component of the complex. Russell gave an illustration of what he
meant,
For instance, the word ‘Socrates,’ you will say, means a certain man; the word
‘mortal’ means a certain quality; and the sentence ‘Socrates is mortal’ means a
certain fact. But these three sorts of meaning are entirely distinct, and you will get
into the most hopeless contradictions if you think the word ‘meaning’ has the same
meaning in each of these three cases. It is very important not to suppose that there
is just one thing which is meant by ‘meaning,’ and that therefore there is just one
sort of relation of the symbol to what is symbolized. A name would be a proper
symbol to use for a person; a sentence (or a proposition) is the proper symbol for
a fact. (Russell, 1918, p. 509)
The concept of logical atomism is both logical and metaphysical at the same time.
As a logician, Russell considers the structure of an ideal language; as a metaphysician,
he claims that reality has the same structure. In the past metaphysical doctrines had often
based their general idea of the structure of reality on some scientific discipline. Thus, the
Pythagoreans asserted that reality has a mathematical essence, and used the language
of mathematics to describe it. In the 18th-19th century, Newtonian mechanics was applied
as a model for describing and explaining reality. Nowadays, evolutionary biology, systems
theory, or computer science often become the basis of philosophical reasoning about the
general nature of reality. For Russell, as we can see, logic played this role. He believed
29 Bertrand Russell y Ludwig Wittenstein
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
that the largest metaphysical systems, e.g., the systems of Spinoza, Leibniz, Hegel, and
Bradley, are based precisely on the logical views of their authors and essentially depend
on the fact that in traditional logic the sentence was assigned a subject-predicate
structure. Corresponding to such logic, metaphysics describes the world as a single
substance and its attributes. Therefore, Russell consciously undertook the construction
of new metaphysics corresponding to the new logic developed by G. Frege, G. Peano, A.
Whitehead, and himself.
One of the main features of this metaphysics is the assumption of various and
independent ‘simple objects’ (Russell calls them particulars). What are these ‘simple
objects?’ In what sense are they simple? These objects are independent, which means
that there is no causal relationship between them. These are not the objects of physics.
Physical objects and physical laws, according to Russell, are logical constructions. They
can be analysed. The analysis ends when it comes to simple symbols and, accordingly,
to simple objects. The latter can only be named, they cannot be described. I suppose
Russell was referring to ‘sense data.’ Here he followed the tradition of British empiricism.
This is also indicated by Russell's distinction between two kinds of knowledge, that can
help to obtain knowledge about simple objects and about complexes - knowledge by
direct acquaintance and knowledge by description. The method of logical analysis itself
was specific to Russell's concept of logical atomism. It is based on the fact that the naming
expression is replaced by a description. With this, we get rid of the naming expression
and from the problem of the existence of what is denoted by this expression. This is
Russell's approach to many problems in the philosophy of mathematics. Instead of
arguing whether there are (exist), and if they do exist, therefore in what sense, numbers,
sets, and other mathematical objects; Russell constructs definitions that replace them—
descriptions of known properties and relationships. Then, in all sentences in which there
are expressions for numbers and sets, they are replaced by the corresponding
descriptions. In metaphysical disputes, Russell says, phrases such as ‘God exists,’
‘Subject exists,’ and so on are common. Problems of existence are typical for
metaphysical disputes. There is a tendency to declare everything that is denoted by some
noun, numbers, sets, properties, relations, Pegasus, the ‘Golden Mountain’, a round
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
that the largest metaphysical systems, e.g., the systems of Spinoza, Leibniz, Hegel, and
Bradley, are based precisely on the logical views of their authors and essentially depend
on the fact that in traditional logic the sentence was assigned a subject-predicate
structure. Corresponding to such logic, metaphysics describes the world as a single
substance and its attributes. Therefore, Russell consciously undertook the construction
of new metaphysics corresponding to the new logic developed by G. Frege, G. Peano, A.
Whitehead, and himself.
One of the main features of this metaphysics is the assumption of various and
independent ‘simple objects’ (Russell calls them particulars). What are these ‘simple
objects?’ In what sense are they simple? These objects are independent, which means
that there is no causal relationship between them. These are not the objects of physics.
Physical objects and physical laws, according to Russell, are logical constructions. They
can be analysed. The analysis ends when it comes to simple symbols and, accordingly,
to simple objects. The latter can only be named, they cannot be described. I suppose
Russell was referring to ‘sense data.’ Here he followed the tradition of British empiricism.
