The Logical Structure of Russell's Negative Facts

12 Pages·2007·1.2 MB·English

by  Wayne A. Patterson

THE LOGICAL STRUCTURE OF
RUSSELLS NEGATIVE FACTS
WAYNE A. PATTERSON
Philosophy/ NationalUniversityofSingapore
Singapore119260
I nhis1918lecturesonLogicalAtomismRussellcommentsthat,while
lecturingatHarvardin1914, his admission thattheworldcontained
negative facts "nearlyproduced a riot".! Since then manycommen
tators (Ayer,2 Klemke,3 and McDonough,4 for example) have regarded
Russell's admission as indefensible. The fact that Russell himself
subsequentlydenied the existence ofnegative facts adds weight to these
conclusions. This paperwill attempt to uncover the logical structure of
Russell's negative facts. Byso doing it can be demonstrated, firstly, that
Russell's 1918 view on negative facts was perfectlyconsistentwith other
fundamental principles oflogical atomism which he held at that time,
andsecondly,whyRussellfeltsubsequentlyforced to abandon his belief
in theexistenceofnegativefacts. Finallyitwill be arguedthatthis aban
donment was the unnecessary result ofRussell's rigid adherence to a
questionable epistemological principle. A fine-tuning ofthis principle
leads to the conclusion that Russell's postulation ofnegative facts repre
sents an acceptable solution to the problem of negation which his
atomism mustface.
Before investigating the structure ofnegative facts, a prior question
must be answered. WhydidRussell feeLthathe needed negative facts in
LK,p.2II; Papers8:187.
I
A.]. Ayer, RussellandMoore: theAnalyticalHeritage (London: Macmillan, 1971),
2
pp.86-7·
J E. D. K1emke, "LogicandOntologyinRussell'sPhilosophy",inEssaysonBertrand
Russell,ed. K1emke(Urbana: U.ofIllinoisP.,1970),p.425.
4 R. M. McDonough, TheArgument ofthe "Tractatus"(Albany, N.Y.: State U. of
NewYork,1986),pp. 21-4.
russell:theJournaloftheBertrandRussellArchives n.s.16(summer1996):45-66
McMasterUniversiryLibraryPress ISSN0036-01631
46 WAYNE A. PATTERSON TheLogicalStructureofRussell'sNegativeFacts 47
thefirstplace?Theanswerto this questionliesin thefundamental prin languagewhich purport t~ standfor these negative facts.
ciples oflogical atomism which Russell held at this time, and which
mustnow beenunciated. P2 The Principle ofAcquaintance. This is most clearly stated in an
earlierwork, TheProblemsofPhilosophy. "Everypropositionwhich
PI The LogicallyPerfectLanguagePrinciple. For ease ofdiscussion, we wecan understand must be composedwhollyofconstituentswith
shall henceforth restrictourselves to atomic facts. We are attempt which we are acquainted" (PP p. 58). By 1918, however, Russell
2,
ing to uncoverthestructureofanegativefact, andthatisbestdone no longer believed in propositions as some sort ofabstract entity
by considering the simplest ofsuch forms, a negative atomic fact. whichconstitutedthe meaningofasentence.Ashesaysinhis1918
But first we must understand what Russell means by a positive lectures, "Aproposition isjustasymbol", and "Aproposition, one
atomic fact. Russell at the outsetmakes it clear that there is adis may say, is a sentence in the indicative...."9 So thePrinciple of
tinction between positive and negative facts when he writes, Acquaintance mustat thisstage be reinterpretedassayingthatany
"Another distinction, which is perhaps a little more difficult to proposition (i.e. sentence)whichwecanunderstandmustbecom
make, is between positive and negative facts, such as 'Socrates was posed wholly ofexpressions whose meaning can only be grasped
alive'-a positive fact-and 'Socrates was not alive'-you might through acquaintance with what those expressions stand for. This
say a negative fact."5 As for positive atomic facts, Russell explains is made clearwhen Russell says "That the components ofa prop
that "The simplest imaginable facts are those which consistin the ositionare thesYlllbolswe mustunderstandinorderto understand
possessionofaquality bysome particularthing. Such facts, say, as the proposition; That the components ofthe fact which makes a
'This is white'."6 Such facts are called atomicfacts and "The prop~ proposition true or false, as the case may be, are the meaningsof
ositions expressing them are what I call atomicpropositions."? In thesymbolswhichwemust understand inorderto understandthe
the proposition "This is white", the referring expression "this" is proposition."1O
functioningfor Russell as alogicallypropername, asymbolwhich
refers to an object but does not describe that object in any way. Two points of clarification are in order. Firstly, the Principle of
The logical form ofan atomic proposition like "This is white" is Acquaintance is intended to apply to every proposition ofthe logically
thereforesubject-predicate. perfectlangauge. The theoretical goal ofRussell's logical atomism is that
all sentences ofordinarylanguagewill, ultimately, be analyzed in terms
TheLogicallyPerfectLanguagePrinciplestatesthatalogicallyperfect ofsentences ofthe logicallyperfectlanguage, the theoryofdescriptions
language "willshowataglance the logicalstructureofthe facts asserted beingaparadigmexample. Secondly, the Principledoes notapplyto the
or denied."8 This implies that if there are negative facts, as Russell logical constants ofthe logicallyperfectlanguage. The meaningoflogi
believes, then the logically perfect language which he is attempting to cal constants such as "or", "and", etc. is purely syntactic and the Prin
constructwillcontainpropositionswhichwillimmediatelyandperspica ciple ofAcquaintance, asemantic principle, is not intended to apply to
ciously reveal the logical structure ofsuch negative facts. In the search them.
