The emergence of Russell's logical construction of physical objects by Sajahan M iah
1. INTRODUCTION
IN THE PREFACEto Our Knowledge of the External World (1914), Rus sell states that
The central problem by which I have sought to illustrate method is the prob lem of the relation between the crude data of sense and the space, time, and matter of mathematical physics. I have been made aware of the importance of this problem by my friend and collaborator Dr. Whitehead, to whom are due almost all the differences between the views advocated here and those suggested in The Problems oj Philosophy [1912]. lowe to him the definition of points, the suggestion for the treatment of instants and "things," and the whole conception of the world of physics as a construction rather than an inference. I
This passage conveys several impressions: that Russell became a con struction'ist, for the first time, in Our Knowledge; that the construc tionist theory emerged directly out of The Problems of Philosophy; and that Whitehead deserves full credit for Russell's becoming a construc tionist. The received view accepts all of these impressions. In this paper, I dispute them all. My aim is to establish the following theses:
'Our Knowledge of the External World, 2nd ed. (London: Allen and Unwin, 1926), pp. 7-8.
11 a
13
of
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P.H.
table. there
infer, sense
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claims, see simple by
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In sense-data
rev.
sense-data.
the perception,
of
object,
objects
It possibility
principle
objects.
any
able
ed.
steps:
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arises sceptic
rejects
table, transcend
directly
physical
external".4 hypothesis from
brings
any claims based
are
physical
2nd
single
objects
physical
to
the
private
table.
we the but
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objects? is
that
and
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induction
interprets
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physical beyond", physical
physical
and bridge
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sense-data.
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problem
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Russell following
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see the simplicity
as and
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objects
the Selby-Bigge,
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sense-data
of
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at anything
which principle, the
beyond
sceptic only
to
independent soon
nothing are
189.
L.A.
construction sense-data
from
of
himself
on cannot
as or this p. and
us from with
reasoning look knowledge
ed.
The inductive
physical objects,
sense-data
sometimes physical
cut
fundamental
we to
there
accepts
or
we restricted appearances
passing
of
a logical
pass
1978),
he
inductive
partly receive
and application
is
between
Nature,
that
knowledge conditions, sense-data to
the
"distinct
an
but The intimation
However, we
identified
inductive
abolishing us of
between does Press, physical
scepticism
gap
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inferential happily
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that scepticism.
of involves be
or gives Human
deductive sense-data, whenever of
least
gap
the
of to
tells
only our
bridge. knowledge
attempt
from
which of
can different data. sense-data
fact
anything
objects, the
perception
that assuming to
senses
no
valid
Russell
not objects. Clarendon
of lead
any
us objects
process see
sceptic's
sense-data. the inference
Treatise
By
no bridging a
the justify aside
them
these
relationship'
Russell A
under
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direct of
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scene,
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(Oxford: the possible
in
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since
steps physical
vary
logically
physical
gap Hume, (sense-data) our way Problems, is
the
none epistemological
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Our experience. Sense-experience to points There So
never a not
claim
While procesS
Having causes
appears
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is the
David Nidditch He table, that
sense-data, sometimes
invariably onto viewing what terms,
and sions representations
since know
It would is any find it
(I)
(2) 4 (3)
(4)
In (4). Russell
logical enumeration). from this are
3
in
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term
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Rus
(Cam
Sense
White
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world
the
common objects regarded read
White- of [Galaxy],
numbers.
directly
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ed.
149; Matter"
method
sceptical
18;
and Problems
hold
be
to Mathematics
use
he
relying
p.
I
real p.
the (Evanston
of 2nd
proceeding,
;
not
the
intermediate
not "On epistemology
Oxford
12 Relation
external
could property
and
Russell
of
construction
and
physical
1953),
mathematico-logical hand.
it
did VIEW hardnesses,
the
19
1919), which
There
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applies
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Before "The
to York: the
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Principles
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unpublished
to Morrell.
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supplemented
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Matter",
theory.
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weaknesses (although
sense-data; and Russell
the
in
perceive
cardinal,
1912),
Logic,
1946;
problem given
empiricists.
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Ottoline led
1903
"On
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Russell
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PRE-CONSTRUCTIONIST
12 this
PHYSICAL
philosophy
II
constructions
114-16.
