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Bertrand Russell’s Life
and Legacy
Edited by
Peter Stone
Trinity College Dublin
Authors
Nancy C. Doubleday
McMaster University
Tim Madigan
St. John Fisher College
Nikolay Milkov
University of Paderborn
Eileen O’Mara Walsh
Independent Scholar
Alan Schwerin
Monmouth University
Peter Stone
Tim
Trinity College Dublin
Chad Trainer
Bertrand Russell Society
Ádám Tamás Tuboly
Hungarian Academy of Sciences
Raymond Aaron Younis
Australian Catholic University
Vernon Series in Philosophy
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Tim Madigan tmadigan@sjfc.edu
Copyright © 2017 Vernon Press, an imprint of Vernon Art and Science Inc, on
behalf of the author.
All rights reserved. No part of this publication may be reproduced, stored in a
retrieval system, or transmitted in any form or by any means, electronic,
mechanical, photocopying, recording, or otherwise, without the prior
permission of Vernon Art and Science Inc.
www.vernonpress.com
Tim
In the Americas:
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Product and company names mentioned in this work are the trademarks of
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responsible for any loss or damage caused or alleged to be caused directly or
indirectly by the information contained in it.
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Tim
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Table of Contents
Foreword
ix
I.
xi
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Editor´s Introduction
Chapter 1
Russell the Man
1
An Affair Remembered: Bertrand Russell
and Joan Follwell, 1927-1929
3
Eileen O’Mara Walsh
Chapter 2
Philosophical Biography Reconsidered
21
Peter Stone
II.
Chapter 3
Russell’s Philosophical World
43
The Limits and Basis of Logical Tolerance:
Carnap’s Combination of Russell and
Wittgenstein
45
Ádám Tamás Tuboly
Chapter 4
Edmund Husserl and Bertrand Russell,
1905-1918: The Not-So-Odd Couple
73
Nikolay Milkov
Is Russell's Conclusion about the Table
Coherent?
Tim
Chapter 5
97
Alan Schwerin
III.
Chapter 6
Russell, Religion, and Spirituality
127
“Waking Up” to Bertrand Russell’s
Anticipation of Sam Harris’ “Spirituality”
without Religion
129
Chad Trainer
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Raymond Aaron Younis
IV.
Chapter 8
Peace, Protest, and Politics
Lord John Russell and Crimes against
Humanity: The Great Famine Tribunal
157
159
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Chapter 9
143
Russell on Religion and Science
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Chapter 7
Engaged Learning: Paths to Peace Praxis
through the Russell Archives
171
Nancy C. Doubleday
187
Index
191
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About the Contributors
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The Limits and Basis of Logical
Tolerance: Carnap’s Combination of
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Russell and Wittgenstein
Ádám Tamás Tuboly1
The aim of this paper is to consider the context of, and possible
influences on, Rudolf Carnap’s Principle of Tolerance (PoT). This
principle could be approached from very different angles—either by
considering it from the viewpoint of logic and saying something
about its technical aspect or by considering its importance for
Carnap’s (meta)philosophy. I shall take, however, a different
approach and say something about its history.
One can acknowledge the important influence of Hans Hahn, Karl
Menger and Otto Neurath (the left wing of the Vienna Circle), along
with Moritz Schlick and Friedrich Waismann (the right wing of the
Vienna Circle), and try to place the PoT in the context of Carnap’s
immediate allies and opponents (Uebel 2009). But, as I claim, one
could locate it in a broader context, namely in Bertrand Russell and
Ludwig Wittgenstein’s philosophy of logic.
Tim
It is well-known that Russell introduced certain practical elements
into the considerations of logic (and the justifications of axioms).
But to obtain Carnap’s PoT, we have to extend the boundaries of
Russell’s version of freedom. Carnap did this by relying on
Wittgenstein’s idea that logic is devoid of empirical content. Since
logic is tautological (which Russell denied at various periods), we
1
I am indebted to the Carnap Archives at Pittsburgh (Rudolf Carnap Papers,
1905-1970, ASP.1974.01, Special Collections Department, University of
Pittsburgh) for permission to quote the archive materials. All rights
reserved. I cite their materials as follows: ASP RC XX-YY-ZZ, where XX is
the box number, YY the folder number, and ZZ the item number. All
translations of the German archive materials are mine. I am also
indebted to Richard Creath, Anssi Korhonen and Anthony Dardis for
their helpful comments.
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have the sort of freedom needed for the PoT. Hence Carnap’s
writings about logic and philosophy in the 1930s could be seen and
reconstructed as a synthesis (intended or unintended) or special
combination of Russell’s inductive/practical considerations on logic
and Wittgenstein’s idea of an empty logic.
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It is not my aim, of course, to state that this reading fills all the
gaps in our understanding of the PoT, or manifests itself as an
exclusive interpretation; there is much more to be said about the
principle. One could, for example, review the contribution and
influence of Tarski, Gödel, the metamathematical approach of
Hilbert, and the conventionalism of Poincaré. My thesis forms only
a necessary constituent on the road to the PoT and not a sufficient
one.
The PoT was first presented officially in Carnap’s Logical Syntax of
Language (original German in 1934, English translation in 1937) and
it says that “everyone is free to build up his own logic and language
as she wishes.” There is no fundamentally right and absolute logical
system or linguistic framework. And thus the aim of philosophy (or
better, the logic of science [Wissenschaftslogik]) is not to construct
one final logic and language, but to investigate the linguistic
foundations of scientific theories.
Tim
The paper is organized as follows. Section 1, prompted by Nikolay
Milkov’s recent remarks, considers the possible impact and
influence of Frege and Russell/Wittgenstein in and on the Vienna
Circle. As we will see, both Russell and Wittgenstein played a more
important role in the Circle than Frege. For this reason, sections 2
and 3 discuss the main points and concerns of Russell and
Wittgenstein regarding the nature of logic. In section 4, I introduce
Carnap’s PoT and consider its significance and immediate context.
Finally, section 5 connects all the dots about Carnap’s possible
synthesis of Russell and Wittgenstein.
1. In the Vienna Circle: Frege or Russell?
There is (or at least was) a usual narrative about early analytic
philosophy which assigns Frege a central position in its history. As
the grandfather of analytic philosophy, Frege developed modern
formal logic; he demonstrated the significance of logic in the
analysis of language and philosophical practice. One cannot
imagine a textbook about analytic philosophy, logic, or the
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The Limits and Basis of Logical Tolerance
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philosophy of language which does not start with the works and
ideas of Frege.
