Bertrand Russell (1872–1970) described his philosophy as“logical atomism”, by which he meant to endorse both ametaphysical view and a certain methodology for doing philosophy. Themetaphysical view amounts to the claim that the world consists of aplurality of independently existing things exhibiting qualities andstanding in relations. According to logical atomism, all truths areultimately dependent upon a layer of atomic facts, which consisteither of a simple particular exhibiting a quality, or multiple simpleparticulars standing in a relation. The methodological view recommendsa process of analysis, whereby one attempts to define or reconstructmore complex notions or vocabularies in terms of simpler ones. Thisprocess often reveals that what we take to be brute necessities areinstead purely logical. According to Russell, at least early on duringhis logical atomist phase, such an analysis could eventually result ina language containing only words representing simple particulars, thesimple properties and relations thereof, and logical constants, which,despite this limited vocabulary, could adequately capture all truths.

Russell’s logical atomism had a profound influence on analyticphilosophy in the first half of the 20th century; indeed, it isarguable that the very name “analytic philosophy” derivesfrom Russell’s defense of the method of analysis.

• 1. Introduction
• 2. Origins and Development of Russell’s Logical Atomism
  • 2.1 The Break with Idealism and the Nature of Relations
  • 2.2 Propositions inThe Principles of Mathematics
  • 2.3 The Theory of Descriptions
  • 2.4 Classes, Propositions and Truth inPrincipia Mathematica
• 3. Russell’s Philosophical Method and the Notion of Analysis
• 4. Ontological Aspects of Russell’s Logical Atomism
  • 4.1 Russellian Facts: Atomic, Negative and General
  • 4.2 Logical Atoms and Simplicity
  • 4.3 Atomic Propositions, Logical Independence and Necessity
• 5. Influence and Reception
• Bibliography
  • Works By Russell
  • Secondary Literature
• Academic Tools
• Other Internet Resources
• Related Entries

1. Introduction

Bertrand Russell (1872–1970) introduced the phrase“logical atomism” to describe his philosophy in 1911(RA, 94), and used the phrase consistently throughout the1910s and 1920s (OKEW, 12;SMP, 84;PLA,178;LA, 323;OOP, 259). Russell’s logicalatomism is perhaps best described as partly a methodologicalviewpoint, and partly a metaphysical theory.

Methodologically, logical atomism can be seen as endorsement ofanalysis, understood as a two-step process in which oneattempts to identify, for a given domain of inquiry, set of beliefs orscientific theory, the minimum and most basic concepts and vocabularyin which the other concepts and vocabulary of that domain can bedefined or recast, and the most general and basic principles fromwhich the remainder of the truths of the domain can be derived orreconstructed.

Metaphysically, logical atomism is the view that the world consists ina plurality of independent and discrete entities, which by comingtogether form facts. According to Russell, a fact is a kind ofcomplex, and depends for its existence on the simpler entities makingit up. The simplest sort of complex, anatomic fact, wasthought to consist either of a single individual exhibiting a simplequality, or of multiple individuals standing in a simple relation.

The methodological and metaphysical elements of logical atomism cometogether in postulating the theoretical, if not the practical,realizability of a fully analyzed language, in which all truths couldin principle be expressed in a perspicuous manner. Such a“logically ideal language”, as Russell at times called it,would, besides logical constants, consist only of words representingthe constituents of atomic facts. In such a language, the simplestsort of complete sentence would be what Russell called an“atomic proposition”, containing a single predicate orverb representing a quality or relation along with the appropriatenumber of proper names, each representing an individual. The truth orfalsity of an atomic proposition would depend entirely on acorresponding atomic fact. The other sentences of such a languagewould be derived either by combining atomic propositions usingtruth-functional connectives, yieldingmolecularpropositions, or by replacing constituents of a simplerproposition by variables, and prefixing a universal or existentialquantifier, resulting ingeneral andexistentialpropositions. According to the stronger form of logical atomismRussell at times adopted, he held that in such a language,“[g]iven all true atomic propositions, together with the factthat they are all, every other true proposition can theoretically bededuced by logical methods” (PM2, xv; cf.OKEW, 50). This puts the truth or falsity of atomicpropositions at the core of Russell’s theory of truth, andhence, puts atomic facts at the center of Russell’smetaphysics.

