RTR*ND R*SS*LL ***
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THE PHILOSOPHY OF
MR. B*RTR*ND R*SS*LL
WITH AN APPENDIX OF LEADING
PASSAGES FROM CERTAIN OTHER WORKS
EDITED BY
PHILIP E. B. JOURDAIN
[Illustration]
LONDON: GEORGE ALLEN & UNWIN LTD.
RUSKIN HOUSE 40 MUSEUM STREET, W.C. 1
CHICAGO: THE OPEN COURT PUBLISHING CO.
_First published in 1918_
(_All rights reserved_)
EDITOR'S NOTE
When Mr. B*rtr*nd R*ss*ll, following the advice of Mr. W*ll**m J*m*s,
again "got into touch with reality" and in July 1911 was torn to pieces
by Anti-Suffragists, many of whom were political opponents of Mr.
R*ss*ll and held strong views on the Necessity of Protection of Trade
and person, a manuscript which was almost ready for the press was
fortunately saved from the flames on the occasion when a body of eager
champions of the Sacredness of Personal Property burnt the late Mr.
R*ss*ll's house. This manuscript, together with some further fragments
found in the late Mr. R*ss*ll's own interleaved copy of his _Prayer-Book
of Free Man's Worship_, which was fortunately rescued with a few of the
great author's other belongings, was first given to the world in the
_Monist_ for October 1911 and January 1916, and has here been arranged
and completed by some other hitherto undecipherable manuscripts. The
title of the above-mentioned _Prayer-Book_, it may perhaps be mentioned,
was apparently suggested to Mr. R*ss*ll by that of the Essay on
"The Free Man's Worship" in the _Philosophical Essays_ (London, 1910,
pp. 59-70[1]) of Mr. R*ss*ll's distinguished contemporary, Mr. Bertrand
Russell, from whom much of Mr. R*ss*ll's philosophy was derived. And,
indeed, the influence of Mr. Russell extended even beyond philosophical
views to arrangement and literary style. The method of arrangement of
the present work seems to have been borrowed from Mr. Russell's
_Philosophy of Leibniz_ of 1900; in the selection of subjects dealt
with, Mr. R*ss*ll seems to have been guided by Mr. Russell's _Principles
of Mathematics_ of 1903; while Mr. R*ss*ll's literary style fortunately
reminds us more of Mr. Russell's later clear and charming subtleties
than his earlier brilliant and no less subtle obscurities. But, on the
other hand, some important points of Mr. Russell's doctrine, which first
appeared in books published after Mr. R*ss*ll's death, were anticipated
in Mr. R*ss*ll's notes, and these anticipations, so interesting for
future historians of philosophy, have been provided by the editor with
references to the later works of Mr. Russell. All editorial notes are
enclosed in square brackets, to indicate that they were not written by
the late Mr. R*ss*ll.
At the present time we have come to take a calm view of the question so
much debated seven years ago as to the legitimacy of logical arguments
in political discussions. No longer, fortunately, can that intense
feeling be roused which then found expression in the famous cry,
"Justice--right or wrong," and which played such a large part in the
politics of that time. Thus it will not be out of place in this
unimpassioned record of some of the truths and errors in the world to
refer briefly to Mr. R*ss*ll's short and stormy career. Before he was
torn to pieces, he had been forbidden to lecture on philosophy or
mathematics by some well-intentioned advocates of freedom in speech who
thought that the cause of freedom might be endangered by allowing Mr.
R*ss*ll to speak freely on points of logic, on the grounds, apparently,
that logic is both harmful and unnecessary and might be applied to
politics unless strong measures were taken for its suppression. On much
the same grounds, his liberty was taken from him by those who remarked
that, if necessary, they would die in defence of the sacred principle of
liberty; and it was in prison that the greater part of the present work
was written. Shortly after his liberation, which, like all actions of
public bodies, was brought about by the combined honour and interests of
those in authority, occurred his lamentable death to which we have
referred above.
Mr. R*ss*ll maintained that the chief use of "implication" in politics
is to draw conclusions, which are thought to be true, and which are
consequently false, from identical propositions, and we can see these
views expressed in Chapters III and XIX of the present work. These
chapters were apparently written before the Government, in the spring
of 1910, arrived at the famous secret decision that only "certain
implications" are permitted in discussion. Naturally the secret decision
gave rise to much speculation among logicians as to which kinds of
implication were barred, and Mr. R*ss*ll and Mr. Bertrand Russell had
many arguments on the subject, which naturally could not be published at
the time. However, after Mr. R*ss*ll's death, successive prosecutions
which were made by the Government at last made it quite clear that the
opinion held by Mr. R*ss*ll was the correct one. There had been numerous
prosecutions of people who, from true but not identical premisses, had
deduced true conclusions, so that the possible legitimate forms of
"implication" were reduced. Further, the other doubtful cases were
cleared up in course of time by the prosecution of (1) members of the
Aristotelian Society for deducing true conclusions from false premisses;
(2) members of the _Mind_ Association for deducing false conclusions
from false premisses; and also by the attempted prosecution of an
eminent lady for deducing true conclusions from identities. Fortunately
this lady was able to defend herself successfully by pleading that one
eminent philosopher believed them to be true--which, of course, means
that the conclusions are false. Thus appeared the true nature of
legitimate political arguments.