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It is usually thought that this narrative could also be upheld about
logical empiricism and the Vienna Circle; i.e., Frege was the
intellectual precursor of the Circle, the man who made logic ready
for them so that they could go on to eliminate metaphysics, to
analyze science, and so on. Recently, however, Nikolay Milkov has
suggested that
[one could say] that the philosophers of the Vienna Circle,
excepting Carnap, scarcely ever referred to Frege. This point,
however, only suggests that Frege’s influence on them came
through some indirect channel. Our guess is that this was
Wittgenstein’s Tractatus—so that following the Tractatus,
Logical Positivists accepted two leading ideas of Frege’s,
which they occasionally refer to as the “new logic” (Milkov
2003, p. 353).
In the next few pages, I will provide examples from the history of
the Circle which show that the direct influence of Frege on the
Circle was indeed low. The members of the Circle referred to Frege
quite rarely, and when they did, Frege’s name was just one element
in a longer list. As we will see, one should name Russell (and after
1925, Wittgenstein) if one wishes to reconstruct the logical (and
philosophical) foreground of logical empiricism and partly even of
Carnap.
Tim
Though Victor Kraft (1925, p. 65) discussed the nature of logic,
mathematics, and geometry in his Die Grundformen der
wissenschaftlichen Methode, he referred to Frege’s lesser-known
“Über die Grundlagen der Geometrie” only once regarding the selfevidence of axioms. Neither did Kraft pay much attention to Frege
in his later writings: in his book from 1947 (Mathematik, Logik und
Erfahrung), he did not consider Frege at all, while in his
historiography of the Vienna Circle (1950, pp. 59, 75) he mentioned
Frege’s name (only) twice without citing his works, while
Wittgenstein and Russell were consistently in the foreground.
Hans Hahn played an interesting role in the story of the Vienna
Circle. He taught logic in a department of mathematics; thus, he
was always up to date regarding the theoretical and historical
importance of “the new logic.” Hahn indeed utilized his knowledge
and institutional bearings since “[he] directed the interest of the
Circle toward logic” (Menger 1980, x). Hahn, however, focused his
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attention, not on the works of Frege, but on Russell and Whitehead’s
Principia Mathematica. Karl Menger recalled Hahn’s course as
follows:
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[Hahn] offered a lecture on the algebra of logic in the fall and
winter of 1922; and during the academic year 1924-25 he
devoted a seminar…to Russell and Whitehead’s Principia
Mathematica. There was a large attendance, and the
participants reported on the various chapters of the
book…Together with Schlick’s courses on the theory of
knowledge and on philosophy of science, Hahn’s seminar
created the background and the basis for the development of
the Vienna Circle (Menger 1994, p. 30).
In the 1980 preface to the selected philosophical works of Hahn,
Menger (1980, pp. x-xi) recalled the significance of the events in an
even more emphatic manner: “This seminar had a very large
audience and was of great influence not only on the development of
many Viennese students of mathematics and philosophy but also
on the trend of the discussions in the Circle.”
The mathematical and technical writings of Hahn (1995; 1996) do
not contain any relevant or full-blooded reference to the works of
Frege. Neither do his selected philosophical works (1980). There is
only one reference to Frege in his “Superfluous Entities, or Occam’s
Razor” ([1930] 1980a, p. 15) but Hahn put Frege next to Russell as
just another scholar who contributed to the logical constitution of
2
numbers.
Tim
Hahn’s case seemingly supports Milkov’s position. Hahn did not
cite or discuss Frege, taught the Principia Mathematica for years,
and in his later works focused only on Wittgenstein’s Tractatus (see
e.g., Hahn [1933] 1987). But even if Frege oozed into the Circle via
Wittgenstein (through Hahn), it was only at a relatively late
moment, since according to Menger (1980, p. xviii, n. 4), “[c]ontrary
to what has sometimes been written about Hahn’s seminars,
Wittgenstein’s name had, certainly up to that time, never been
mentioned in them.”
2
In an earlier review, when Hahn wrote about the development of, and need
for, a more precise logic, he did not consider Frege, and while Russell
and Whitehead’s magnum opus is mentioned as a positive example, he
claims that it is too complex for mathematicians to start their work with
it. See Hahn ([1919] 1980, pp. 53-54).
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The Limits and Basis of Logical Tolerance
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It would be important to note that Otto Neurath (1930, pp. 312313), in his historical remarks for the first issue of Erkenntnis (which
was an abbreviated version of the Circle’s official manifesto),
mentioned the name of Frege only twice as part of a broader list,
and did not consider it to be of utmost importance. One could
object that Neurath is not known for his work in logic or for his
competence in that area. But given his historical interest in the
topic, and the fact that he wrote papers about logic with his second
wife (Olga Hahn-Neurath, the sister of Hans Hahn), he certainly
could have known about Frege (see Neurath and Hahn 1909a,
1909b, 1910).
Though during the 1910s and 1920s Schlick was working on the
philosophy of nature (Naturphilosophie) and epistemology, in his
Allgemeine Erkenntnislehre [General Theory of Knowledge] from
1918 (second edition 1925) he dealt with the nature and
connections of thinking [Denkprobleme]. He connected the
problem of classical logic with the Aristotelian syllogism, writing
with great enthusiasm:
Modern logic (anticipated by Leibniz) is in the process of
creating a much more serviceable symbolism than the one
fashioned by Aristotle. However, in the discussion that
follows, we shall base ourselves on the latter, because it is the
one that is most familiar and because in my opinion it still
provides a means of presenting all logical relationships, and
in particular the interconnections of judgements found in
syllogistic inference (emphasis in original; Schlick [1925]
1974, pp. 102-103).
Tim
Though this remark is admittedly astonishing given the logical
empiricists’ characteristic dismissal of the “old logic,” Schlick
([1925] 1974, p. 107) went even further and claimed that “[t]he
Aristotelian theory of inference needs no modification or extension
in order to be applicable to modern science.”
One could say that perhaps Schlick was not fully aware of the
achievements of the new logic in 1918, but given his up-to-date
general scientific knowledge (note that he was the first to give an
account of the philosophical consequences of Einstein’s theory of
relativity), this seems somewhat implausible. On the other hand,
while the second quotation given above was already in the first
edition of Schlick’s book, the first quotation, which also shows a
preference for the old logic, appeared only in the second edition,
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from the time when Schlick started to organize the regular meetings
of the Vienna Circle. Later, in his review of Carnap’s Aufbau, Schlick
(1929) interestingly suggested that Carnap’s most important
achievement was that he used the tools of the new logic to connect
the various special sciences. Schlick’s “turn” might be connected to
Hahn’s aforementioned seminar (Grattan-Guinness 200, p. 514) and
Carnap’s arrival in Vienna in 1925: in his 1927 review of Russell’s The
Problems of Philosophy, Schlick already conveyed a more
understanding attitude towards the importance of the new logic.