Russell also at times suggests that analysis demonstrates that what wetake to be essential or necessary properties of things and relationsbetween things are the result of the logical forms the these things,properties and relations are logically constructed to have. Thissuggests that there are no such connections between simple entities,that all atomic propositions are independent of each other, and thatall forms of necessity reduce to (formal) logical necessity. Somecommentators interpret these theses to be central to Russell’slogical atomism, though explicit commitment to them is scant in hiswritings. A plausible reading is that while Russell did not want tocommit himself to the view that no non-logical necessities exist, hethought it is nonetheless sound methodology in analysis to attempt todo away with them.

In what follows, various aspects of Russell’s logical atomismare discussed in greater detail. The next section discusses theorigins of logical atomism in the break made by Russell and G.E. Moorefrom the tradition of British Idealism, and its development during theyears in which Russell worked onPrincipia Mathematica. Insection 3, we examine Russell’s notion of analysis as aphilosophical method, and give various examples of analysis as Russellunderstood it. In section 4, we turn to a more detailed look atcertain metaphysical aspects of Russell’s atomism, and inparticular, the nature and classification of facts, as well certainpoints of controversy regarding his views. In particular, we’llexamine whether or not Russell’s logical atomism necessarilypresupposes a fundamental realm of ultimate simples, and whether ornot the atomic propositions of Russell’s atomism were understoodas logically independent. The final section is dedicated to adiscussion of the influence and reception of Russell’s logicalatomism within the subsequent philosophical tradition.

2. Origins and Development of Russell’s Logical Atomism

2.1 The Break with Idealism and the Nature of Relations

In 1959, Russell himself dated his first acceptance of logical atomismto the years 1899–1900, when he and G.E. Moore rejected the maintenets of the dominant school of philosophy in Britain at the time (towhich both had previously been adherents), the tradition ofneo-Hegelian Idealism exemplified in works of F.H. Bradley and J.M.E.McTaggart, and adopted instead a fairly strong form of realism(MPD, 9). Of their break with idealism, Russell wrote that“Moore led the way, but I followed closely in hisfootsteps” (MPD, 42).

In 1899, Moore published a paper entitled “The Nature ofJudgment”, in which he outlined his main reasons for acceptingthe new realism. It begins with a discussion of a distinction made byBradley between different notions of idea. According to Bradley, thenotion of idea understood as a mental state or mental occurrence isnot the notion of “idea” relevant to logic or to truthunderstood as a relationship between our ideas and reality. Instead,the relevant notion of idea is that of a sign or symbol representingsomething other than itself, or an idea understood as possessingmeaning. Bradley understood meaning in terms of “a part of thecontent … [of an idea] cut off, fixed by the mind, andconsidered apart from the existence of the sign” (Bradley 1883,8). Moore agreed with Bradley that it is not the mental occurrencethat is important to logic. However, with regard to Bradley’ssecond notion of “idea”, Moore accused Bradley ofconflating the symbol with the symbolized, and rejectedBradley’s view that what is symbolized is itself a part of theidea and dependent upon it. Moore introduces the term“concept” for the meaning of a symbol; for Moore, what itis for different ideas to have a common content is for them torepresent the same concept. However, the concept itself is independentof the ideas. When we make a judgment, typically, it is not our ideas,or parts of our ideas, which our judgment is about. According toMoore, if I make an assertion, what I assert is nothing about my ideasor my mental states, but a certain “connexion ofconcepts”.

Moore went on to introduce the term “proposition” forcomplexes of concepts such as that which would be involved in a beliefor judgment. While propositions represent the content of judgments,according to Moore, they and their constituents are entirelyindependent from the judging mind. Some propositions are true, someare not. For Moore, however, truth is not a correspondencerelationship between propositions and reality, as there is nodifference between a proposition—understood as amind-independent complex—and that which would make it true(Moore 1899, 5; Moore 1901). The facts of the world then consist oftrue propositions, themselves understood as complexes of concepts.According to Moore, something “becomes intelligible first whenit is analyzed into its constituent concepts” (Moore 1899, 8).“The Nature of Judgment” had a profound influence onRussell, who later heralded it as the first account of the “newphilosophy” to which he and Moore subscribed (MPD,42).