for such logical structure we will naturally be led to acareful consider Sainsbury argues that the Principle of Acquaintance must be
ationofthelogicalstructureofthosepropositionsofthelogicallyperfect rejected. However at thispoint we are not concerned with the ques
II
tionofwhether the principleswhich underpin Russell's logical atomism
5PIA, in Lf(,p.184: Papers8:165.
6 Lf(,p.198:Papers8:176. 9 Lf(,p.185; Papers8:165.
7 LK,p.199; Papers8:177. IO Lf(,p.196;Papers8:175.
8 Lf(,p.198;Papers8:176. II R. M.Sainsbury. Russell(London: Routledge& KeganPaul,1979).p.36.
48 WAYNE A. PATTERSON The LogicalStructureofRussell'sNegativeFacts 49
areorare notacceptable. Ourconcernis inshowingthatRussell's analy propositions?
sis ofnegative facts is consistentwith these principles. The reason is that we have at this stage no idea ofwhat it means to
say that a proposition is false. We could take falsehood as primitive, an
P3 The Correspondence TheoryofTruth. Russellwrites, "Thatbrings us ideawhichseems to have beenexploited byFregewhen he asserted that
on to the question ofstatements or propositions orjudgments, all all false propositions refer to an entity "The False". But this solution is
those things that do have the duality oftruth and falsehood. For not open to Russell for two reasons. Firstly it would offend against his
thepurposesoflogic ... itis natural to concentrateupon the prop "robustsense ofreality" to introduce into his ontologysuch aprimitive
osition as the thingwhich is going to beour typical vehicle on the abstract entity. Secondly, and more importantly, such a move violates
dualityoftruth and falsehood."12 "The essence ofaproposition is P3.Apropositionisfalse inso far as itcorrespondsfalselywithsomefact
that it can correspond in two ways with a fact, in what one may in the world. Falsehood is a relation between a proposition and a fact,
call the true way or the false way."13 These statements make it and anycorrespondence theoryoftruth owes us an accountofprecisely
clear that Russell held that propositions were made true or false what this relation is.
depending upon whether theycorresponded trulyorfalselywith a Truth poses no problem. Ifa proposition, "This is red", is true then
particular fact in the world. Moreover there is just onefact which "In alogicallyperfectlanguage thewords·in aproposition would corre
makes each proposition true or false. "There are, ofcour~e, two spond one byonewith the components ofthe corresponding fact...."15
propositions corresponding to every fact, one true and one In atrue positiveproposition therewill be an isomorphism between the
false."14 elements ofthe proposition and theelements ofthe correspondingfact,
and the Principle ofAcquaintance will (at least partially) establish the
P4 The Unanalyzability Principle. All predicates which appear in the truth of the proposition. However ifa positive proposition, 'This is
logically perfect language will be unanalyzable. By this is meant red", is false there will be no such propertyofredness in the correspon
that the meaning ofsuch a predicate can onlybe grasped through ding fact which makes this proposition false. We are face to face here
acquaintance with the propertywhich that predicatestands for. withwhatRussellcallsthe"theoryoferror". "Youwill notice thatwhen
everonegets to reallyclosequarters with the theoryoferroronehas the
With these principles in mind we can return to the question ofwhy puzzle ofhow to deal with error without assuming the existence ofthe
Russellfeltitnecessaryto introducenegativefacts intohisontology.The non-existent."I6 Given the Correspondence Theory ofTruth Russell is
obvious answer is that Russell needed them to account for the truth of at aloss to explain howpropositions can be false.
negativepropositions.Thus thenegativeatomicproposition"Thisisnot Russell's solution is to define falsehood in terms ofnegation: "p" is
red", where the logically proper name "this" refers to an object having false =df"not-p" is true. This is progress because we already have some
the property ofbeing a black dot, is made true by its correspondence idea ofwhat is involved in saying thataproposition is true. The conse
with the negative fact that the dot is not red. Primajacie this seems an quence, however, is that Russell is forced to admit a new kind offact
odd way of accounting for the truth of such propositions. Why not into his ontology. A negative atomic proposition is true in virtue of
simplysay that"not-p" is true ifand only if"p" is false? In otherwords corresponding trulywith some negative fact. That brings us to the key
why doesn't Russell simply employ the usual truth-table definition of question. Whatis the logicalstructure ofthese negative facts?
"not" in order to give an account ofthe truth conditions ofnegative The answer lies with PI. In the logically perfect language the true
IK,pp. ~84-5; Papers8:165.