Schlick did not consider Frege’s role or possible influence: in the
first edition of Schlick’s book Frege is not even mentioned, and
Schlick connected the achievements of the new logic to Russell
(Schlick [1925] 1974, p. 107). He refers to Frege, however, once in the
second edition of his book with respect to mathematics ([1925]
1974, p. 356): “That all mathematical propositions can be deduced
from a small number of axioms has been conclusively
”
demonstrated by the recent work of Frege, Peano and others.
After the publication of his Allgemeine Erkenntnislehre’s second
3
edition, Schlick started to read the Tractatus at the Circle’s regular
meetings and to fall under the influence of Wittgenstein. Later he
propagated the Wittgensteinian view of the practice of linguistic
analysis. Thus, from the late 1920s, Schlick was known, alongside
Waismann, as the official defender of Wittgenstein.
The only genuine exception to this narrative—one that leaves little
room for Frege as compared to Russell and Wittgenstein—might be
4
Carnap, but he is quite hard to categorize. On the one hand, before
3
Tim
Schlick wrote to Carnap in 1925 (November 29) that “at our Thursday-Circle
we read in this semester Wittgenstein’s treatise from sentence-tosentence” (ASP RC 029-32-34). During the next spring Schlick told
Carnap that they did not finish Wittgenstein’s book, so they will
continue reading it for one more semester. See Schlick’s letter to Carnap
from March 7, 1926 (ASP RC 029-32-27). In response (March 13, 1926,
ASP RC 029-32-24), Carnap said that he would like to participate in the
discussion of Wittgenstein’s book.
4
One should also mention Karl Menger, who in his influential lecture “The
New Logic” discussed alongside Russell such authors as Peano, Peirce,
Schröder and Frege. See Menger (1937; originally 1933). It should be
mentioned also that Carnap recorded in his diary (January 26, 1925)
that when he talked with Menger (presumably in one of their first
discussions) about Brouwer and Russell, Menger indicated that he “did
not like [Russell’s] logic” (ASP RC 025-72-04).
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The Limits and Basis of Logical Tolerance
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the First World War, Carnap attended Frege’s seminars on logic and
mathematics at the University of Jena; thus, he knew of Frege’s work
and achievements at first hand. He also regularly referred to Frege
from the time of his doctoral dissertation (Der Raum, published in
1922 in Kant-Studien) and he was sort of an authoritative person in
the Circle regarding Frege. In a letter from September 11, 1932, for
instance, Gödel (2003, pp. 346-348) asked Carnap whether Frege
published anything about Russell’s paradox after the publication of
the second volume of his Basic Laws of Arithmetic. Interestingly,
though, in the discussions of the Circle, according to Carnap’s
diaries, he did not lecture about Frege’s ideas but instead presented
Russell’s theory of numbers (November 25, 1926. ASP RC 025-725
05).
Carnap’s Logical Syntax of Language also has an ambiguous
relationship with the ideas of Frege (cf. Friedman [1988] 1999). The
philosophy of mathematics in Syntax embraces the ideas of
intuitionism (Carnap’s Language I was a constructivist-intuitionist
language), the formalism of Hilbert, as well as the logicism of Frege
and Russell-Whitehead. Thus, Frege was not at the center of the
Syntax project. This should come as no surprise. After all, we find
the following remark in Carnap’s student notes from Frege’s 1913
seminar entitled “Begriffsschrift II”:
Some people think that the symbols are what arithmetic is
about. But that doesn’t work in the end. One contradicts
oneself continually. Instead, the symbols are just tools for
inquiry, not what the inquiry is about; just as the microscope
is a tool for botanical inquiry, not what the inquiry is about
(emphasis in original; Carnap 2004, p. 133).
Tim
In the light of this remark, Frege would surely oppose Carnap’s
project, for the latter’s metalogical ideas in the Syntax are simply
about the signs and language of logic and mathematics in a way
that abstracts from the extra-logical referents.
On the other hand, even though Carnap referred to Frege in the
early 1920s and 1930s, he did not embrace the key ideas of Frege,
5
It should be also mentioned that later Carnap defended Russell’s approach
to identity against Hahn. See his diary entry from May 19, 1927 (ASP RC
025-72-06). The definition of identity was a regular theme of the Circle
in the context of Wittgenstein (Tractatus, 5.533), and Carnap argued
against his conception of the identity-sign in his Abriss der Logistik
(1929, §7).
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with respect, for example, to logic. Clinton Tolley (2016) argued that
from a logical point of view Russell offered much more of an ideal to
Carnap in the Aufbau. Though Quine’s oversimplified narrative (in
“Two Dogmas” and “Epistemology Naturalized”) about the
Russellian lines and aims of the Aufbau is considered to be outdated
by most scholars (see, however, Pincock 2002), Carnap did indeed
choose as his motto for the Aufbau ([1928] 2005, p. 5) a quotation
from Russell (1914, p. 155): “The supreme maxim in scientific
philosophizing is this: Wherever possible, logical constructions are
to be substituted for inferred entities.”
Carnap also sent his book to Russell with a letter, claiming that:
I believe [myself ] to have made here a step towards the goal
that you also bear in mind: clarification of epistemological
problems (and the removal of metaphysical problems) with
the aid that the new logic, particularly through your own
works, provides. I would like already here to indicate two
points on which I had to depart from your view. These points
of difference do not rest on differences in basic attitude,
which appears to me thoroughly in agreement. The
differences arise rather just because I have attempted to
carry out your basic view in a more consistent way than has
happened before. I believe I am here “more Russellian than
Russell” (quoted in Pincock 2007, p. 114; for the original
6
letter see ASP RC 102-68-24).
Tim
We know from Carnap’s diaries that when he met Russell later
(October 10, 1934), the latter was quite enthusiastic about the
Aufbau: “[Russell] said that he followed my earlier works with
interest, especially the Aufbau, but he did not read the Syntax yet
properly. I said that the ‘Aufbau’ is out-of-date” (ASP RC 025-75-12).
Later in his A History of Western Philosophy, Russell ([1945] 2004, p.
874) mentioned only the Syntax of Carnap when he dealt with the
ideas of “The Philosophy of Logical Analysis.”
In actuality, Frege became a major source for Carnap only in the
1940s, when he was dealing with the question of modality. This
involved the publication in 1947 of his ground-breaking work
Meaning and Necessity. In that book, alongside Alonzo Church’s
intensional approach (based on the notion of sense and denotation)
6
For the details of the connection between Carnap’s Aufbau and Russell, see
Carus (2007, ch. 6).