This is also indicated by Russell's distinction between two kinds of knowledge, that can
help to obtain knowledge about simple objects and about complexes - knowledge by
direct acquaintance and knowledge by description. The method of logical analysis itself
was specific to Russell's concept of logical atomism. It is based on the fact that the naming
expression is replaced by a description. With this, we get rid of the naming expression
and from the problem of the existence of what is denoted by this expression. This is
Russell's approach to many problems in the philosophy of mathematics. Instead of
arguing whether there are (exist), and if they do exist, therefore in what sense, numbers,
sets, and other mathematical objects; Russell constructs definitions that replace them—
descriptions of known properties and relationships. Then, in all sentences in which there
are expressions for numbers and sets, they are replaced by the corresponding
descriptions. In metaphysical disputes, Russell says, phrases such as ‘God exists,’
‘Subject exists,’ and so on are common. Problems of existence are typical for
metaphysical disputes. There is a tendency to declare everything that is denoted by some
noun, numbers, sets, properties, relations, Pegasus, the ‘Golden Mountain’, a round
Natalia Tomashpolskaia 30
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
square, etc., as existing. To avoid this, one should subject phrases that assert existence
or the non-existence of something, to logical analysis. If we consider the sentence
“Pegasus never existed,” we understand its meaning. For the understanding of a
sentence, an understanding of the simple names included in it is required, but we cannot
understand the meaning of the name ‘Pegasus’ precisely because Pegasus never
existed, and we do not know what it is. The solution to this difficulty lies in the fact that
“Pegasus” is not a constituent of this proposal, as the analysis should show. The fact is
that “Pegasus” is not a name, but a description - a propositional function, “Horse (x) and
Winged (x).” Therefore, the sentence “Pegasus never existed,” as a result of Russell's
analysis, becomes the sentence, “There has never been an x such that the Horse (x) and
the Winged (x) and x is the only object that is both the Horse and the Winged.” Here, as
we see, the word “Pegasus” is missed, and therefore there is no reason to raise the
question of the existence of Pegasus, real or ideal. But why does Russell believe that
such an analysis is legitimate? Because, as he explains, the sentence must consist of
constituents that uniquely correspond to the constituents of the corresponding fact.
However, in many sentences, some parts do not correlate with the constituents of the
fact. Thus, in the phrase “Walter Scott is the author of Waverley,” the phrase “the author
of Waverley” is not a constituent of the sentence, because in real facts there is no
corresponding constituent. There is only one real person - Walter Scott. And the
combination ‘the author of Waverley’ is a description, and it should be eliminated so as
not to create the impression that it is a matter of establishing the existence of two persons
where there is only one person. Russell considered his method of eliminating descriptions
to be an effective tool for solving a wide variety of philosophical problems, for instance,
for criticising philosophical theories that abuse the concept of the absolute or invent
various ‘kinds’ and ‘modes’ of existence.
Critique of Russell’s ‘logical atomism’ by early Wittgenstein
The main statements:
First, Wittgenstein was not satisfied with Russell's rationale for the procedure of logical
analysis, which connects logical analysis with the empiricist theory of knowledge.
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
square, etc., as existing. To avoid this, one should subject phrases that assert existence
or the non-existence of something, to logical analysis. If we consider the sentence
“Pegasus never existed,” we understand its meaning. For the understanding of a
sentence, an understanding of the simple names included in it is required, but we cannot
understand the meaning of the name ‘Pegasus’ precisely because Pegasus never
existed, and we do not know what it is. The solution to this difficulty lies in the fact that
“Pegasus” is not a constituent of this proposal, as the analysis should show. The fact is
that “Pegasus” is not a name, but a description - a propositional function, “Horse (x) and
Winged (x).” Therefore, the sentence “Pegasus never existed,” as a result of Russell's
analysis, becomes the sentence, “There has never been an x such that the Horse (x) and
the Winged (x) and x is the only object that is both the Horse and the Winged.” Here, as
we see, the word “Pegasus” is missed, and therefore there is no reason to raise the
question of the existence of Pegasus, real or ideal. But why does Russell believe that
such an analysis is legitimate? Because, as he explains, the sentence must consist of
constituents that uniquely correspond to the constituents of the corresponding fact.