12
13 IK,p. 208; Papers8:185. Ij LK,p.197;Papers8:176.
14 LK,p.209; Papers8:185. 16 LK,p.225; Papers8:198.
50 WAYNE A. PATTERSON The LogicalStructureofRussell'sNegativeFacts 51
negative proposition, "This is not red", will showat aglance the logical "All men are wise" is false =df"All menare non-wise" is true.
structureofthefact asserted. Unfortunatelywedo not, asyet, haveafull
understanding ofthe logical structure of the proposition, 'This is not Such a definition is clearly unacceptable. So too with our proposed
red". The obviousinterpretation is to treat the negation operator "not" definition:
as negating the entire sentence, so that the structure becomes "Not(this
is red)".-Ifthisproposition is to showat aglance the logicalstruqure of "This is red" is false =df"This is non-red" is true
the correspondingfact then we are in trouble. For the word "not" must
on this viewstandfor some entity (notness?) in the correspondingfact. unlesswecanshowthat"Not(thisis red)" islogicallyequivalentto"This
Russell adamantly denies such a possibility in the same way that he is non-red".
denies that words like "or" stand for entities. In giving his provisional A. C. Benjamin argued that for Russell the negation operator can
definitionofthecomponentsoffacts Russelladds that"itdoes notapply never be taken as aqualification ofthe predicate. "One cannot say that
to words which, like 'or' and 'not', are parts of propositions without the notion, 'not red' is equivalent to the notion 'not-red'."20Yet there
corresponding to any part of the corresponding facts."I7 The point is is evidence to show that Russell did hold the proposed logical equival
repeated a little later: "In a logically perfect language the words in a ence. Benjamin bases his conclusion on apassage in Russell's lectures in
proposition would correspond one by one with the components ofthe which Russell is taking issue with a view of negation proposed by
21
corresponding fact, with the exception ofsuch words as 'or', 'not', 'if, Demos. The passage begins, "His thirdpoint I do not entirely agree
'then', which have a different function."18 And again, "You must not with: thatwhen the word 'not' occurs, itcannotbe taken as aqualifica
lookabout the real world for an objectwhich you can call 'or', and say, tion of the predicate",22 and ends, "so that in all cases where a 'not'
'Now, look at this. This is "or".' There is no such thing, and ifyou try comes in, the 'not' has to be taken to apply to the whole proposi
to analyze 'p or q' in that way you will get into trouble."19 A precisely tion."23
similar remark may be made concerning the word "not". According to Benjamin'sconclusionwasbasedonaseriousmisinterpretationofthe
Russellitwouldbe "monstrous" to concludethattherewereentitieslike passage. The keyword incorrectlyinterpretingRussell here is the word
"orness" and"notness" goingabout the world. "entirely". Russell certainly agrees with Demos that when dealing with
Fortunatelywe have an alternative analysis ofthe logical structure of non-atomic propositions (such as "The present King ofFrance is not
"Thisisnotred". Insteadofnegatingthepropositionexternallyweapply bald") the negation operator must be taken as applying to the whole
the negation operatorto the predicate "red" to give "This is not-red" or proposition, external negation that is. For non-atomic propositions the
"This is non-red". This forces us to argue that "Not(this is red)" and internal and external negations are not in general logically equivalent,
"This is non-red" are logically equivalent. The reason is that we are and Russell's discussion ofthe point makes this abundantly clear. That
tryingtodefinefalsehoodin termsofnegation. Suchadefinitionwillfail Russelldoes not "entirely" agree withDemos concerningthe role ofthe
unless thenotionofnegation takes truths intofalsehoods andfalsehoods negation operator strongly suggests that he disagrees with Demos with
into truths. If there were a difference between external and internal respect to atomic propositions. In such cases "not" can be taken as a
negation then our proposed definition offalsehood would fail, as the
following example illustrates:
. 20A. C. Benjamin, The LogicalAtomism ofBertrandRussell (Ann Arbor: U:M.I.,
1992;1sred.,1924),p.35.
21 RaphaelDemos,"ADiscussionofaCertainTypeofNegativeProposition",Mind,
17 r.f(,p.196;Papers8:175. n.s. 26(1917):188-96.
18 LK,p.197;Papers8:176. 22 Lf(,p.212; Papers8:188.
19 Lf(,p'p. 2°9-10; Papers8:186. 2} LI<,p. 213; Papers8:188.
52 WAYNE A. PATTERSON TheLogicalStructureofRussell'sNegativeFacts 53
qualification ofthe predicate. "Not-p" is true =df"There is some proposition qwhich is true and is
Romane Clarkargues that"ais non-F" implies butis not implied by incompatiblewithp."
"Not(a is F)", citing G. H. von Wright ·in support.24 That "Not(a is
F)" does not imply"a is non-F" obviouslyholds when "a" is a definite Theproposition qwhich is incompatiblewithp isapositiveproposition,
description. Thelackofentailmentis notso obviouswhen"a" is alogi sothat"Not(thisis red)" getsdefinedas "Thereissomepositiveproposi
cally proper name. Indeed there is a clear statement in Russell that he tion (say 'this is green') which is true and which is incompatible with
did maintain the logical equivalence of"Not(a is F)" and"ais non-F". (the positive proposition) 'This is red'." It is to be noted that it is not
"When you say 'Scott is human' there is no possibility of a double open to Demos to define thenotionofincompatibilityin the usualway.
denial.Theonlywayyoucandeny'Scottishuman' is bysaying'Scottis
not human'."25 (Russell here is using the name "Scott" as a logically "p is incompatiblewith q" =df"pand qare not both true."
propername.)