For his own part, Russell often described his dissatisfaction with thedominant Idealist (and largely Monist) tradition as primarily havingto do with the nature and existence of relations. In particular,Russell took issue with the claim found in Bradley and others, thatthe notion of a fundamental relation between two distinct entities isincoherent. Russell diagnosed this belief as stemming from awidespread logical doctrine to the effect that every proposition islogically of subject-predicate form. Russell was an ardent opponent ofa position known as the “doctrine of internal relations”,which Russell stated as the view that “every relation isgrounded in the natures of the related terms” (MTT,139). Perhaps most charitably interpreted (for other interpretationsconsidered by Russell, seeBReal, 87), this amounts to theclaim thata’s bearing relationR tob is always reducible to properties held bya andb individually, or to a property held by the complex formedofa andb.

In the period leading up to his own abandonment of idealism, Russellwas already pursuing a research program involving the foundations ofarithmetic (see, e.g.,AMR). This work, along with hisearlier work on the foundations of geometry (seeEFG), hadconvinced him of the importance of relations for mathematics. However,he found that one category of relations, viz., asymmetrical transitiverelations, resisted any such reduction to the properties of the relataor the whole formed of them. These relations are especially importantin mathematics, as they are the sort that generates series. Considerthe relation ofbeing taller than, and consider the fact thatShaquille O’Neal is taller than Michael Jordan. It might bethought that this relation between O’Neal and Jordan can bereduced to properties of each: O’Neal has the property of being7′2″ tall, and Jordan has the property of being6′6″ tall, and thetaller than relation in thiscase is reducible to their possession of these properties. Theproblem, according to Russell, is that for this reduction to hold,there must be a certain relation between the properties themselves.This relation would account for the ordering of the various heightproperties, putting the property of being-6′8″-tall inbetween that of being-7′2″-tall and that ofbeing-6′6″-tall. This relation among the properties woulditself be an asymmetrical and transitive relation, and so the analysishas not rid us of the need for taking relations as ultimate. Anotherhypothesis would be that there is such an entity as the whole composedof O’Neal and Jordan, and that the relation between the two menis reducible to some property of this whole. Russell’s complaintwas that since the whole composed of O’Neal and Jordan is thesame as the whole composed of Jordan and O’Neal, this approachhas no way to explain what the difference would be betweenO’Neal’s being taller than Jordan and Jordan’s beingtaller than O’Neal, as both would seem to be reduced to the samecomposite entity bearing the same quality (seePOM,221–26).

Russell’s rejection of the doctrine of internal relations isvery important for understanding the development of his atomisticdoctrines in more than one respect. Certain advocates of the claimthat a relation must always be grounded in the “nature” ofits relata hold that in virtue ofa relating tob,a must have a complex nature that includes its relatedness tob. Since every entity presumably bears some relation to anyother, the “nature” of any entity could arguably bedescribed as having the same complexity as the universe as a whole (ifindeed, it even makes sense on such a picture to divide the world intodistinct entities at all, as many denied). Moreover, according to somewithin this tradition, when we considera, obviously we donot consider all its relations to every entity, and hence graspa in a way that falsifies the whole of whata is.This led some to the claim that “analysis isfalsification”, and even to hold that when we judge thata is the father ofb, and judge thata isthe son ofc, thea in the first judgment is notstrictly speaking the samea as involved in the secondjudgment; instead, in the first we deal only witha-quâ-father-of-b in the first, anda-quâ-son-of-c in the second (cf.BReal, 89;MTT, 140).

In contradistinction to these views, Russell adopted what he called“the doctrine of external relations”, which he claimed“may be expressed by saying that (1) relatedness does not implyany corresponding complexity in therelata; (2) any givenentity is a constituent of many different complexes”(BReal, 87). This position on relations allowed Russell toadopt a pluralist philosophy in which the world is conceived ascomposed of many distinct, independent entities, each of which can beconsidered in isolation from its relations to other things, or itsrelation to the mind. In 1911 Russell claimed that this doctrine wasthe “fundamental doctrine” of his realistic position(BReal, 87; cf.RA, 92;POM, 226), and itrepresents perhaps the most important turning point in the developmentof his logical atomism.