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(London:
approach of
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17
Philosophy
the concentrate Russell's
such Mathematics
(1914;
RUSSELL'S
all Problems, acknowledgement position; in
which
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of
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to 1925, apply
U.P.,
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emergence construction
relativity,
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stipulate
Northwestern
emergence
I
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construction")
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Physics" early the p.
V.P.,
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jointly
Problems
epistemological
to Problems
logical
peculiar private Principles
sceptical position Russell's the it Russell as Cardiff from head
text special
Russell
for Criticisms", a sense-data:
an
the
similar
of
1959), The head problems. The bridge to Chicago: duction as data Russell "logical Instead and (Cambridge
wish
l
2
perceptual but In is 12 and I sell's is be physical Russell (a) (c) (d) The (b) 14 Russell summer 1987" The logical construction of physical objects 15 partly on instinctive belief. Ottoline Morrell what he was hoping to accomplish in it: "I haven't It is a simple hypothesis that "there really are objects independent had enough courage hitherto about matter, I haven't been sceptical of us, whose action on us causes our sensations" (Problems, p. 23). enough. I want to write a paper which my enemies will call the bank Russell both appeals to and supports the simplicity hypothesis with an ruptcy of realism" (#423, pmk. 24 April 1912). Three days later, while example of a moving cat. I see a cat at the corner of the room at one reporting to Ottoline Morrell that he had started writing "On Matter" moment. At another moment it goes into another room out of my sight. and had reached page 9, Russell reiterated the position he had in mind: After a while, when it returns, I see it again. But if I say that the cat "I will shock people, especially those who would like to agree with is nothing more than a series of sense-data, we cannot admit that it me-it ['On Matter'] is altogether too sceptical" (#[427] enclosed with existed during the interval when I did not see it, because at such time #4 26, pmk. 28 April 1912). the cat was not sense-data to me. This view seems absurd. It seems absurd to say that the cat ceased to exist when I did not see it and then III. INFLUENCE OF WHITEHEAD AND WITTGENSTEIN "suddenly sprang into being in a new place" (Problems, p. 23). To avoid UPON "ON MATTER" such absurdity, Russell contends, we take the natural view dictated by the principle of simplicity that "there really are objects other than our Before considering Russell's sceptical arguments in "On Matter", let selves and our sense-data which have an existence not dependent upon us look for any external influence behind his change of position from our perceiving them" (Problems, p. 24). Such a belief helps us to fill the Problems. I shall examine Whitehead's pre-publication criticisms of certain gaps in our sense-experience. The moving cat example suggests the Problems manuscript and Wittgenstein's earliest criticisms of Rus that between my separate sets ofcat sense-data, the real cat moved from sell's philosophical position in the Problems. In the middle of August one part of the room to the other. 1911, Russell sent a typescript of the Problems to Whitehead. On 23 Russell further strengthens his simplicity hypothesis by pointing out August Whitehead wrote to Russell: that we instinctively believe that we see, touch and smell physical objects. "We find this belief ready in ourselves as soon as we begin to Thanks for the typed copy of your book. May I keep it for a week or two? reflect" (Problems, p. 24). However, Russell certainly realizes that this It is really excellent. As I read it, the extreme difficulty of condensing such instinctive belief cannot stand up to the argument from relativity of a disputable subject as philosophy and the lucidity of your exposition strike perception. So he shifts the defence to the view that sense-data are me more and more. caused by and correspond to physical objects (Problems, p. 24). He There are some arguments in it which do not convince me.... [I]n a few finds it more reasonable to suppose that since we are never acquainted days I will write at length. with physical objects but always with sense-data, these sense-data are the results of something external to ourselves and acting on our sense Three days later Whitehead sent a letter along with fourteen pages of organs. Russell admits that there is no logical impossibility that our critical comment on the Problems. It is not known what Russell wrote instinctive beliefs are false, but still they are worthy of acceptance, since to Whitehead just before or after receiving the comment, for Russell the contrary hypothesis does not seem to be warranted by the facts. then did not make copies of such letters and Whitehead was not a pres But, just three months after the publication of the Problems, Russell erver of letters. But it seems evident that there is no passage in the changed his view about physical objects. This change arose from his Problems which looks like a response to an objection raised by White coming to take a complete sceptical attitude towards beliefs which do head. As Victor Lowe has noted, in the published Problems "all the not follow with deductive validity from any facts we perceive to be true. passages that Whitehead quoted from the typescript as targets of his Russell's sceptical attitude is evident in his unpublished paper "On Matter". Before he started writing "On Matter"S Russell explained to