Theviewthat the internal and external negations ofatomic proposi Thiswouldobviouslybecircular. Demosis tryingto definethe negation
tions are logically equivalent is supported by Sainsbury. "[F]or atomic operatorin termsofincompatibility, inorderto avoidthe postulationof
propositionsthere is no distinguishing the case inwhich the predicate is negative facts. So on the Demos account incompatibility becomes a
negated from the case in which the whole atomic sentence is negated fundamental unanalyzable notion.
..." (Russel~ p. 222). Indeed it is arguable thatRussell is forced to admit Russell attacks this proposed analysis using PI, the Logically Perfect
the proposedlogical equivalence, for if"not" can onlyactexternallyon LanguagePrinciple. Ifthe proposition"pis incompatiblewith q" isnow
atomic propositions ifour definition offalsehood is to be acceptable, to beapropositionofthelogicallyperfectlanguage then itmustshowat
then Russell must either surrender PI or claim (contra his own state a glance the logical structure of the fact asserted. This requires that
ments) that "not" does in fact standfor an entity. incompatibility becomes a component ofthe corresponding fact, that
We have apparently established that Russell must admit negative incompatibilitybecomesa"fundamentalandobjective"relationbetween
facts. Demos objects. He argues that falsehood can be defined, not in tWo facts. Russell protests that incompatibility is a relation which can
terms ofnegation, but in terms ofincompatibility. We begin first with holdonlybetween propositions. "It is clear that no twofacts are incom
thefollowing definition offalsehood. patible. The incompatibilityholds between thepropositions, between the
pandtheq...."26
"This is red" is false =df"Not(this is red)" is true. Asitstands this isaweakobjection. IndeedDemosmightrespondby
saying that Russell has simply begged the question against him, for
Note thatDemos takes the negationoperatorasactingexternallyon the Russell has given no justification for his claim that no two facts can be
wholeproposition. Indeedhefeels that negation, in thefull sensewhich incompatible. As an atomist Demos can argue that incompatibility
takes truths into falsehoods and vice versa, alwaysoperates externally, a between facts is indeed fundamental and objective, and that the word
pointwhich as we sawearlierRussell does notentirelyagreewith. Now "incompatible", as applied to proIJositions, can only be understood
it is incumbent upon Demos to account for the truth of"Not(this is through acquaintance with what it stands for! The proposition, "p is
red)". He doessoas follows: incompatiblewith q", does therefore showat aglance the logical struc
ture ofthefact asserted.
It is suggested that the real reason Russell rejects Demos' account is
24 Romane Clark, "Ontology and the Philosophy ofMind in Sellars' Critique of
Russell"; in Bertrand Russell's Philosophy, ed. G. Nakhnikian (London: Duckworth,
1974),p.II4·
25 Lf(,p.251; Papers8:220. 26 Lf(,p.214; Papers8:189.
54 WAYNE A. PATTERSON The LogicalStructureofRussell'sNegativeFacts 55
that the incompatibility will be between, not two facts existing in the property ofnon-redness. Hence the logical structure ofa true negative
actual world, but between an actual fact and apossiblefact. To say that atomicfact consists ofaparticularwhich possesses anegative property.
this is notred is to saythat the possiblefact that this is red is incompat This possibilityisconsidered byMcDonough:
ible with the actual fact that this is (say) green. There is no evidence to
suggestthat Russelleverentertained the notion ofapossible fact. In his Russellsuggeststhat"not"can,atleastsometimes,betakenasaqualificationof
the predicate and suggests that this is connected with his view that there are
1918 lectures, possibility for Russell is strictly a property ofa proposi
negative facts. That is, "aF" "refers" to aand Fand "-aF" refers to aand a
tional function. Secondly, the introduction of possible facts into his
qualitydistinct from F, namely that referred to by"not-F"! (Argumento/the
ontologywould no doubt offend against his robust sense ofreality, and
"Tractatus", p. 258).
thatwhen one is dealingwith the theoryoferror"one has the puzzle of
howto deal with errorwithoutassuming the existenceofthe non-exist
The appearance of the exclamation mark indicates that McDonough
ent." (No doubt Russell would be sympathetic to Quine's attack on
finds this suggestion, at the very least, surprising. He goes on to argue
possibleworld ontologies.) thatsuch aviewdoes nothing to explain the nature offalsehood, which
Finally, the introduction of possible facts would violate Russell's
is ofcourse Russell's ultimate objective and the reason why he finds it
Principle ofAcquaintance. Sellars holds that for Russell facts are objects
necessary to introduce negative facts. McDonough's argument is as
ofacquaintance.27 This is clearlyfalse, as Russell held that the Principle
follows.