2.2 Propositions inThe Principles of Mathematics

Russell’s first published account of his newfound realism camein the 1903 classicThe Principles of Mathematics(POM). Part I ofPOM is dedicated largely to aphilosophical inquiry into the nature of propositions. Russell tookover from Moore the conception of propositions as mind-independentcomplexes; a true proposition was then simply identified by Russellwith a fact (cf.MTCA, 75–76). However, Moore’scharacterization of a proposition as a complex ofconceptswas largely in keeping with traditional Aristotelian logic in whichall judgments were thought to involve a subject concept, copula andpredicate concept. Russell, owing in part to his own views onrelations, and in part from his adopting certain doctrines stemmingfrom Peano’s symbolic logic, sought to refine and improve uponthis characterization.

In the terminology introduced inPOM, constituents of aproposition occur either “as term” or “asconcept”. An entity occurs “as term” when it can bereplaced by any other entity and the result would still be aproposition, and when it is one of the subjects of the proposition,i.e., something the proposition is “about”. An entityoccursas concept when it occurs predicatively, i.e., only aspart of the assertion made about the things occurring as term. In thepropositionSocrates is human, the person Socrates (the manhimself) occurs as term, but humanity occurs as concept. In thepropositionCallisto orbits Jupiter, Callisto (the moonitself) and Jupiter (the planet) occur as term, and the relation oforbiting occurs as concept. Russell used the word“concept” for all those entities capable of occurring asconcept—chiefly relations and other universals—and theword “thing” for those entities such as Socrates, Callistoand Jupiter, that can only occur as term. While Russell thought thatonly certain entities were capable of occurring as concept, at thetime, he believed that every entity was capable of occurring as termin a proposition. In the propositionWisdom is a virtue, theconcept wisdom occurs as term. His argument that this held generallywas that if there were some entity,E, that could not occuras term, there would have to be a fact, i.e., a true proposition, tothis effect. However, in the propositionE cannot occur as term ina proposition,E occurs as term (POM,44–45).

Russell’s 1903 account of propositions as complexes of entitieswas in many ways in keeping with his views as the nature of complexesand facts during the core logical atomist period of 1911–1925.In particular, at both stages he would regard the simple truth that anindividuala stands in the simple relationR to anindividualb as a complex consisting of the individualsa andb and the relationR. However, thereare a number of positions Russell held in 1903 that were abandoned inthis later period; some of the more important were these: (1) in 1903,Russell was committed to a special kind of propositional constituentcalled a “denoting concept”, involved in descriptive andquantified propositions; (2) in 1903, Russell believed that there wassuch a complex, i.e., a proposition, consisting ofa,b andR even when it is nottruethata bears relationR tob, and (3) in 1903,Russell believed in the reality of classes, understood as aggregateobjects, which could be constituents of propositions. In each case, itis worth, at least briefly, discussing Russell’s change ofheart.

2.3 The Theory of Descriptions

InPOM, Russell expressed the view that grammar is a usefulguide in understanding the make-up of a proposition, and even that inmany cases, the make-up of a proposition corresponding to a sentencecan be understood by determining, for each word of the sentence, whatentity in the proposition is meant by the word (POM, 46).Perhaps in part because such phrases as “all dogs”,“some numbers” and “the queen” appear as agrammatical unit, Russell came to the conclusion that they made aunified contribution to the corresponding proposition. Because Russellbelieved it impossible for a finite mind to grasp a proposition ofinfinite complexity, however, Russell rejected a view according towhich the (false) proposition designated by

1. All numbers are odd.

actually contains all numbers (POM, 145). Similarly, althoughRussell admitted that such a proposition as (1) is equivalent to aformal implication, i.e., a quantified conditional of the form:

2. ∀x(x is a number ⊃x is odd)

Russell held that they are nevertheless distinct propositions(POM, 74). This was perhaps in part due to the difference ingrammatical structure, and perhaps also because the former appearsonly to be about numbers, whereas the latter is about all things,whether numbers or not. Instead, Russell thought that the propositioncorresponding to (1) contains as a constituent the denoting conceptall numbers. As Russell explained them, when denotingconcepts occur in a proposition, the proposition is not about them butabout other entities to which the denoting concepts bear a specialrelation. So when the denoting conceptall numbers occurs ina proposition, the proposition is not about the denoting concept, butinstead about 1 and 2 and 3, etc.