FOOTNOTES:
[1] [This Essay is also reprinted in Mr. Russell's _Mysticism and
Logic_, London and New York, 1918, pp. 46-57.--ED.]
"Even a joke should have some meaning...."
(The Red Queen, _T. L. G._, p. 105).
CONTENTS
PAGE
EDITOR'S NOTE 3
ABBREVIATIONS 9
CHAPTER
I. THE INDEFINABLES OF LOGIC 11
II. OBJECTIVE VALIDITY OF THE "LAWS OF THOUGHT" 15
III. IDENTITY 16
IV. IDENTITY OF CLASSES 18
V. ETHICAL APPLICATIONS OF THE LAW OF IDENTITY 19
VI. THE LAW OF CONTRADICTION IN MODERN LOGIC 21
VII. SYMBOLISM AND MEANING 22
VIII. NOMINALISM 24
IX. AMBIGUITY AND SYMBOLIC LOGIC 26
X. LOGICAL ADDITION AND THE UTILITY OF SYMBOLISM 27
XI. CRITICISM 29
XII. HISTORICAL CRITICISM 30
XIII. IS THE MIND IN THE HEAD? 31
XIV. THE PRAGMATIST THEORY OF TRUTH 32
XV. ASSERTION 34
XVI. THE COMMUTATIVE LAW 35
XVII. UNIVERSAL AND PARTICULAR PROPOSITIONS 36
XVIII. DENIAL OF GENERALITY AND GENERALITY OF DENIAL 37
XIX. IMPLICATION 39
XX. DIGNITY 43
XXI. THE SYNTHETIC NATURE OF DEDUCTION 45
XXII. THE MORTALITY OF SOCRATES 48
XXIII. DENOTING 53
XXIV. THE 54
XXV. NON-ENTITY 56
XXVI. IS 58
XXVII. AND AND OR 59
XXVIII. THE CONVERSION OF RELATIONS 60
XXIX. PREVIOUS PHILOSOPHICAL THEORIES OF MATHEMATICS 61
XXX. FINITE AND INFINITE 63
XXXI. THE MATHEMATICAL ATTAINMENTS OF TRISTRAM SHANDY 64
XXXII. THE HARDSHIPS OF A MAN WITH AN UNLIMITED INCOME 66
XXXIII. THE RELATIONS OF MAGNITUDE OF CARDINAL NUMBERS 69
XXXIV. THE UNKNOWABLE 70
XXXV. MR. SPENCER, THE ATHANASIAN CREED, AND THE ARTICLES 73
XXXVI. THE HUMOUR OF MATHEMATICIANS 74
XXXVII. THE PARADOXES OF LOGIC 75
XXXVIII. MODERN LOGIC AND SOME PHILOSOPHICAL ARGUMENTS 79
XXXIX. THE HIERARCHY OF JOKES 81
XL. THE EVIDENCE OF GEOMETRICAL PROPOSITIONS 83
XLI. ABSOLUTE AND RELATIVE POSITION 84
XLII. LAUGHTER 86
XLIII. "GEDANKENEXPERIMENTE" AND EVOLUTIONARY ETHICS 88
APPENDIXES 89
ABBREVIATIONS
_A. A. W._ Lewis Carroll: _Alice's Adventures in Wonderland_, London,
1908. [This book was first published much earlier, but
this was the edition used by Mr. R*ss*ll. The same applies
to _H. S._ and _T. L. G._]
_A. C. P._ John Henry Blunt (ed. by): _The Annotated Book of Common
Prayer_, London, new edition, 1888.
_A. d. L._ Ernst Schroeder: _Vorlesungen ueber die Algebra der Logik,
Leipzig_, vol. i., 1890; vol. ii. (two parts), 1891 and
1905; vol. iii.: _Algebra und Logik der Relative_, 1895.
_E. N._ Richard Dedekind: _Essays on the Theory of Numbers_,
Chicago and London, 1901.
_E. L. L._ William Stanley Jevons: _Elementary Lessons in Logic,
Deductive and Inductive. With copious Questions and
Examples, and a Vocabulary of Logical Terms_, London,
24th ed., 1907 [first published in 1870].