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The Limits and Basis of Logical Tolerance
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Carnap became the first to introduce Frege’s philosophy and logic
into mainstream philosophy. But in 1947, already more than ten
years had passed since the formulation of the PoT and Carnap’s
emigration to the United States. (The Vienna Circle also disbanded
in the late 1930s after the murder of Moritz Schlick.)
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All of this seems to strengthen Milkov’s claim that Frege did not
have much direct and significant influence on the Vienna Circle at
its peak. Rather, the texts and contextual information of the Circle
7
points toward Russell (and Wittgenstein).
2. Russell on the Nature of Logic
Russell is notorious for his regular (and sometimes fundamental)
changes in his philosophical development. These changes create
several intricate difficulties for any coherent and comprehensive
reconstruction of his ideas. Nevertheless, three important and
recurring ideas of his will be discussed here: (1) logic is the most
general and universal science; (2) there is a close connection
between logic and metaphysics; (3) logic is not free from intuition
and inductive-practical considerations. But first, we have to draw
out the context for his ideas.
According to Jean van Heijenoort ([1967] 1997), one might draw a
distinction with respect to the history of modern logic: there is a
8
universalist and a model-theoretic tradition. Heijenoort argued that
Frege, Russell, and Wittgenstein belong to the universalist tradition,
but the early Carnap might also be said to reside in this first camp.
Some passages of Carnap, however, indicate otherwise, and his
placement problem is still not settled (see, e.g., Loeb 2014; Schiemer
2013).
Tim
In his characterization of the universalist tradition, van Heijenoort
evoked a short passage from Frege:
I did not want to present an abstract logic with formulas, but
to give an expression to a content with written signs more
clearly and precisely than is possible with words. In fact, I did
not want to create a bare calculus ratiocinator but a lingua
7
Interestingly Neurath recognized the different paths of Frege and Russell
already in the early 1930s. See Neurath ([1933] 1987, p. 275, n. 2).
8
Hintikka ([1988] 1997) later generalized this narrative to any language.
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character[ist]ica in Leibniz’ sense… (Frege [1883] 1993, pp.
97-98).
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It is acknowledged that Frege’s Begriffsschrift is not just a mere
calculus, a mathematical device, but a language. Since this language
codifies the general laws of truth, all rational discourses have to take
place within it. This means van Heijenoort claims that there is no
place for a meta-perspective or a metalanguage in the universalist
tradition since every act of rational discourse is internal to it. For
that reason, logic is the “skeleton” (Korhonen 2013, p. 8) of all
languages which codifies rational and meaningful discourses.
Henry Sheffer pointed out in his review of Principia
Mathematica’s second edition that a certain fear of circularity is
detectable in the logicians’ practices:
Just as the proof of certain theories in metaphysics is made
difficult, if not hopeless, because of the “egocentric”
predicament, so the attempt to formulate the foundations of
logic is rendered arduous by a corresponding “logocentric”
predicament. In order to give an account of logic we must
presuppose and employ logic (emphasis in original; Sheffer
1926, pp. 227-228).
Whether Sheffer is right or not regarding the motivation lying
behind certain practices of logicians, it is true that neither Frege nor
Russell usually recognized the usefulness and necessity of a
metalanguage, or more generally, the possibility of a
metaperspective. There is no trace of it in Russell’s informal
Principles of Mathematics or any edition of the Principia
9
Mathematica.
Tim
It should be noted that Russell claimed in his notorious preface to
the English translation of Wittgenstein’s Tractatus that the hierarchy
of languages could solve some problems of the book:
These difficulties suggest to my mind some such possibility
as this: that every language has, as Mr. Wittgenstein says, a
structure concerning which, in the language, nothing can be
said, but that there may be another language dealing with
the structure of the first language, and having itself a new
9
Some scholars aim to revisit this view. See Landini (1998); Mares (2013);
Blanchette (2013); Korhonen (2012, 2013).
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The Limits and Basis of Logical Tolerance
an
structure, and that to this hierarchy of languages there may
be no limit (emphasis in original; Russell [1922] 1983, p. 23).
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Interestingly though, in his own formulations, Russell did not use
this idea in any consequent and direct manner. (At an earlier point,
Russell mentioned what seems to be a metaperspective when he
claimed that “we need true propositions about implication”
(emphasis in original; Russell [1913] 1973, p. 290), but he did not act
on this claim in any detail.) Peter Hylton formulated this point as
follows:
Logic, for Russell, is a systematization of reasoning in general,
of reasoning as such. If we have a correct systematization, it
will comprehend all correct principles of reasoning. Given
such a conception of logic there can be no external
perspective. Any reasoning will, simply in virtue of being
reasoning, fall within logic; any proposition that we might
wish to advance is subject to the rules of logic (emphasis
10
added; Hylton [1990] 1992, p. 203).
The other part of my reconstruction of Russell concerns the logic
world relation. I do not want to state that Russell was a logical realist
of some kind, but I certainly claim that he was committed to the
idea that logic and the world are closely connected. When Carnap
visited Russell in 1935 (at the end of September), he recorded in his
diary talking “with [Russell] about my conception of logic. He has
misgivings from the viewpoint of his realistic logic [realistischen
Logik]” (ASP RC 025-75-13). What was this “realistic logic” of
Russell?
Tim
Alberto Coffa, in his important The Semantic Tradition from Kant
to Carnap (1991, pp. 273-280), reconstructed a monolinguistic
project (pursued by Russell and the early Carnap), according to
which there isn’t any difference between the object and the
metalanguage—but more importantly, there is only one correct
object language. One language which describes in a right and true
10
It should be noted, however, that the implicit gist in Hylton’s quotation is
that if one obtains the correct systematization of reasoning in general,
then one cannot step outside of it and take the metasystematical
viewpoint. But if one is just after the correct systematization, then the
metasystematical perspective is essential to find out whether the given
systematization is the correct one or not. I am indebted to Anssi
Korhonen for calling my attention to this.
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manner either the world or the laws of thought (and in the case of
Frege, the laws of truth).
Russell periodically emphasized that logic is much more about the
world than about our cognitive capacities or the norms of our
thinking in themselves:
Ma
dig
The name “laws of thought” is also misleading, for what is
important is not the fact that we think in accordance with
these laws, but the fact that things behave in accordance
with them; in other words, the fact that when we think in
accordance with them we think truly (emphasis in original;
Russell 1912, p. 113).