In 1905, Russell abandoned this theory in favor of his celebratedtheory of definite and indefinite descriptions outlined in the paper“On Denoting”. What precisely lead Russell to becomedissatisfied with his earlier theory, and the precise nature of theargument he gave against denoting concepts (and similar entities suchas Frege’s senses), are a matter of great controversy, and havegiven rise to a large body of secondary literature. For presentpurposes, it can merely be noted that Russell professed an inabilityto understand the logical form of propositionsabout denotingconcepts themselves, as in the claim that “The present Kingof France is a denoting concept” (cf.OD,48–50). According to the new theory adopted, the propositionexpressed by (1) was now identified with that expressed by aquantified conditional such as (2). Similarly, the propositionexpressed by

3. Some number is odd.

was identified with the existentially quantified conjunctionrepresented by

4. ∃x(x is a number &x isodd)

Perhaps most notoriously, Russell argued that a proposition involvinga definite description, e.g.,

5. The King of France is bald.

was to be understood as having the structure of a certain kind ofexistential statement, in this case:

6. ∃x(x is King of France &∀y(y is King of France ⊃x =y) &x is bald)

Russell cited in favor of these theories that they provided an elegantsolution to certain philosophical puzzles. One involves how it is thata proposition can be meaningful even if it involves a description orother denoting phrase that does not denote anything. Given the aboveaccount of the structure of the proposition expressed by “theKing of France is bald”, while France and the relation ofbeing King of are constituents, there is no constituentdirectly corresponding to the whole phrase “the King ofFrance”. The proposition in question is false, since there is novalue ofx which would make it true. One is not committed toa nonexistent entity such as the King of France simply in order tounderstand the make-up of the proposition. Secondly, this theoryprovides an answer to how it is that certain identity statements canbe both true and informative. On the above theory, the propositioncorresponding to:

7. The author of Waverly = Scott

would be understood as having the following structure:

8. ∃x(x authored Waverly &∀y(y authored Waverly ⊃x =y) &x = Scott)

If instead, the proposition corresponding to (7) was simply a complexconsisting of the relation of identity, Scott, and the author ofWaverly himself, since the author of Waverly simplyis Scott,the proposition would be the same as the uninformative propositionScott = Scott. By showing that the actual structure of theproposition is quite a bit different from what it appears from thegrammar of the sentence “The author of Waverly = Scott”,Russell believed he had shown how it might be more informative than atrivial instance of the law of identity (OD,51–54).

The theory of “On Denoting” did away with Russell’stemptation to regard grammar as a very reliable guide towardsunderstanding the structure or make-up of a proposition. Especiallyimportant in this regard is the notion of an “incompletesymbol”, by which Russell understood an expression that can bemeaningful in the context of its use within a sentence, but does notby itself correspond to a constituent or unified part of thecorresponding proposition. According to the theory of “OnDenoting”, phrases such as “the King of France”, or“the author of Waverly” were to be understood as“incomplete symbols” in this sense. The general notion ofan “incomplete symbol” was applied by Russell in waysbeyond the theory of descriptions, and perhaps most importantly, tohis understanding of classes.

2.4 Classes, Propositions and Truth inPrincipia Mathematica

InPOM, Russell had postulated two types of compositeentities:unities andaggregates (POM,140f). By a “unity” he meant a complex entity in which theconstituent parts are arranged with a definite structure. Aproposition was understood to be a unity in this sense. By an“aggregate”, he meant an entity such as a class whoseidentity conditions are governed entirely by what members or“parts” it has, and not by any relationships between theparts. By the time of the publication of the first edition ofPrincipia Mathematica in 1910, Russell’s views aboutboth types of composite entities had changed drastically.