However, in many sentences, some parts do not correlate with the constituents of the
fact. Thus, in the phrase “Walter Scott is the author of Waverley,” the phrase “the author
of Waverley” is not a constituent of the sentence, because in real facts there is no
corresponding constituent. There is only one real person - Walter Scott. And the
combination ‘the author of Waverley’ is a description, and it should be eliminated so as
not to create the impression that it is a matter of establishing the existence of two persons
where there is only one person. Russell considered his method of eliminating descriptions
to be an effective tool for solving a wide variety of philosophical problems, for instance,
for criticising philosophical theories that abuse the concept of the absolute or invent
various ‘kinds’ and ‘modes’ of existence.
Critique of Russell’s ‘logical atomism’ by early Wittgenstein
The main statements:
First, Wittgenstein was not satisfied with Russell's rationale for the procedure of logical
analysis, which connects logical analysis with the empiricist theory of knowledge.
31 Bertrand Russell y Ludwig Wittenstein
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
Wittgenstein is concerned with showing the justification and necessity of logical analysis,
but he tries to achieve this in quite different ways.
Second, it is important for Wittgenstein to grasp the true meaning of the analytic method.
It is not enough for him that this method allows one to reveal and eliminate the confusion
that existed earlier in someone's philosophical concepts, i.e., the eternal questions of the
meaning of life, of good and evil, of death and immortality. He felt the need to relate the
method developed by him and Russell to these questions and understand its significance
and its possibilities against their background.
Third, Wittgenstein considered it necessary to make a much more rigid and consistent
separation of logical and factual reasoning than Russell did. It is obvious to him that those
logical truths cannot be discovered by examining some existing circumstances. The
question of the nature and status of logic must be defined more correctly than was the
case in Russell's reasoning.
Fourth, Wittgenstein in his Tractatus resolved several logical difficulties and special
questions concerning the foundations of mathematics.
Critique of Russell’s ‘logical atomism’ by middle and later Wittgenstein
In his lectures on philosophy from 1932-33, Wittgenstein (2001) was talking that Russell
and he expected to find the first elements (or individuals), and thus the possible atomic
propositions by logical analysis. Russell thought that the result of the final analysis would
be the subject-predicate proposition (2-term relations). But this was wrong, according to
Wittgenstein, Russell took logical analysis as it was like the chemical (scientific) analysis.
And the fault of both Russell and Wittgenstein was that they did not give any examples of
atomic propositions or of individuals. They both in different ways pushed the question of
examples aside. Also, atomic propositions should not contain ‘and’, ‘or’, etc.
Russell and I both expected to find the first elements, or “individuals”, and thus the
possible atomic propositions, by logical analysis. Russell thought that subject-
predicate propositions, and 2-term relations, for example, would be result of a final
analysis. This exhibits a wrong idea of logical analysis: logical analysis is taken as
being like chemical analysis. And we were at fault for giving no examples of atomic
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
Wittgenstein is concerned with showing the justification and necessity of logical analysis,
but he tries to achieve this in quite different ways.
Second, it is important for Wittgenstein to grasp the true meaning of the analytic method.
It is not enough for him that this method allows one to reveal and eliminate the confusion
that existed earlier in someone's philosophical concepts, i.e., the eternal questions of the
meaning of life, of good and evil, of death and immortality. He felt the need to relate the
method developed by him and Russell to these questions and understand its significance
and its possibilities against their background.
Third, Wittgenstein considered it necessary to make a much more rigid and consistent
separation of logical and factual reasoning than Russell did. It is obvious to him that those
logical truths cannot be discovered by examining some existing circumstances. The
question of the nature and status of logic must be defined more correctly than was the
case in Russell's reasoning.
Fourth, Wittgenstein in his Tractatus resolved several logical difficulties and special
questions concerning the foundations of mathematics.
Critique of Russell’s ‘logical atomism’ by middle and later Wittgenstein
In his lectures on philosophy from 1932-33, Wittgenstein (2001) was talking that Russell
and he expected to find the first elements (or individuals), and thus the possible atomic
propositions by logical analysis. Russell thought that the result of the final analysis would
be the subject-predicate proposition (2-term relations). But this was wrong, according to
Wittgenstein, Russell took logical analysis as it was like the chemical (scientific) analysis.
And the fault of both Russell and Wittgenstein was that they did not give any examples of
atomic propositions or of individuals. They both in different ways pushed the question of
examples aside. Also, atomic propositions should not contain ‘and’, ‘or’, etc.