Or, as he put it later (Russell 1912, p. 138), “The belief in the law of
contradiction is a belief about things, not only about thoughts…and
although belief in the law of contradiction is a thought, the law of
contradiction itself is not a thought, but a fact concerning the things
in the world.” In Russell’s highly oversimplified narrative (albeit a
narrative that reveals his inner perspective), the law of
contradiction had its origins in certain worldly experiences; actually
it was “discovered by generalizing from instances” which means that
“it is both an empirical and a logical premise” in any scientific
argumentation (Russell [1907] 1973, p. 274).
Tim
After all, for Russell, since the rules of logic seem to be also the
rules of the world and things within it, there must be a logic and a
language based on it, which is the ultimate one; here we find some
traces of the monolinguistic project. And actually Russell seems to
11
support the first part of this claim when he said in his Introduction
to Mathematical Philosophy (1919, p. 169) that “logic is concerned
with the real world just as truly as zoology, though with its more
abstract and general features.”
There were, of course, differences over time in Russell’s ideas
about the objects of logic (and mathematics). Earlier, in The
Principles of Mathematics (1903, p. vii), he argued that pure
mathematics does not deal with actual objects in the world but only
with “hypothetical objects having those general properties upon
which depends whatever deduction is being considered.”
Seemingly this is a weaker claim than the 1919 one, but actually in
11
The second part of it is confirmed by the universality and uniqueness of
his logic. About the various senses of universality in Russell’s early
philosophy see Korhonen (2013).
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an
1911 he already showed the signs, for example, of his later realism
regarding universals (documented in The Problems of Philosophy).
He indicated in a lecture that ([1913] 1973, p. 293) “[l]ogic and
mathematics forces us…to admit a kind of realism in the scholastic
sense, that is to say, to admit that there is a world of universals and
of truths which do not bear directly on such and such a particular
existence.” Taking logic and mathematics as such disciplines which
commit one to special ontological considerations, the connection
between logic and world is just contrary to the later views of
Wittgenstein and Carnap.
But Russell differed from these authors about the questions of
analyticity and tautologies too—and this takes us to my third point.
For Russell, logic was not without content. In his book on the
philosophy of Leibniz he even argued that
[a]s regards the meaning of analytic judgments, it will assist
us to have in our minds some of the instances which Leibniz
suggests. We shall find that these instances suffer from one or
other of two defects. Either the instances can be easily seen
to be not truly analytic—this is the case, for example, in
Arithmetic and Geometry—or they are tautologous, and so
not properly propositions at all (Russell 1900, §11).
Tim
Being analytical, mathematical and tautologous did not form one
group for Russell in 1900. If something is tautological, then it cannot
be a proper proposition. (And of course what is not a proposition
cannot be meaningful. I do not want to suggest, however, that
Russell had such a threefold distinction at that time as did later
Wittgenstein—namely, a distinction between meaningful,
meaningless, and senseless propositions.) Mathematics, for Russell
at that time, was not even analytical, though this changed for
Russell later when he started propagating his logicism. Anyways,
12
this idea had some interesting effects on Russell’s thinking.
12
It should be noted, though, that logic was synthetic rather than analytic in
The Principles of Mathematics (Russell 1903, §434). Later Russell
accepted the tautological character of logic (e.g. in Russell 1927, p. 171;
1931, p. 477), but admitted that “[f]or the moment, I do not know how
to define ‘tautology’” (Russell 1919, p. 205). As a result, it is not clear
whether the tautological logic is also without content and factually
empty or not in Russell’s writings from that time. I am indebted to Anssi
Korhonen for these remarks.
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Already in 1900, we found the idea that at the end of our
investigations we are faced with the problem of statements that
cannot be defined easily or at all. According to Russell,
Ma
dig
[d]efinition, as is evident, is only possible in respect of
complex ideas. It consists, broadly speaking, in the analysis
of complex ideas into their simple constituents. Since one
idea can only be defined by another, we should incur a
vicious circle if we did not admit some indefinable ideas
(Russell 1900, §11).
One has to account for the acceptance of these indefinable
elements. Russell distinguished two different ways for doing that.
First, when he discussed the methodology of philosophy, he was
always against the Bergsonian conception of intuition as a primary
source of knowledge (see, e.g., Russell [1917] 1949). But when he
considered the rules and axioms of logic he vigorously defended the
idea that
[t]heir truth is evident to us, and we employ them in
constructing demonstrations; but they themselves, or at least
some of them, are incapable of demonstration. All
arithmetic…can be deduced from the general principles of
logic, yet the simple propositions of arithmetic, such as “two
and two are four,” are just as self-evident as the principles of
logic (Russell 1912, p. 176).
Tim
Most of the rules and propositions of logic and mathematics are
thus self-evident and intuitively true. Given the fact that we have the
logical/mathematical knowledge, and “since all knowledge must be
either self-evident or deduced from self-evident knowledge”
(Russell [1913] 1973, p. 293), “self-evidence” oozed into the
characterization of logic. For Russell ([1906] 1973, p. 194), “[t]he
object is not to banish ‘intuition’, but to test and systematize its
employment.” However, Russell did not define or explore what is
involved in claiming the self-evidence or intuitiveness of logic and
mathematics. Though he did not provide any detailed answer to the
question of what is the base of the evidential character of logic, he
did provide some hints about the nature and role of obviousness
connected to self-evidence.
First of all, obviousness is not an absolute concept; whether a
certain axiom (or rule) is obvious is always a matter of degree (or
relative to a context and frame); as Russell ([1907] 1973, p. 273) said:
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“premises which are ultimate in one investigation may cease to be
so in another; that is, we may find logically simpler propositions
from which they can be deduced.” Secondly, we are not infallible
regarding the distribution of obviousness; it may easily happen that
what we regarded as obvious (“with the highest degree”) turns out to
be not obvious after all, or even false. Thirdly, “[a]ssuming the usual
laws of deduction, two obvious propositions of which one can be
deduced from the other both become more nearly certain than
either would be in isolation” (Russell [1907] 1973, p. 279).
Following these guidelines, added Russell, is not enough for the
pursuit of science. “[A]lthough intrinsic obviousness is the basis of
every science, it is never…the whole of our reason for believing any
one proposition of the science” (Russell [1907] 1973, p. 279). Or, as
he said earlier ([1906] 1973, p. 194), “[t]he ‘primitive propositions’
with which the deductions of logistic begin should, if possible, be
evident to intuition; but that it is not indispensable, nor is it, in any
case, the whole reason for their acceptance.”