ofAcquaintance appliesonlyto unanalyzable expressions, and the latter
stand for unanalyzable (simple) objects. Facts (and the propositions
Russell points out that two propositions correspond to each fact, but it is also
which correspond with them) are complex, and cannot therefore be true in his view that thereare at least twopossiblefacts relevant to the truth of
objectsofacquaintance. However,Russelldidholdthatonecanperceive eachproposition. Buttherelationshipbetweenapropositionandthefactwhich
facts.28 This forces us to say that in determining the truth of "p is makes itfalse is obscure. If"p" is "aRIb" then"-p" is, for example, equivalent
incompatible with q" we would be required to perceive the actual fact to"aR,b"where"aR,b" ismadetruebyacomplexdistinctfrom, butincompat
which is represented by the proposition p and to perceiv~ the possible iblewith,thatwhichmakes"aRIb"true. Butonthefaceofit"p"onlymentions
a, band R It does not mention R" a constituent ofthe fact which makes it
fact represented bythe proposition q, and then apprehend byacquaint I•
false. Itdoes notappearto maketheadditionalclaimthat aisnotR,to l(.P. 23)
ancethe relationofincompatibilitybetweenthem. Butitisobviousthat
one cannot perceive a non-existent possible fact, and consequentlycan
McDonough then goes on to argue that Russell is committed to the
not apprehend by acquaintance the relation which is supposed to hold
same "fundamental objective incompatibilities" as is Demos. "In both
between the actual andpossiblefact. Unable to countenancethe ideaof
Demos's and Russell's views one simply comes to the point at which
incompatibilityasafundamental andobjectiverelationholdingbetween
distinct propositions are arbitrarily stated to be logically incompatible"
actual and possible facts, Russell is driven to admit negative facts. The
(ibid). The error in this argument is the attribution to Russell ofthe
latteratleasthave the advantageofbeingactual.
viewthatthereareatleasttwo possiblefacts relevantto the truthofeach
We are now in a position to discuss the logical structure ofRussell's
proposition. Russell held no such view. Possible facts are not part of
negative facts. Ifthe true negative atomic proposition "This is non-red"
Russell's ontologyand playno role in his analysis ofnegative facts. This
is to showat a glance the logical structure ofthe fact asserted we must
is to be contrastedwith Wittgensteinwho readilyadmits possible states
regard the predicate "non-red" as standing for a negative property, the
of affairs.29 Equating Wittgenstein's "states of affairs" with Russell's
"facts"onemaybe tempted to thinkthatRussell countenancedpossible
27WilfridSdlars, ~'Ontologyand the PhilosophyofMind in Russell", in Nakhni
kian, ed., BertrandRussell'sPhilosophy,p.58.
28 LK,p.228; Papers8:200. 29 L.Wittgenstein, TractatusLogico-Philosophicus(London: Routledge, (961), 2.013.
56 WAYNE A. PATTERSON TheLogicaLStructureofRusseLL'sNegativeFacts 57
facts. In interpretingRussell one must resist the temptation to attribute work, An Inquiry intoMeaningand Truth, Russell says this. "In aword:
to himviews held byhis friend andpupilWittgenstein, despite Russell's it is possible, in a certain sense, to notice what is not there as well as
confessed indebtedness to him. whatis there. Thisconclusion, iftrue, isimportant" (IMT,., p. 164).The
Secondly, the incompatibilitybetween distinct propositions is not, as concept ofnoticing involves the notion ofacquaintance, but this is not
claimedbyMcDonough, "arbitrary" in thesensethatwe haveno reason quite the notionofacquaintancewhich Russellwasworkingwithin his
or explanation for such incompatibility. Even on the viewofDemos it 1915lectures,apointtowhichwewillreturnshortly. Neverthelessitisat
can be argued that the reason whysome proposition pis incompatible . least plausible to suggest that in his lectures Russell was consideringthe
with another distinct proposition qis that we are acquainted with the possibilitythatonecould beacquaintedwith negative properties. Ifthis
incompatibilitybetweenthe correspondingfacts. ForRussell the incom is the case then Russell's·analysis of the structure of negative facts
patibility between the two propositions "This is red" and "Not(this is becomesconsistentwithalloftheprinciplesofJogicaiatomismwhichhe
red)" is explained through the perceivedincompatibility of the prop held at that time.
erties ofredness and non-redness. Aserious objection to this consistenCyis raised bySainsbury. Heasks
The advantage of Russell's view is that the incompatibility is not simply, "What makes afact genuine?" (RusseLL, p. 220). Russell's analysis
between an actual and a possible entitybut between two actual entities, ofnegative propositions led him to postulate the existence ofnegative
redness and non-redness. Ifthere were no actual property ofredness in facts in order to account for the truth ofsuch propositions. But byset
theworld then the predk:ate "red", beingunanalyzable, would bemean ting down certain criteria which a logically perfect language ought to
ingless. Consequentlythe proposition,"This is red",wouldbemeaning possess, and then arguing that the truth ofcertain propositions express
less.Insuchacasethequestionofhowsuchapropositioncouldbefalse, ible in this language can onlybe accounted for bypostulatingthe exist
and theassociatedquestion ofnegativefacts, would notarise. enceofcertainkinds offacts, Russell is perilouslycloseto readingoffhis
Russell'sviewrequires thatwecanbeacquaintedwith the propertyof ontologyfrom hislanguage. Is thereanyothercriteriontowhichRussell
non-redness. That requirementis further forced upon us because ofthe can appeal to establishthat negativefacts are indeed genuine? Sainsbury
way in which negative atomic propositions have b~en analyzed. proposes the following:
"Not(thisis red)" islogicallyequivalentto "This is non-red". The predi
cate "non-red" is unanalyzable; it's meaning can only be grasped·by afactstatedbyatrue PL-sentence'p' isgenuineiffthereisnonon-emptysetX
oftrue PL-sentences, each shorter than 'p', such that X entails 'p'..(For this
acquaintancewith the negative propertywhichitstands for. This brings
purposeone needs tostipulate thatonePL-sentenceisshorterthan another iff
us to the most critical question which the proposed analysis ofnegative
[he first contains fewer symbols than the second, where parentheses are not
facts mustface. Canone be acquaintedwith anegative property?