of Philosophy at the University of Wales, Cardiff, on 17 May 1912 (#457, pmk. 19 5 Unpublished ms., 1912 (RA 220.0II360). Russell started writing "On Matter" on 27 May 1912). He revised the paper heavily on 16 Oct. 1912 (#606, pmk. 16 Oct. 1912). April 1912 and finished on 13 May 1912 (Russell to Morrell, #[427] attached to #426, "On Matter" is scheduled for publication in The Collected Papers of Bertrand Russell, pmk. 28 April; #449, pmk. 13 May 1912). Russell read this paper to the Department Vol. 6: 1909-13, ed. John G. Slater (forthcoming 1989?). 17
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16
criticism ities Problems 6
1911). 7 Russell's had to did publication to changes;
whatever account "On Whitehead's that of enced head's (presumably be lishing charges. direction 18 Russell summer 1987 The logical construction of physical objects 19 nuity (#320, pmk. 23 Jan. 1912). had made him "more of a sceptic" (#459, pmk. 21 May 1912). And As soon as Russell was impressed by Wittgenstein's ingenuity, he again, the day he started writing "On Matter" Russell wrote to Morrell began to be infected by Wittgenstein's sceptical attitude. How much that "Wittgenstein (who has just been here) is delighted [to know that so is explained in his 1 March 1912 letter: the paper is going to be 'too sceptical'] but no one else will be" (#[427], enclosed with 426, pmk. 28 April 1912). It seems evident that Russell In my lecture yesterday I changed my mind in the middle. I had gone to must have discussed with Wittgenstein the possible sceptical outcome prove that there probably is an external world, but the argument seemed to of "On Matter". Even when Russell had finished a substantial part of me fallacious when I began to give it, so I proved to my class that there was "On Matter" he was encouraged by Wittgenstein who, in Russell's no reason to think anything existed except myself.... This was very sad, but judgment, "is the only man I have ever met with a real bias for phil it doesn't seem to matter much. It made a better lecture than if it had been osophical scepticism; he is glad when it is proved that something can't more pat. (#363) be known" (#435, pmk. 2 May 1912).10 And it was Wittgenstein who "thinks my paper on Matter the best thing I have done" although he As soon as Russell came to appreciate his student's sceptical attitude, read only the beginning and end of it (#460, pmk. 22 May 1912). Rus he began to like Wittgenstein very much, although he was a "severe sell's correspondence with Lady Ottoline Morrell and Lucy M. Don critic" of Russell's lectures: "I like Wittgenstein more and more. He nelly give clear indication that Wittgenstein was a great influence on has the theoretical passion very strongly-it is a very rare passion and his developing a sceptical view in "On Matter". one is glad to find it. ... There is very much more in him than in any of my other pupils" (#373, pmk. 8 March 1912). IV. SCEPTICISM IN "ON MATTER" Wittgenstein also attended Moore's lectures. Once Russell asked Moore about what he thought of Wittgenstein. Moore replied that he "On Matter" is intended to upset any defence of our knowledge of had a high opinion of him. Russell was delighted to let Ottoline Morrell physical objects. In the Problems, the argument by which Russell tries know this (#368, pmk. 5 March 1912). to bridge the gap between perception and physical objects is based on By the time Russell came to write "On Matter" Wittgenstein had an inductive principle or on what some would call "inference to the become a friend and a valued colleague. On 26 March 1912, Russell best explanation". By supposing that there are physical objects, phys wrote to Lucy M. Donnelly: ical science is able to frame theories which fit the facts in all verifiable respects, and thus form a simple system. Otherwise many facts would I have now an Austrian pupil who is after my own heart-he never believes remain isolated and chaotic. Our sense-data are all fleeting and perish what I say, & always has admirable reasons for his dissent; it is not barren ing. But by supposing them caused by physical objects all of these iso dissent, but that of a man who has absorbed what one has to teach and gone lated and fleeting sense-data can be brought under general laws which farther. are simple and allow sense-data, to some extent, to be predictable. In the Problems Russell employs this inductive principle to strengthen the Russell even came to think of Wittgenstein as his own successor. inference from sense-data to physical objects. But he was not happy in doing this. He agreed with Hume that such a principle cannot be log He [Wittgenstein] is a treasure. I have got a number of new technical ideas ically proved to be true. However in the Problems, instead of becoming from him, which I think are quite sound and important. I shan't feel the a sceptic, Russell embraces the simplicity argument by accepting the subject neglected by my abandoning it, as long as he takes it up. (Russell principle on the ground of its intrinsic plausibility (Problems, p. 68). to Morrell, #422, 23 April 1912)9 In "On Matter", Russell finds no satisfactory reason for inferring