The second way of justifying axioms and logical propositions
comes into play when these elements are either not self-evident or
in need of more motivation and justification beyond self-evidence
and obviousness. The motivation for this form of justification stems
from inductive-practical reasons. In Principia Mathematica, for
example, Russell (and Whitehead) claimed in the context of the
axiom of reducibility that
Tim
[t]he reason for accepting an axiom, as for accepting any
other proposition, is always largely inductive, namely that
many propositions which are nearly indubitable can be
deduced from it, and that no equally plausible way is known
by which these propositions could be true if the axiom were
false, and nothing which is probably false can be deduced
from it (Russell and Whitehead 1910, p. 62).
When we choose an axiom, we cannot do it simply because we are
able to derive it from more fundamental ones. But, as Russell said,
we can choose it according to its usefulness. If one knows that there
are certain propositions which seem to be or hold to be true in a
certain context, then she needs such axioms from which she can
derive those true statements. If there are seemingly equally good
possibilities and choices, then one has to check them for their
consequences: we have to know whether something false can be
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deduced from them or not. In logic and mathematics, “[t]he chief
difficulty throughout consists in reconciling the two aims of
avoiding the false and keeping what we cannot but think true”
(Russell [1907] 1973, p. 280).
This picture of the decision procedure for the selection of axioms
and logical rules, however, is highly similar to that employed in
other sciences:
Ma
dig
The method of logistic is fundamentally the same as that of
every other science. There is the same fallibility, the same
uncertainty, the same mixture of induction and deduction,
and the same necessity of appealing, in confirmation of
principles, to the diffused agreement of calculated results
13
with observation (Russell [1906] 1973, p. 194).
This seems to imply in a way the marriage of epistemology and
the idea of truth (which also recurred in the discussions of the
Vienna Circle before the mid-1930s) and Russell indeed seems to
suggest this:
Degrees of self-evidence are important in the theory of
knowledge, since, if propositions may…have some degree of
self-evidence without being true, it will not be necessary to
abandon all connexion between self-evidence and truth, but
merely to say that, where there is a conflict, the more selfevident proposition is to be retained and the less self-evident
rejected (Russell 1912, p. 184).
Tim
For Russell, therefore, there was a point regarding questions of
logic in which practical freedom came into the picture; this
freedom, however, was restrained by close adherence to logic and
the world. Though one could build one’s logic, at least partly, as one
wishes, the majority of the logic is still bound by some previouslydetermined nodes and considerations which are not apt for
revision.
13
Cf. Russell ([1907] 1973, p. 272), where he tries to show “the close analogy
between the methods of pure mathematics and the methods of the
sciences of observation.” Or a few pages later (ibid., p. 274), where he
writes, “the method in investigating the principles of mathematics is
really an inductive method, and is substantially the same as the method
of discovering general laws in any other science.”
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3. Wittgenstein on the Nature of Logic
Ma
dig
Though Wittgenstein is usually grouped together with Frege and
Russell, at some points he was against them and called their
approach the “old logic” (Tractatus 4.126; cf. Ricketts 1996). While
Russell said that logic is similar to the other sciences—with its
infallibility as well as its inductive and partly intuitive content—
Wittgenstein claimed, in a letter to Russell, that “[l]ogic must turn
14
out to be of a totally different kind than any other science.”
While Russell and Frege used to claim that logic is the most
general and universal science in the sense that its statements hold
for everything, Wittgenstein argued that “The mark of logical
propositions is not their general validity…An ungeneralized
proposition can be tautologous [i.e., logical] just as well as a
generalized one” (Tractatus 6.1231).
On the other hand, while Frege considered logic as the science
whose main object is truth, Wittgenstein was against any kind of
approach that signified truth values as objectivities: “One could e.g.
believe that the words ‘true’ and ‘false’ signify two properties among
other properties” (Tractatus 6.111), but in this case logic would be
similar to the natural sciences after all (as Russell thought), and this
is “a certain symptom of its being falsely understood” (Tractatus
6.111). (It should be mentioned, however, that according to Frege
logic was not about truth per se, but about the laws of truth.)
Tim
Since logic is of a different nature than the other sciences,
Wittgenstein argued that in the justification of logic one has to
abandon the notion of self-evidence and any type of
practical/pragmatic elements. “It is remarkable that so exact a
thinker as Frege should have appealed to the degree of self-evidence
15
as the criterion of a logical proposition” (Tractatus 6.1271).
Therefore he characterized logic in a wholly different way; although
Russell’s logic was contextual in a sense, Wittgenstein argued that
“[t]heories which make a proposition of logic appear substantial are
always false” (Tractatus 6.111). By contrast, in the Tractatus, “the
propositions of logic are tautologies” (Tractatus 6.1). By showing
14
Wittgenstein’s letter to Russell, June 22, 1912. In McGuinness ([1995] 2008,
p. 30).
15
The same is told about Russell too (Tractatus 5.4731): “Self-evidence,
which Russell talked about so much, can become dispensable in logic,
only because language itself prevents every logical mistake. – What
makes logic a priori is the impossibility of illogical thought.”
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that the propositions of logic are tautologies, hence devoid of
empirical content, Wittgenstein held that they say nothing: “all
propositions of logic say the same thing. That is nothing” (Tractatus
5.43). For Wittgenstein, it follows that we can also criticize the
logicist program; according to him, it would be hard to believe that
the infinite number of propositions of logic and mathematics
“should follow from half a dozen ‘primitive propositions’” (Tractatus
5.43).
Ma
dig
Though he did not consider in the Tractatus the axiom of choice,
Wittgenstein criticized the axioms of reducibility and infinity
heavily. He said that “[p]ropositions like Russell’s ‘axiom of
reducibility’ are not logical propositions, and this explains our
feeling that, if true, they can only be true by a happy chance”
(Tractatus 6.1232). Note that Russell argued that this proposition or
axiom should be regarded as logical due to pragmatic and inductive
reasons.
But even if we were to accept that these axioms are logical,
logicism would be still a failed approach for Wittgenstein because
while logic is tautological, mathematics is not: “The propositions of
mathematics are equations, and therefore pseudo-propositions”
(Tractatus 6.2). It would be an interesting historical project to show
how the Vienna Circle and others arrived at the idea that
mathematics and logic have the same nature—that neither of them
has empirical content, so both are tautologies.
Tim
Wittgenstein was against conventions in logic, though the
conventional character of logic later played an important role in the
Circle (and according to them, they get it from Wittgenstein). He
said that “in logic it is not we who express, by means of signs, what
we want, but in logic the nature of the essentially necessary signs
itself asserts” (Tractatus 6.124). Here we find again an important and
interesting transition: how the Circle invented the conventionallybased tautologies.