counted as symbols, and each name and simple predicate counts as a single
An immediate problem presents itself Properties are what Russell symbol.) (Russell, ibid.)
calls "universals, that is to say, general ideas, such as whiteness, diversity,
brotherhood, andso on" (PP2, p. 52).Thedifficultyis thatuniversals, not Bya"PL-sentence" Sainsburyofcourse means aproposition expressible
being part of the sensory world, cannot be objects of acquaintance, in the logicallyperfectlanguage.
including therefore negative universals such as non-redness. This prob Thiscriterionposes aserious threat to thegenuine natureofnegative
lem is met bypointingout that for Russell whatone is acquainted with facts. Foras Sainsburyargues, "thetruth of'-red(this)' will not, accord
are instances of universals, and on the basis of this acquaintance we ing to our principle, generate agenuine negative fact, sinceitis entailed
abstract to the universal itself (Sainsbury, p. 31). The question now by the shorter '(white(this))', and, as we have seen, Russell appears to
arises,canwebeacquaintedwithan instanceofanegativeuniversalsuch allow that both predicateswill occurin the perfectlanguage" (p. 223).
as non-redness. Sainsbury's argument rests upon the assumption that "(white(this))"
Russell himselfdoes not give a definitive answer. However in a later entails, that is logically implies "-red(this)". The entailment goes
58 WAYNE A. PATTERSON TheLogicalStructureofRussell'sNegativeFacts 59
through if and only if the predicates "red" and "white" are logically not.'"31 If Russell, identifying Wittgenstein's elementary propositions
incompatible. Yet this is aviewwhich Russell does not hold. "Red and with his own atomic propositions, were have to taken this remark seri
blue are no more logicallyincompatible than red and round" (IMT,., p. ously, then our proposedanalysiswould collapse. For "This is non-red"
82). (Note again the contrastwith Wittgenstein. "The statement that a would no longer be a (negative) atomic proposition, the meaning of
point in the visual field has two different colours at the same time is a which could only be grasped through the Principle ofAcquaintance. If
contradiction" [Tractatus, 6.3751].) AdmittedlyRussell's viewwas stated Russell did take the remark seriously it may go some way towards
at alater point in his career, but there is no evidence to suggest that he explaining his subsequent rejection ofnegative facts, a point we shall
felt otherwise at the time ofhis 1918 lectures. Accordingly Sainsbury's discuss shortly. But Russell need not adhere to the Wittgenstein sugges
proposedentailmentfails. tion. It is arguable that both "This is red" and "This is non-red" are
Finallyone might question Sainsbury's criterion for what constitutes atomic, in the sense that understanding such propositions requires
agenuine fact. According to that criterion afact is genuine ifthe corre acquaintanc~ withwhat theconstituents ofthe propositions standfor.
sponding proposition satisfies certain linguistic criteria ofthe logically AsRussell is ultimatelyconcernedwithprovidinganaccountoffalse
perfect language. It is likely that Russell would protest that we cannot hood, we are naturally required to say that "This is red" and "This is
settle questions ofontologyin this way. Hewrites, "Itseems to me that non-red" are mutually contradictory. This contradicts Wittgenstein's
the business ofmetaphysics is to describe the world, and it is in my claim that "the logical productoftwo elementarypropositions can nei
opinionarealdefinitequestionwhetherinacompletedescriptionofthe ther be a tautology nor a contradiction" (Tractatus, 6.3751). In other
worldyou would have to mention negative facts or not."3°The follow words atomic propositions are logically independent of one another.
ing criterion ofwhat.constitutesagenuine fact seems more in line with Clark attributes this view to Russell, but gives no argument to support
Russell'sviews concerningwhat one must admit into one's ontology. As it.32 Sainsbury, on the other hand, denies the view: "Russell's simplest
the logically perfect language is purportedly adequate for a complete kind ofpropo~itions('atomic propositions') are not logically indepen
descriptionoftheworld, then inaccountingforthe truthofsome prop dent" (Russel~ p. 52). However, Sainsbury bases his argument on the
ositioninthatlanguageweadmitintoourontologyanewkindoffactif view that "This is white" and 'This·is red" cannot both be true and so
the truth ofthat proposition cannot be accounted for by appealing to are not logically independent. But as we have seen earlier, these two
facts alreadyadmittedinto ourontology. propositions for Russell are not logicallyincompatible andconsequently
.On this criterion Russell is forced to admit negative facts because he ate logically independent. Accordingly Russell cannot adopt the Sains
feels that the truth ofnegative propositions cannot be accounted for in buryview that all atomicpropositions are notlogicallyindependent.