Moreover, Russell himself confessed that it was Wittgenstein who 10 In his Tractatus Logico-Philosophicus (trans. D.F. Pears and B.F. McGuinness, witlt an Introduction by Russell, London: Routledge, 1961), what Wittgenstein says from 9 It is interesting to note that Russell expressed this view the day before he planned to proposition 6.3 to 6.372 (where he deals with scientific theory and natural laws) clearly write "On Matter" (#423, pmk. 24 April 1912). reflects this sceptical attitude. 20 Russell summer 1987 The logical construction of physical objects 21 physical objects from sense-data. He comes to accept the futility of which is in space breaks down" (fol. 6). using the inductive principle to support the hypothesis that sense-data In the Problems, RusseJI says that he cannot tell us about the qualities are signs of physical objects. The simplicity argument, he now thinks, of physical objects. The most he can do is to offer the suggestion that "has absolutely no weight whatever" ("On Matter", fol. 16). Russell there is in the physical object some quality which corresponds to brown agrees that in some situations when we have nothing to choose between when we see brown, some quality which corresponds to red when we two hypotheses, there may be a practical reason to accept the simpler see red, and so on. In "On Matter" Russell claims that even if we of the two. "But this affords no reason whatever for supposing that the assume that some of our sense-data correspond to qualities independent simpler theory is actually true" (ibid.). Elsewhere Russell expresses the of perception "we could know nothing as to [their] intrinsic nature" same view that "there is no very good ground for supposing that a (fol. 29). This is also the conclusion in the Problems (see p. 34), but simple law is more likely to be true than a complicated law" (The Anal now RusseJI is taking his argument one step further: we cannot even ysis of Mind [London: Allen and Unwin, 1921], p. 132). know the structural properties of things. Even if in two cases where A variant of the inductive argument, argument from confirmation, everything we can directly observe is exactly similar, it does not foJIow holds that if a certain hypothesis fits all relevant known facts it is at that there is no unobserved difference. We can always cast doubt as to least probable that the hypothesis is true. But Russell insists that such whether even in some cases sense-data correspond structurally to the "a contention is only valid if it is known that there are not likely to be reality behind them. other hypotheses which also fit the facts. In our case this knowledge is Since we have no means of identifying physical objects, we have no absent" ("On Matter", fos. 17-18). reason to believe that they play any role in the production of our sense The argument from continuity states that if a cat appears at different data or even that they exist at all. Considering Russell's initial places at different times it is quite reasonable to suppose that over and announcement to Lady Ottoline, this could be the final conclusion of above the various cat sense-data there is a real cat which changes its "On Matter". But the story is quite different. Having realized that the position and exists when it is not seen. "But I doubt", Russell now defence of physical objects in the Problems cannot stand up to sceptical contends, "if there is any real force in considerations of this kind" (fol. arguments, he does not join the sceptic; rather he goes in a new direc I8i). Russell does not give any further explanation of this objection; tion to defend physical objects from the threat of scepticism. but he seems to think that since the principle of continuity (a variant of the simplicity hypothesis) depends on inductive argument and since V. CONSTRUCTIONISM AND RUSSELL'S CREDIT TO WHITEHEAD inductive argument has been shown to be invalid, the continuity prin ciple loses any real force. Russell proposes that in order to escape a sceptical conclusion we No defensible reason is found in favour of the existence of physical should assume "that all that could be a sense-datum to any possible objects. Can we then have any satisfactory account of the nature of observer actually exists, and that collections of such actual and possible physical objects? The answer is: we can't. In the Problems, Russell sense-data are bound together in ways which enable us to regard them argues that physical objects exist in physical space. Now he realizes as one 'thing'" (fol. 35). This provides him with two advantages, viz. that this view gives rise to a difficult question as to what is meant by "(I) that it avoids an unknown noumenon, since matter will consist "space". "Real" space is not present to the senses. The one space in entirely of things