What is more important for now is Wittgenstein’s view of the
nature of logic. As a consequence of the picture theory, one cannot
talk about the language-world relation, i.e., about semantics. But
one cannot talk about language either, and here again surfaces the
logocentric predicament of Sheffer: in order to talk about language,
we have to presuppose language. Hence we cannot talk about logic
either; for Wittgenstein, “logic must take care of itself,” and logical
properties (e.g., being a tautology) can be shown but cannot be said:
“every tautology itself shows that it is a tautology” (Tractatus 6.127).
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The Limits and Basis of Logical Tolerance
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Therefore, one cannot develop further, change, or extend logic; it is
tied up with an isomorphic one-to-one relation to the world. Seen
this way, logic became a prerequisite of meaningfulness; it is
transcendental, as Wittgenstein said. It cannot be the subject of
rational discourse; logic marks the boundaries of meaningful
discourse. This is “Wittgenstein’s prison,” since “[t]he very nature of
language, in Wittgenstein’s view, prevented us from ever stepping
outside it” (Awodey and Carus 2009, pp. 88-89).
4. Carnap’s Principle of Tolerance
Carnap had a long and interesting way of reaching the principle of
tolerance. Some aspect of this principle can be found in his The
Logical Structure of the World ([1928] 2005), but he did not consider
there the nature of logic in detail. Neither did he do so in his lesserknown Abriss der Logistik (1929), which was a short textbook on
Russell and Whitehead’s Principia Mathematica (Carnap 1963, p.
14), with a particular focus on the application of the logistic
method. He even described his intentions in a letter to Schlick as “to
present the Logistic [Logistik] as such a method which could be used
16
in the various (non-logical) fields.”
During the end of the 1920s, Carnap was preparing two
manuscripts about logic which dealt with its nature
(Untersuchungen zur allgemeinen Axiomatik and Neue
Grundlegung), but neither of them contained any hint of the
principle of tolerance or of the metalogical approach which
17
characterized the later years of his work.
Tim
According to Carnap’s quite dramatic narrative, he gave up his
earlier projects on the 21st of January, 1931: after a sleepless night
he wrote down his ideas on “forty-four pages under the title
‘Attempt at a metalogic.’ These shorthand notes were the first
16
Carnap’s letter to Schlick, October 7, 1927. ASP RC 029-31-06 (emphasis in
the original typed version). It should be noted for reasons of historical
curiosity that Springer, the publisher of the Abriss, rejected Carnap’s
Logical Structure because of perceived financial risks. Though in the
1930s the Abriss was quite a success, nowadays it is less well-known
than the Logical Structure. See Grattan-Guinness (2000, p. 502).
17
The Untersuchungen was published posthumously as Carnap (2000), but
the Grundlegung could be found only as a manuscript in his Nachlass
as ASP RC 089-64-01 and ASP RC 089-64-02. About these projects see
Carus (2007, pp. 191-203).
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version of my book Logical Syntax of Language” (Carnap 1963, p.
18
54). Carnap started to lecture about the new “metalogic” at the
19
Circle’s discussion nights in the summer of 1931, but the PoT did
not surface in them.
Ma
dig
One hint of the principle can be found, however, in two articles
from 1932. In “Psychology in Physical Language” ([1932] 1959, p.
192), Carnap claimed that we are free to choose our methods in a
given investigation (“every method of inquiry is justified…we may
apply any method we choose”), for what actually matters are the
obtained consequences, whether the method is fruitful for a given
aim or not. In the other article, “On Protocol Sentences,” which was
Carnap’s own contribution to the famous protocol-sentence debate,
and which aimed to reconcile (or at least mediate between) Schlick
and Neurath’s opposed approaches, Carnap said that
[m]y opinion here is that this is a question, not of two
mutually inconsistent views, but rather of two different
methods for structuring the language of science both of which
are possible and legitimate…I now think that the different
answers do not contradict each other. They are to be
understood as suggestions for postulates; the task consists in
investigating the consequences of these various possible
postulations and in testing their practical utility (emphasis in
original; Carnap [1932] 1987, pp. 457-458).
Tim
Schlick and Neurath’s approaches are just two different
methods—based on different language forms—to consider the
protocol sentences, and we can (re)construct these language forms
as we wish. The statements of Schlick and Neurath cannot
contradict each other because they actually do not state anything;
they are simply proposals which could have such theoretical and
practical virtues as fruitfulness, simplicity, inner consistency, etc.,
but not truth or falseness.
The actual PoT was introduced into the discussion during the
summer of 1933 when Carnap admitted the following
considerations (or “main points” as he called them):
18
About the transition from the earlier logical writings to the Syntax-project
see Awodey and Carus (2007).
19
The records of Carnap’s lectures are preserved at the Pittsburgh Archive as
ASP RC 081-07-17, ASP RC 081-07-18, and ASP RC 081-07-19. For the
transcription of these lecture-notes see Stadler ([2001] 2015, pp. 107123).
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The Limits and Basis of Logical Tolerance
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(1) Our problems concern language.
(2) So one always has to specify: about which language one
talks?
(3) Do not consider what you already know, but make a
proposal [vorgeschlagene], one has total freedom [völlige
Freiheit] in that! (emphasis in original; ASP RC 110-07-22).
Ma
dig
Carnap upheld the idea that “philosophical” discourse is about
language throughout his entire career; he claimed in his “Testability
and Meaning” (1937, p. 3) that “[i]n the first place we have to notice
that this problem [the criterion of meaning] concerns the structure
of language. (In my opinion, this is true for all philosophical
20
questions…).” But in order to narrow down the range of our
inquiries, we have to specify which language concerns us, just as the
second point above states. But we could extend Carnap’s point by
making explicit his implicit idea, namely that we must decide in
which metalanguage we analyze our object language.
Languages are constituted by their logical core (by their logical
constants, formation and transformation rules as Carnap called
them), and logic is just tautological, without any empirical content.
As Carnap said:
Tim
(Meaningful) statements are divided into the following kinds.
First there are statements which are true solely by virtue of
their form (‘tautologies’ according to Wittgenstein…). They
say nothing about reality. The formulae of logic and
mathematics are of this kind. They are not themselves factual
statements, but serve for the transformation of such
statements. Secondly there are the negations of such
statements (‘contradictions’). They are self-contradictory,
hence false by virtue of their form. With respect to all other
statements the decision about truth or falsehood lies in the
protocol sentences. They are therefore (true or
false) empirical statements and belong to the domain of
empirical science (emphasis in original; Carnap [1932] 1959,
p. 76).