Russell and I both expected to find the first elements, or “individuals”, and thus the
possible atomic propositions, by logical analysis. Russell thought that subject-
predicate propositions, and 2-term relations, for example, would be result of a final
analysis. This exhibits a wrong idea of logical analysis: logical analysis is taken as
being like chemical analysis. And we were at fault for giving no examples of atomic
Natalia Tomashpolskaia 32
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
propositions or of individuals. We both in different ways pushed the question of
examples aside. […]
Atomic propositions are not the result of an analysis which has yet to be made. We
can talk of atomic propositions if we mean those which on their face do not contain
“and”, “or”, etc., or those which in accordance with methods of analysis laid down
do not contain these. There are no hidden atomic propositions. (Wittgenstein,
2001, p. 11)
Wittgenstein continued that with the means of the concept of language-games, he wanted
to show the vague cases in which we use such words as ‘language’, ‘proposition’,
‘sentence’. “There are many things, such as orders, which may or may not be call
propositions; and not only one game can be called language.” Moreover, “Language-
games are a clue to the understanding of logic”. (p. 12) Wittgenstein said, “what we call
logic plays a different role from that which Russell and Frege supposed”. (p. 13) That
means:
When Frege tried to develop mathematics from logic he thought that calculus of
logic was the calculus, so that what followed from it would be correct mathematics.
Mathematics and logic were one building, with logic the foundation. This I deny;
Russell’s calculus is one calculus among others. (p. 13).
Moreover, Wittgenstein (1970) criticised both Russell and Frege arguing that “they
take concepts as, as it were, properties of things. But it is very unnatural to take the words
man, tree, treatise, circle, as properties of a substrate”. (p. 122e) Wittgenstein criticised
his contemporaries for the misleading use of calculus trying to apply it to the problems of
language and logic. “A calculus can’t be true or false; nor more or less fundamental (as
Russell and Frege believed of logical calculus: it is merely a bit of mathematics). Tarski
has added a new calculus; & made a mistake as to how it can be used”. (Wittgenstein &
Moore, 2016, p. 31) For instance, Martin Heidegger, the other prominent philosopher of
language of the 20th century, agreed that it is erroneous to consider language as calculus,
moreover as well as later Wittgenstein, he criticised the approach of logicians to find the
foundation of language in logic. Furthermore, both later Wittgenstein and Heidegger
realised that this artificial placing of language in the frames of logic leads to tautologies.
According to Heidegger (2001), “The understanding that is schooled in logic, thinking of
everything in terms of calculation and hence usually overbearing, calls this proposition an
empty tautology”. (p. 188) To conclude, for Wittgenstein (2005) calculating is an activity
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
propositions or of individuals. We both in different ways pushed the question of
examples aside. […]
Atomic propositions are not the result of an analysis which has yet to be made. We
can talk of atomic propositions if we mean those which on their face do not contain
“and”, “or”, etc., or those which in accordance with methods of analysis laid down
do not contain these. There are no hidden atomic propositions. (Wittgenstein,
2001, p. 11)
Wittgenstein continued that with the means of the concept of language-games, he wanted
to show the vague cases in which we use such words as ‘language’, ‘proposition’,
‘sentence’. “There are many things, such as orders, which may or may not be call
propositions; and not only one game can be called language.” Moreover, “Language-
games are a clue to the understanding of logic”. (p. 12) Wittgenstein said, “what we call
logic plays a different role from that which Russell and Frege supposed”. (p. 13) That
means:
When Frege tried to develop mathematics from logic he thought that calculus of
logic was the calculus, so that what followed from it would be correct mathematics.
Mathematics and logic were one building, with logic the foundation. This I deny;
Russell’s calculus is one calculus among others. (p. 13).
Moreover, Wittgenstein (1970) criticised both Russell and Frege arguing that “they
take concepts as, as it were, properties of things. But it is very unnatural to take the words
man, tree, treatise, circle, as properties of a substrate”. (p. 122e) Wittgenstein criticised
his contemporaries for the misleading use of calculus trying to apply it to the problems of
language and logic. “A calculus can’t be true or false; nor more or less fundamental (as
Russell and Frege believed of logical calculus: it is merely a bit of mathematics). Tarski
has added a new calculus; & made a mistake as to how it can be used”. (Wittgenstein &
Moore, 2016, p. 31) For instance, Martin Heidegger, the other prominent philosopher of
language of the 20th century, agreed that it is erroneous to consider language as calculus,
moreover as well as later Wittgenstein, he criticised the approach of logicians to find the
foundation of language in logic. Furthermore, both later Wittgenstein and Heidegger
realised that this artificial placing of language in the frames of logic leads to tautologies.