terms of positive atomic facts in the way that Demos suggests. However, thete is another way ofdenying Wittgenstein's claim that
(Incidentally this criterion fits well with Russell's postulation ofgeneral all aromic propositions are logically independent. Rather than take the
facts, as he argues that the truth of general propositions cannot be contraryofthis claim, as Sainsbury does, we take its contradictory; not
accountedfor byappealing to particular facts.) all atomic propositions are logically independent. We can now claim
Onefinal objectionto theproposedanalysisofRussell's negativefacts that some atomic propositions are logically independent, "This is red"
mustnowbefaced. Anscombewrites that"Russell in hisletters toWitt
genstein after receiving the text ofthe Tractatusonce asked whether the
negations ofelementarypropositionswere themselves elementaryprop
ositions, and received the indignant-sounding rejoinder: 'Of course 31 G. E. M. Anscombe, AnIntroduction to Wittgenstein's Tractatus, 3rded. (London:
Hutchinson, 1967), p. 34. [We now know that Russell didn't actually ask, but com
mented (Q Wingenstein: "4.21I I gather no dementary prop is negative." See B. E
McGuinness and G. H. von Wrighr, "Unpublished Correspondence between Russdl
andWingenstein", RusselL, n.s.10(1990):108.-Ed.]
3° Lf(,p.215; Papers8:190. 31 BertrandRussell'sPhilosophy,p.1I5.
60 WAYNE A. PATTERSON TheLogicalStructureofRussell'sNegativeFacts 61
and "This is white" for instance, while others are not. In particular the product is neither atautologynor acontradiction. (We maydefine a
logical product of any atomic proposition and its negation will be a tautologyas the falsehood ofacontradiction.)
contradiction. As Russell nowhere explicitly embraces Wittgenstein's 7. Twopropositionsarelogicallyincompatibleifandonlyiftheirlogical
position, and since the proposed denial ofthat view does not conflict productis acontradiction.
with any ofthe principles underpinning his 1918 atomism, Russell can
freely rejectit. We now turn to the question ofwhy Russell subsequently rejected
Lest there be any confusion about what constitutes a positive and negative facts. Sainsbury claims that the rejection is based on Russell's
negative predicate in the logically perfect language, the answer lies in unwillingness to admitthatinalogicallyperfectlanguagetherewill bea
Russell's replyto aquestion raisedattheendofhisthirdlecture. Is there simple contradictory of every simple predicate (Russell p. 222). As
any formal test as to whether a proposition is positive or negative? Russell permits analysis in terms ofnegation, a predicate like "is dead"
Russell replies that "There is no formal test."33 He is ofcourse referring could be analyzed as "is not alive" (p. 223). Consequently "is dead",
to ordinarylanguages in which it is completely arbitrary as to whether being analyzable, is not apredicatewhich would appear in the logically
we regard"Harryis absent" or"Harryis present" as positiveornegative. perfect language as "this would involve a redundancy of vocabulary
Butinthelogicallyperfectlanguagethere wouldbeaformal test. "Inthe whichwould notobtain inaperfectlanguage" (ibid).
perfect logical language that I sketched in theory, it would always be This argument deserves careful scrutiny. We can eliminate "is dead"
obvious atoncewhether a propositionwas positive or negative" (ibid). from thelanguagebecauseitisanalyzableintermsof"isnotalive". Note
The presence ofthe negation operator "not" (or "non"), which applies that thefunction of"not" in "is notalive" mustbe interpretedas negat
solelyto predicates ofthe perfectlanguage, immediatelyannounces that ing the predicate, in effect, "non-alive". Sainsbury's point is that in the
the proposition (and the predicate) is negative. logically perfect language no positivepredicate ("dead") will contain its
By taking the notion of a negative property as fundamental and simple positive contradictory ("alive") as one of these predicates is
objectiveRussellisinapositiontogiveexplicitdefinitionsoftheinterre analyzablein termsoftheother. To thiswecanreadilyagree. But"alive"
lated notions of falsehood, incompatibility, logical independence and and "non-alive" are not both positive predicates and our not, on this
conttadiction. To summarizewe have thefollowing: view, analyzable in terms ofone another. Theyare simple unanalyzable
predicateswhichare nevertheless contradictory.
I. "Not{a is F)" is logically equivalent to "a is non-F". In other words, Itissuggestedthatthefundamental reasonwhyRussellrejectednega
necessarily"Not{a isF)" is true ifand onlyif"a is non-F" is true. tive facts lies with what appears to be an insuperable epistemological
2. "a is non-F" is tiue ifand onlyifthat proposition corresponds truly problem. The central difficulty with Russell's account is that a simple
with the negativefact that ahas the propertyofnon-F-ness. predicate such as "non-red", standing for the negative propertyofnon
3. "a isF" isfalse ifand onlyif"aisnon-F" is true. redness, is unanalyzable. An unanalyzable predicate for Russell is one
4. The predicates "F" and "non-F" are contradictory ifand only ifthe whose meaning can only be grasped by acquaintance with what the
propositions "a isF" and"a isnon-F" arecontradictory. predicatestands for. A typical example is the predicate "red". "You can
5. The propositions "a is F" and "a is non-F" are contradictory ifand not understandthe meaningoftheword 'red' exceptthroughseeing'red
only if they cannot both be true and cannot both be false. (We things. There is no other way in which it can be done. It is no use to
alreadyknowwhat is meant bysayingthataproposition is false.) learn languages, or to look up dictionaries. None ofthese things will
6. Two propositions are logicallyindependentifand onlyiftheir logical helpyou to understand the meaningoftheword 'red'."34
33 IK,p.215; Papers8:190. 34 IK,p.194;Papers8:173-
TheLogicalStructureofRussell'sNegativeFacts 63
62 WAYNE A. PATTERSON
If"non-red" issimilarlyunanalyzable thentheonlywaywecangrasp theexistenceofnegativefacts.