_E. u. I._ Ernst Mach: _Erkenntnis und Irrtum: Skizzen zur
Psychologie der Forschung_, Leipzig, 1906.
_F. L._ Augustus De Morgan: _Formal Logic: or The Calculus of
Inference, Necessary and Probable_, London, 1847.
_Fm. L._ John Neville Keynes: _Studies and Exercises in Formal
Logic_, 4th ed., London, 1906.
_Gg._ Gottlob Frege: _Grundgesetze der Arithmetik
begriffschriftlich abgeleitet_, Jena, vol. i., 1893;
vol. ii., 1903.
_Gl._ Gottlob Frege: _Die Grundlagen der Arithmetik: eine
logisch-mathematische Untersuchung ueber den Begriff der
Zahl_, Breslau, 1884.
_G. u. E._ G. Heymans: _Die Gesetze und Elemente des
wisenschaftlichen Denkens_, Leiden, vol. i., 1890;
vol. ii., 1894.
_H. J._ _The Hibbert Journal: a Quarterly Review of Religion,
Theology and Philosophy_, London and New York.
_H. S._ Lewis Carroll: _The Hunting of the Snark: an Agony in
Eight Fits_, London, 1911.
_M._ _The Monist: a Quarterly Magazine Devoted to Science and
Philosophy_, Chicago and London.
_Md._ _Mind: a Quarterly Review of Psychology and Philosophy_,
London and New York.
_Pa. Ma._ Alfred North Whitehead and Bertrand Russell: _Principia
Mathematica_, vol. i., Cambridge, 1910. [Other volumes
were published in 1912 and 1913.]
_P. E._ Bertrand Russell: _Philosophical Essays_, London and New
York, 1910.
_Ph. L._ Bertrand Russell: _A Critical Exposition of the Philosophy
of Leibniz, with an Appendix of Leading Passages_,
Cambridge, 1900.
_P. M._ Bertrand Russell: _The Principles of Mathematics_,
vol. i., Cambridge, 1903.
_R. M. M._ _Revue de Metaphysique et de Morale_, Paris.
_S. B._ Lewis Carroll: _Sylvie and Bruno_, London, 1889.
_S. L._ John Venn: _Symbolic Logic_, London, 1881; 2nd ed., 1894.
_S. o. S._ William Stanley Jevons: _The Substitution of Similars, the
True Principle of Reasoning derived from a Modification of
Aristotle's Dictum_, London, 1869.
_T. L. G._ Lewis Carroll: _Through the Looking-Glass, and what Alice
found there_, London, 1911.
_Z. S._ Gottlob Frege: _Ueber die Zahlen des Herrn H. Schubert_,
Jena, 1899.
CHAPTER I
THE INDEFINABLES OF LOGIC
The view that the fundamental principles of logic consist solely of the
law of identity was held by Leibniz,[2] Drobisch, Uberweg,[3] and
Tweedledee. Tweedledee, it may be remembered,[4] remarked that certain
identities "are" logic. Now, there is some doubt as to whether he, like
Jevons,[5] understood "are" to mean what mathematicians mean by "=," or,
like Schroeder[6] and most logicians, to have the same meaning as the
relation of subsumption. The first alternative alone would justify our
contention; and we may, I think, conclude from an opposition to
authority that may have been indicated by Tweedledee's frequent use of
the word "contrariwise" that he did not follow the majority of
logicians, but held, like Jevons,[7] the mistaken[8] view that the
quantification of the predicate is relevant to symbolic logic.
It may be mentioned, by the way, that it is probable that
Humpty-Dumpty's "is" is the "is" of identity. In fact, it is not
unlikely that Humpty-Dumpty was a Hegelian; for, although his ability
for clear explanation may seem to militate against this, yet his
inability to understand mathematics,[9] together with his synthesis of a
cravat and a belt, which usually serve different purposes,[10] and his
proclivity towards riddles seem to make out a good case for those who
hold that he was in fact a Hegelian. Indeed, riddles are very closely
allied to puns, and it was upon a pun, consisting of the confusion of
the "is" of predication with the "is" of identity--so that, for example,
"Socrates" was identified with "mortal" and more generally the
particular with the universal--that Hegel's system of philosophy was
founded.[11] But the question of Humpty-Dumpty's philosophical opinions
must be left for final verification to the historians of philosophy:
here I am only concerned with an _a priori_ logical construction of what
his views might have been if they formed a consistent whole.[12]
If the principle of identity were indeed the sole principle of logic,
the principles of logic could hardly be said to be, as in fact they are,
a body of propositions whose consistency it is impossible to prove.[13]
This characteristic is important and one of the marks of the greatest
possible security. For example, while a great achievement of late years
has been to prove the consistency of the principles of arithmetic, a
science which is unreservedly accepted except by some empiricists,[14]
it can be proved formally that one foundation of arithmetic is
shattered.[15] It is true that, quite lately, it has been shown that
this conclusion may be avoided, and, by a re-moulding of logic, we can
draw instead the paradoxical conclusion that the opinions held by
common-sense for so many years are, in part, justified. But it is quite
certain that, with the principles of logic, no such proof of
consistency, and no such paradoxical result of further investigations is
to be feared.