According to Heidegger (2001), “The understanding that is schooled in logic, thinking of
everything in terms of calculation and hence usually overbearing, calls this proposition an
empty tautology”. (p. 188) To conclude, for Wittgenstein (2005) calculating is an activity
33 Bertrand Russell y Ludwig Wittenstein
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
that differs from all the others, “especially as concerns its reason” (p. 181e). The
calculation process consists of acts, each of which is an individual act of thought. In
language, we meet another state of affairs, as well as the other relationship between
language and thought. In general, Wittgenstein (2005) says about his later work: “Our
task is not to improve our language, to make it more exact, or possibly even to try to
replace it with an ‘ideally exact’ one. We have absolutely no concept of such a language”.
(p. 200e)
Conclusion: Basic statements of Wittgenstein’s critique of Russell’s
ideas
To conclude, I will list the fundamental statements of Wittgenstein’s critique of
Russell and Frege as well as his own earlier ideas.
1) “Impression that logic is not a thing within our control”; (Wittgenstein, 2001, p. 99)
2) “Logicians make up an ideal language to which our normal language only
approximate”; (p. 99)
3) “Logic describes the use of language in a vacuum”; (p. 99)
4) “Logical Concepts are Pseudo-concepts”; (Wittgenstein, 2016, p. 24)
5) “Logicians have had an obsession that the life of a proposition is the copula ‘is’”,
however, not every proposition can be reduced to subject-copula-adjective form
(subject-predicate); (Wittgenstein, 2001, p. 100)
6) “We have created an enormously complicated language for our use”, it cannot be
reduced to simplifications, otherwise, we get errors and erroneous understanding
of the whole phenomenon of language; (p. 101)
7) A language in general is a conglomerate including special languages (the
languages of chemistry, meteorology, physics, etc.) consisting of a “mixture of
descriptions, hypotheses, questions, orders, etc., but any list we made of this
would be entirely inadequate”; (p. 102)
8) “Russell & Frege translated ordinary language into a symbolism”; (Wittgenstein,
2016, p. 222; emphasis in the original)
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
that differs from all the others, “especially as concerns its reason” (p. 181e). The
calculation process consists of acts, each of which is an individual act of thought. In
language, we meet another state of affairs, as well as the other relationship between
language and thought. In general, Wittgenstein (2005) says about his later work: “Our
task is not to improve our language, to make it more exact, or possibly even to try to
replace it with an ‘ideally exact’ one. We have absolutely no concept of such a language”.
(p. 200e)
Conclusion: Basic statements of Wittgenstein’s critique of Russell’s
ideas
To conclude, I will list the fundamental statements of Wittgenstein’s critique of
Russell and Frege as well as his own earlier ideas.
1) “Impression that logic is not a thing within our control”; (Wittgenstein, 2001, p. 99)
2) “Logicians make up an ideal language to which our normal language only
approximate”; (p. 99)
3) “Logic describes the use of language in a vacuum”; (p. 99)
4) “Logical Concepts are Pseudo-concepts”; (Wittgenstein, 2016, p. 24)
5) “Logicians have had an obsession that the life of a proposition is the copula ‘is’”,
however, not every proposition can be reduced to subject-copula-adjective form
(subject-predicate); (Wittgenstein, 2001, p. 100)
6) “We have created an enormously complicated language for our use”, it cannot be
reduced to simplifications, otherwise, we get errors and erroneous understanding
of the whole phenomenon of language; (p. 101)
7) A language in general is a conglomerate including special languages (the
languages of chemistry, meteorology, physics, etc.) consisting of a “mixture of
descriptions, hypotheses, questions, orders, etc., but any list we made of this
would be entirely inadequate”; (p. 102)
8) “Russell & Frege translated ordinary language into a symbolism”; (Wittgenstein,
2016, p. 222; emphasis in the original)
Natalia Tomashpolskaia 34
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
9) “96. Russell and Frege construe a concept as a sort of property of a thing. But it is
very unnatural to construe the words ‘man’, ‘tree, treatise’, ‘circle’ as properties of
a substratum”. (Wittgenstein, 1998, p.120)
Analítica (3), oct. 2023 – sept. 2024, ISSN – L 2805 – 1815
9) “96. Russell and Frege construe a concept as a sort of property of a thing. But it is
very unnatural to construe the words ‘man’, ‘tree, treatise’, ‘circle’ as properties of
a substratum”. (Wittgenstein, 1998, p.120)
35 Bertrand Russell y Ludwig Wittenstein
Analítica (3), oct. 2023 Sept. 2024, ISSN – L 2805 – 1815
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