of the kind with which we are acquainted, (2) that it which common sense believes is obtained by a rough correlation of dif avoids rejecting our instinctive beliefin the independent reality of qual ferent spaces (i.e., those of sight, touch, feeling, etc.). This space is an ities, without which it is hard to find any conclusive ground for retain inference. Moreover, it cannot contain the immediate data of the senses ing our belief in matter or the external world" (fol. 32). This marks but only the "things" which common sense infers from sense-data and the beginning of Russell's constructionist theory of the external world. regards as the sources of correlated sensations of sight, touch, feeling, Even the term "logical construction" appears here for the first time etc. So it appears that the space of common sense is to be identified as (fos. 12, 19), and although he has not yet fully developed the theory, the space in which the physical object is; other than that, the physical he is well aware of its possible uses: " ... to those who rebel against the object is to be defined as that which is in common-sense space. "Hence sceptical conclusions to which we seem otherwise driven, I commend this the attempt to define matter [the collection of physical objects] as that hypothesis [that physical objects are constructed from actual and pos- 22 Russell summer 1987 The logical construction of physical objects 23 sible sense-data] as at least not obviously untrue, and as more in con that Russell got the idea from the work in progress on Principia Math sonance with our instinctive beliefs than any other hypothesis which ematica, Vol. IV (on geometryI2), which was to have been written by the facts permit" (fol. 35; my italics). Thus it is in "On Matter" that Whitehead alone, or from the notes on time (and space) that Whitehead the constructionist theory emerges which Russell fully develops in Our sent to him in late 1911. 13 I suggest that this is not the case. White Knowledge and "The Relation of Sense-data to Physics". head's work on geometry and his notes on time contain no hint of the It is now clear that the seeds of Russell's constructionist theory are logical construction of physical objects. In fact there are noepiste contained in "On Matter", that this discussion grew out of his sceptical mological issues involved in Whitehead's works prior to 1914.14 Until doubts about physical objects, and that it was probably Wittgenstein then his work deals only with mathematics and mathematical physics who made him sceptical. It is interesting to notice that what Wittgen and is limited to applying logical techniques to abstract problems of stein says in the Traetatus (esp. 6.363-6.37) is a clear indication of his space and time. 15 agreement with Russell in "On Matter" that induction, which consists How, then, should we evaluate Russell's giving Whitehead full credit in accepting as true the simplest laws, has no logical justification. I am for the changes he made from the Problems to Our Knowledge? By the not claiming that it was Wittgenstein who influenced Russell into time Russell came to write Our Knowledge he certainly had received becoming a constructionist. What Wittgenstein seems to have done is help from Whitehead and used certain key ideas in Our Knowledge that to make Russell realize that the way he tries to bridge the gap between Whitehead had developed for Vol. IV of Principia. This help came not perception and physical objects in the Problems is doomed to failure by only through various notes that Whitehead sent to Russell in his letters, the sceptic's arguments. Wittgenstein quickened the emergence of log but also through Russell's reading an important paper by Whitehead ical constructionism in that he forced Russell to come up with the view that the sceptic's gap could be bridged in a constructionist way. One might ask why, if Russell had been influenced by Wittgenstein 12 References to works on geometry, before April 1912, are found in the following letters during this time, he does not acknowledge it. The reason, I think, is from Whitehead to Russell: 29 April 1905; 30 April 1905; 22 Sept. 1910. It is not that Wittgenstein's influence was on Russell's direction rather than his known how far the work on Vol. IV of Principia was completed by the time Russell doctrine. It should be noted here that Russell's understanding of scep came 10 write "On Matter" (cf. Martha Harrell's as yel unpublished paper, "Extension ticism is different from Wittgenstein's. One very interesting feature of to Geometry of Principia Mathematica and Related Systems", read at the Toronto Rus Wittgenstein's sceptical attitude is that he does not, as does Russell, sell conference in 1984). I presume that not much had been done. Although in the letter of22 September 1910 Whitehead mentions "the beginning ofGeometry", a letter think that scepticism is a legitimate position which needs to be refuted of 1912 to the Provost of University College, London, shows that much of the scheme (see Tractatus, 6.51). In the Problems Russell clearly sees that there are of work on geometry "remained yet in project" (quoted in Lowe, "A.N. Whitehead certain plausible arguments which show that scepticism is logically ten on His Mathematical