Still, this re-moulding has had the result of bringing logic into a
fuller agreement with common-sense than might be expected. There were
only two alternatives: if we chose principles in accordance with
common-sense, we arrived at conclusions which shocked common-sense; by
starting with paradoxical principles, we arrived at ordinary
conclusions. Like the White Knight, we have dyed our whiskers an unusual
colour and then hidden them.[16]
The quaint name of "Laws of Thought," which is often applied to the
principles of Logic, has given rise to confusion in two ways: in the
first place, the "Laws," unlike other laws, cannot be broken, even in
thought; and, in the second place, people think that the "Laws" have
something to do with holding for the operations of their minds, just as
laws of nature hold for events in the world around us.[17] But that the
laws are not psychological laws follows from the facts that a thing may
be true even if nobody believes it, and something else may be false if
everybody believes it. Such, it may be remarked, is usually the case.
Perhaps the most frequent instance of the assumption that the laws of
logic are mental is the treatment of an identity as if its validity were
an affair of our permission. Some people suggest to others that they
should "let bygones be bygones." Another important piece of evidence
that the truth of propositions has nothing to do with mind is given by
the phrase "it is morally certain that such-and-such a proposition is
true." Now, in the first place, morality, curiously enough, seems to be
closely associated with mental acts: we have professorships and
lectureships of, and examinations in, "mental and moral philosophy." In
the second place, it is plain that a "morally certain" proposition is a
highly doubtful one. Thus it is as vain to expect any information about
our minds from a study of the "Laws of Thought" as it would be to expect
a description of a certain social event from Miss E. E. C. Jones's book
_An Introduction to General Logic_.
Fortunately, the principles or laws of Logic are not a matter of
philosophical discussion. Idealists like Tweedledum and Tweedledee, and
even practical idealists like the White Knight, explicitly accept laws
like the law of identity and the excluded middle.[18] In fact,
throughout all logic and mathematics, the existence of the human or any
other mind is totally irrelevant; mental processes are studied by means
of logic, but the subject-matter of logic does not presuppose mental
processes, and would be equally true if there were no mental processes.
It is true that, in that case, we should not know logic; but our
knowledge must not be confounded with the truths which we know.[19] An
apple is not confused with the eating of it except by savages,
idealists, and people who are too hungry to think.
FOOTNOTES:
[2] Russell, _Ph. L._, pp. 17, 19, 207-8.
[3] Schroeder, _A. d. L._, i. p. 4.
[4] See Appendix A. This Appendix also illustrates the importance
attached to the Principle of Identity by the Professor and Bruno.
[5] _S. o. S._, pp. 9-15.
[6] _A. d. L._, i. p. 132.
[7] Cf., besides the reference in the last note but one, _E. L. L._, pp.
183, 191. "Contrariwise," it may be remarked, is not a term used in
traditional logic.
[8] _S. L._, 1881, pp. 173-5, 324-5; 1894, pp. 194-6.
[9] Cf. Appendix C, and William Robertson Smith, "Hegel and the
Metaphysics of the Fluxional Calculus," _Trans. Roy. Soc., Edinb._, vol.
xxv., 1869, pp. 491-511.
[10] See Appendix B.
[11] [This is a remarkable anticipation of the note on pp. 39-40 of Mr.
Russell's book, published about three years after the death of Mr.
R*ss*ll, and entitled _Our Knowledge of the External World as a Field
for Scientific Method in Philosophy_, Chicago and London, 1914.--ED.]
[12] Cf. _Ph. L._, pp. v.-vi. 3.
[13] Cf. Pieri, _R. M. M._, March 1906, p. 199.
[14] As a type of these, Humpty-Dumpty, with his inability to admit
anything not empirically given and his lack of comprehension of pure
mathematics, may be taken (see Appendix C). In his (correct) thesis that
definitions are nominal, too, Humpty-Dumpty reminds one of J. S. Mill
(see Appendix D).
[15] See Frege, _Gg._, ii. p. 253.
[16] See Appendix E.
[17] See Frege, _Gg._, i. p. 15.
[18] See the above references and also Appendix F.
[19] Cf. B. Russell, _H. J._, July 1904, p. 812.