On account of these distinctions, the world, or better, how things
are arranged in the world, cannot constrain our logic and language
at first place: “The formal sciences do not have any objects at all”
20
See also Carnap’s letter to Neurath (July 24, 1939) where he stated that “I
always stressed that the logic of science is the analysis of language
[Wissenschaftslogik Sprachanalyse ist].” ASP RC 102-53-05.
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(emphasis in original; Carnap [1935] 1953, p. 128). Hence regarding
possible metalanguages—in which we pursue our theoretical
investigations—we have “total freedom,” and we construe them as
we want: “(‘Principle of Tolerance’ (Toleranzprinzip): In logical
questions there is no moral, no commands [Gebote] or prohibitions
[Verbote]” (ASP RC 110-07-22). Or as it was officially documented in
the Logical Syntax of Language:
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dig
It is not our business to set up prohibitions, but to arrive at
conventions…In logic there are no morals. Everyone is at
liberty to build up his own logic, i.e. his own form of
language, as he wishes. All that is required of him is that, if he
wishes to discuss it, he must state his methods clearly, and
give syntactical rules instead of philosophical arguments
(emphasis in original; Carnap [1934] 1937, §17).
Despite its name, the principle of tolerance is not a theoretical
principle, or any kind of thesis, since as such it would require
theoretical argumentation, but rather a philosophical stance, or
attitude, which was held and applied by Carnap throughout his
whole career. The PoT says that it is superfluous to talk about the
correct language since it lies in our power to formulate different
language forms, from which we can choose later with respect to our
practical needs and goals. According to Carnap’s own confession
([1934] 1937, p. xv) one of the main motivations behind PoT is the
recognition that if “we cast the ship of logic off from the terra firma
of the classical forms…we reach the boundless ocean of unlimited
possibilities.” These language forms are on a par regarding their
claim for legitimation and validity. None of them is the correct
21
one—they just serve different purposes.
Tim
So in a more general sense, Carnap claims that regarding the
questions of logic, mathematics and even philosophy, we are not
faced with such theories and statements that could be true/false or
right/wrong (for any of which we have to give a priori or theoretical
arguments), but instead we are dealing with practical decisions.
21
Due to the PoT, the truth of statements is also context-, or more precisely,
linguistic-frame-relative for Carnap (see Carnap 1950) and at this point
he seems to be in conflict with Russell, who claimed that “[i]f, finally, we
can arrive at a set of principles which recommend themselves to
intuition, and which show exactly how we formerly fell into error, we
may have a reasonable assurance that our new principles are at any rate
nearer the truth than our old ones” (emphasis added; Russell [1906]
1973, p. 195).
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an
Carnap’s reasoning, again, is that the rules and statements of logic
are without empirical content, and hence we have the right to
define them as we want. What matters is the fruitfulness of our
linguistic frameworks, and we have to test them against our aims
and goals. Firstly, one is required to give precisely one’s definitions
and rules, then one has to show the consequences that follow from
them, and if the results fit into our space of reasons, then we can
accept them. If the given framework comes with destructive or
inconvenient implications, then we give up either the framework or
our goals. It’s all about costs and benefits, about practical aims.
In the preface of Syntax ([1934] 1937, p. xiv) Carnap centered his
narrative around Russell: “Up to the present, there has been only a
very slight deviation, in a few points here and there, from the form
of language developed by Russell which has already become
classical.” So partly the aim of the PoT is to ensure a path on which
one could leave behind the logic of Russell and support all those
who would like to explore “the boundless ocean of unlimited
possibilities.” Interestingly, though, a year later Carnap recorded in
his diary the followings:
Discussion with Oppenheim and Hempel in the morning. I
explained [to them]: 2 ways to loosen [Auflockerung] the
Aristotelean class-sentences: 1) Russell’s theory of relations;
2) Reichenbach’s many valued logic. I think the first is
sufficient (ASP RC 025-75-13, April 27, 1935).
Tim
Loosening the classical logic of Aristotle is one thing; leaving
behind “the new logic” of Russell and entering the land of free
possibilities is another. It is still interesting that though it was
Russell (and not, for example, Frege) who opened up the gates of
the new logic for Carnap, the former never discovered the new land
entirely. So one could say that if we enter that gate and depart from
the “terra firma of classical forms,” we need to extend the
boundaries of Russellian logic.
5. The Carnapian Synthesis of Russell and
Wittgenstein
Let us recall what we saw in the earlier sections. In the case of
Russell, I argued that he accepted that there are certain pragmatic
and inductive elements in the justification of logic and
mathematics. According to him, there isn’t any final and ultimately
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Tim Madigan tmadigan@sjfc.edu
68
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an
right decision at these points (besides our goals and to-bepreserved true statements). These primitive elements in logic and
mathematics are not fixed, and so we have a certain freedom. But
this freedom is limited by the need to achieve our fixed goals and
aims; it is also restricted by certain epistemological ideas. And so in
order to get Carnap’s principle, we have to extend the boundaries of
Russell’s freedom.
Ma
dig
On the other hand, logic is without empirical content in the
Wittgensteinian framework: it is tautological but it is also
transcendental, and hence makes it possible to talk about the world
while at the same time prohibiting talk about logic and language. To
capture the one world we have to work with one language and logic.
So Wittgenstein’s prison does not allow moving freely between
alternatives. Wittgenstein also excluded from the domain of logic
any pragmatic and conventional moves. This means that we do not
have to extend the boundaries of freedom in Wittgenstein’s system;
we have to introduce freedom first.
I certainly do not want to make the strong thesis that Carnap
intentionally took Russell and Wittgenstein’s ideas of logic (and
language), fused the most sympathetic parts of them together, and
created the PoT. I do not want to exclude this possibility either; this
could be a topic worthy of further research. Nonetheless, I want to
make the weaker claim that Carnap’s PoT could be read or
reconstructed as a synthesis or combination of these approaches.
After all, Carnap was famous for his efforts to make syntheses and to
mediate between his allies.
Tim
Alternatively, if one would like to make an even weaker claim, one
could state that Russell and Wittgenstein offered different views on
the nature of logic (and language). Detaching these ideas from their
defenders, it could be seen as a highly plausible idea in the history of
logic and ideas that these views could be synthesized on a higher
level by someone. That “someone” turned out to be Carnap: he was
the one who united Wittgenstein’s idea of the emptiness of logic
with Russell’s idea of inductive-practical justification in the case of
logic. Since logic is empty, we can vary it as we wish and we can
justify it with some practical reasons, for “in logic there are no
morals.”
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Tim Madigan tmadigan@sjfc.edu
The Limits and Basis of Logical Tolerance
69
an
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