Goals: a Letter of 1912", Annals of Science, 32 [1975]: 86). able (p. 22), but he tries to meet scepticism by inferring physical 13 The notes are found in Whitehead's letters to Russell dated 3 and 20 Sept. [191 I]. objects from sense-data. However, as soon as Wittgenstein came on the " Lowe has mentioned that it is only in 1914 that Whitehead "insists on beginning with perceptual space" ("A.N. Whitehead on His Mathematical Goals", p. 93). scene he tried to convince Russell that any attempt to pass from sense IS I don't think that Russell could have got the idea of the logical construction of physical data to physical objects in this way is vulnerable to sceptical attack. objects from Whitehead during the writing of "On Matter". Russell's appointment Where exactly does Whitehead stand in the emergence oflogical con diary shows that he had a meeting with Whitehead on 27 April 1912, the day he started structions in "On Matter"? As the evidence stands, certainly not in the writing "On Matter", but ifhe had taken up the idea then he would not have reiterated front row, given that he himself had not considered the logical con his sceptical position to Lady Ottoline in the letter postmarked 28 April. After 27 April, Russell met Whitehead again on 10 May at a dinner (#445, pmk. II May 1912). struction of physical objects by 1912,1l nor did he give Russell any hint The structure of the paper strongly suggests that Russell did not come up with the of it (if he had the idea in mind) in his fourteen pages of critical com idea of the logical construction of physical objects at least until he had finished folio ment on the Problems. However, one might think that it most likely 12 of the essay (where the term "logical construction" appears for the first time). Now since folio 9 was finished on 27 April (#[427]), and since the paper was "nearly fin ished" on 6 May 1912 (#44°, prnk. 7 May 1912), I think folio 12 must have been 11 Lowe has suggested that so far as the constructions of physical objects are concerned, written long befoie Russell met Whitehead on 10 May at dinner. I conclude that White Whitehead was a constructionist only during the period 1915-17. See "Whitehead's head must have made little or no contribution to the construction of physical objects 1911 Criticisms of The Problems ofPhilosophy", p. 9. in "On Matter". 24 Russell summer 1987 on space late in 1913.16However, the assistance was only on the appli cation of the theory in the logical construction of the space and time of mathematical physics, not in the construction of physical objects. Since the concern common to the Problems and Our Knowledge is the problem of physical objects and since a major part of Our Knowledge continues the logical construction of physical objects which was under taken in "On Matter", Whitehead does not deserve the amount of credit he was given. 17 But why should Russell have given credit for his discovery to Whitehead, whose contribution was limited to the areas of space and time? My only suggestion is that he was already trying to comfort Whitehead for the use of his ideas, who was shortly to have "the feeling that he had been plagiarized [by Russell] in 1914 [in Our Knowledge]",18 by paying more than he deserved. 19
Department of Philosophy University of Chittagong Bangladesh, and McMaster University
16 This paper is "La Theorie relationniste de l'espace", Revue de Melaphysique et de Morale, 23 (1916): 423-54. (For an English translation, see Patrick J. Hurley, "White head's Relational Theory of Space: Text, Translation, and Commentary", Philosophy Research Archives, 5 [1979]: 676-739.) On I October 1913, Whitehead sent a draft of this paper to Russell for criticism. We have no evidence of what Russell's criticism of the paper was, but on 10 January 1914 Whitehead sent him a rewritten version with the comment: "It has been thoroughly recast, enlarged, and a good many novel views put in. I am pleased with it.... The paper as it stands-provided it survives your crit icisms-will go nearly without change into vol. IV" (enclosed with letter to Morrell #963, pmk. 12 Jan. 1912). Russell thought this version "very good" and "full of admi rable things" (#963). In this paper Whitehead takes into account, among other things, the definition of enclosure and of point; both items are present in Gllr KIlIYlvledge, Lec!. IV.
17 In Russell's later works he attributes to Whitehead only the idea of applying the method of logical construction to reach the space and time of mathematical physics. See "The Relation of Sense-data to Physics", pp. 149-50; "Physics and Perception", Mind, 31 (1922): 483; The Principles of Mathematics, 2nd ed. (London: Allen and Unwin, 1937), Introduction, p. XI; My Philosophical Development (London: Allen and Unwin, 1956), p. 108. 18 Lowe, Alfred North Whitehead: the Man and His Work, Vol. I: 1861-1910 (Baltimore and London: The Johns Hopkins U.P., 1985), p. 229n. 19 I am grateful to Nicholas Griffin and Evan Simpson for their helpful comments and suggestions on an earlier draft of this papcr. The earlier draft was presented to the Department of Philosophy, McMaster University. I am also grateful to the audience for their comments, and for those of the editor and the anonymous referee of Russell.