its meaningis byseeingnon-red things. Butarguablywe neversee non Now the problem looms large. If an image-proposition is always
red things. What we actuallysee is some othercolour, aview which, as positive, since we cannotvisualize a negative property, then how do we
wesawearlier, Demoswishes to propose. Furthermore, ifwewere to try accountfor the falsehood ofsuch propositions? Correspondencewith a
to teachsomeone the meaningof"non-red" byacquainting that person negative fact, containing as constituent a negative property, will no
withan instanceofit, howcouldwe possiblysucceedunless that person longer work, and we are left with are original question. What makes a
alreadyunderstoodthe meaningof"red"?Nowifthe meaningof"non proposition false?
red" is to begrasped through understandingthe meaningof"red", then Russell's answer is that "the 'not' belongs to the feeling, not to the
"non-red" ceasesto be unanalyzable, for the on(ywaythe meaningofan content ofthe proposition" (ibid). This is an important shift which is
unanalyzable predicate can be graspedis through acquaintance, and not further developed in a later work, An Inquiry into Meaningand Truth.
byunderstandingthe meaningsofanyotherwords orexpressions. There the notion ofacquaintance is replacedwith the notion of"notic
EvidenceofRussell's awarenessandconcernwiththisepistemological ing". Noticing involves both perception (acquaintance) and a proposi
problem can befound in his 1919 article, "OnPropositions: WhatThey tional attitude. "A negative basic proposition thus requires a proposi
Are and HowTheyMean". Here Russell distinguishes between "word tionalattitude, inwhich thepropositionconcernedis theonewhich, on
propositions" and "image-propositions". "As a general rule, ~ word thebasisofperception, isdenied" (p. 163). Russelldoes notsaywhatthis
proposition 'means' an image-proposition; this is the case with false propositional attitude is. Still later in Human Knowledge he makes his
propositions as well as with true ones, since image-propositions are as view explicit; it is a disinclination to believe that the positive proposi
capable offalsehood as word-propositions."35 This marks a shift from tion, which has been negated, is true. "I think we may say that 'not'
the1918 lectures in thataproposition is no longersimplyasentence; an means something like: 'You do right to reject the beliefthat....' And
(image) proposition is the meaning ofasentence. What is importantis 'rejection' means, primarily, a movement of aversion. A belief is an
that an image-proposition can be true or false, and is true or false impulse towards some action, and the word 'not' inhibits this impulse"
dependingupon its correspondencewith the factwhich itstands for. (HI(, pp. 519-20). Russell has bythis time completelyrejected negative
As Russell still maintains that there are negative facts, one might be facts because "the world can be described without the use ofthe word
tempted to think that a negative image-proposition is true because it 'not'. Ifthe sun is shining, the statement 'the sun is shining' describes a
corresponds with some negative fact. This interpretation fails immedi fact which takes place independentlyofthe statement. But ifthe sun is
atelywhen Russell states that "Not only are image-propositions always not shining, there is not a fact sun-not-shiningwhich is affirmed by the
positive,buttherearenoteventwo kinds ofpositiveimage-propositions truestatement 'thesunis notshining'" (p. 520).
as thereareofword-propositions.There is no'not' inan image-proposi In the 1918 lectures Russell was wrestling with the fundamental
tion...."36 Most significantly he goes on to say "There is no way of notionsoffalsehood, incompatibilityand negation. At thatstage he felt
visualizing ~-not-to-the-left-of-B'. When we attempt it, we find our that one ofthese notions must somehowhook directlyonto the world,
selves visualizing ~-to-the-right-of-B' or something ofthe sort" (ibid). failingwhichwewouldnothaveanadequateexplanationofwhatweare
Thislookssuspiciouslylike theviewwhichDemosproposes,butwhatis saying when we deny a fact. As falsehood and incompatibility were
relevantfor ourdiscussion is thatclearlyRussell is denyingthatonecan found to be inappropriate candidates, Russell, as he admits somewhat
beacquaintedwith (perceive) anegative property.Yethe refuses to deny reluctantly, chose negation as his vehicle. Having done so, it then
becameastraightforwardmatterto definefalsehood andincompatibility
in terms ofthis fundamental notion. "On Propositions" appears to rep
resent a transitional stage in which Russell is still clinging to the exist
35 LK,p.308; Papers8: 297· ence ofnegative facts, while realizing that there is a serious epistemic
36 LK,p.317;Papers8:304·