Russell fundamentally conceived of a class as the extension of aconcept, or as the extension of a propositional function; indeed, inPOM he claims that “a class may bedefined asall the terms satisfying some propositional function”(POM, 20). However, Russell was aware already at the time ofPOM that the supposition there is always a class, understoodas an individual entity, as the extension of every propositionalfunction, leads to certain logical paradoxes. Perhaps the most famous,now called “Russell’s paradox”, derived fromconsideration of the class,w, of all classes not members ofthemselves. The classw would be a member of itself if itsatisfied its defining condition, i.e., if it were not a member ofitself. Similarly,w would not be a member of itself if itdid not satisfy its defining condition, i.e., if it were a member ofitself. Hence, both the assumption that it is a member of itself, andthe assumption that it is not, are impossible. Another related paradoxRussell often discussed in this regard has since come to be called“Cantor’s paradox”. Cantor had proven that if aclass hadn members, that the number of sub-classes that canbe taken from that class is 2ⁿ, and also that2ⁿ >n, even whenn isinfinite. It follows from this that the number of subclasses of theclass of all individuals, (i.e., the number of different classes ofindividuals) is greater than the number of individuals. Russell tookthis as strong evidence that a class of individuals could not itselfbe considered an individual. Likewise, the number of subclasses of theclass of all classes is greater than the number of members in theclass of all classes. This Russell took to be evidence that there issome ambiguity in the notion of a “class” so that thesubclasses of the class of “all classes” would notthemselves be among its members, as it would seem.

Russell spent the years between 1902 and 1910 searching for aphilosophically motivated solution to such paradoxes. He triedsolutions of various sorts. However, in late 1905, after the discoveryof the theory of descriptions, he became convinced that an expressionfor a class is an “incomplete symbol”, i.e., that whilesuch an expression can occur as part of a meaningful sentence, itshould not be regarded as representing a single entity in thecorresponding proposition. Russell dubbed this approach the “noclasses” theory of classes (see e.g.,TNOT, 145),because, while it allows discourse about classes to be meaningful, itdoes not posit classes as among the fundamental ontological furnitureof the world. The precise nature of Russell’s “noclasses” theory underwent significant changes between 1905 and1910. However, in the version adopted in the first edition ofPrincipia Mathematica, Russell believed that a statementapparently about a class could always be reconstructed, usinghigher-order quantification, in terms of a statement involving itsdefining propositional function. Russell believed that whenever aclass term of the form “{z|ψz}”appeared in some sentence, the sentence as a whole could be regardedas defined as follows (cf.PM, 188):

f({z|ψz})  =_df  ∃φ((x)(φ!x ≡ ψx)&f(φ))

The above view can be paraphrased, somewhat crudely, as the claim thatany truth seemingly about a class can be reduced to a claim about someor all of its members. For example, it follows from this contextualdefinition of class terms that the statement to the effect that oneclassA is a subset of another classB is equivalentto the claim that whatever satisfies the defining propositionalfunction ofA also satisfies the defining propositionalfunction ofB. Russell also sometimes described this as theview that classes are “logical constructions”, not part ofthe “real world”, but only the world of logic. Another wayRussell expressed himself is by saying that a class is a“logical fiction”. While it may seem that a class term isrepresentative of an entity, according to Russell, class terms aremeaningful in a different way. Classes are not among the basic stuffof the world; yet it is possible to make use of class terms insignificant speech,as if there were such things as classes.A class is thus portrayed by Russell as a merefaçon deparler, or convenient way of speaking about all or some of theentities satisfying some propositional function.

During the period in which Russell was working onPrincipiaMathematica, most likely in 1907, Russell also radically revisedhis former realism about propositions understood as mind independentcomplexes. The motivations for the change are a matter of somecontroversy, but there are at least two possible sources. The first isthat in addition to the logical paradoxes concerning the existence ofclasses, Russell was aware of certain paradoxes stemming from theassumption that propositions could be understood as individualentities. One such paradox was discussed already in Appendix B ofPOM (527–28). By Cantor’s theorem, there must bemore classes of propositions than propositions. However, for everyclass of propositions,m, it is possible to generate adistinct proposition, such as the proposition thateveryproposition in m is true, in violation of Cantor’s theorem.Unlike the other paradoxes mentioned above, a version of this paradoxcan be reformulated even if talk of classes is replaced by talk oftheir defining propositional functions. Russell was also aware ofcertain contingent paradoxes involving propositions, such as the Liarparadox formulated involving a personS, whose only assertionat timet is the propositionAll propositions asserted byS at time t are false. Given the success of the rejection ofclasses as ultimate entities in resolving the paradoxes of classes,Russell was motivated to see if a similar solution to these paradoxescould be had by rejecting propositions as singular entities.

Another set of considerations pushing Russell towards the rejection ofhis former view of propositions is more straightforwardlymetaphysical. According to his earlier view, and that of Moore, aproposition was understood as a mind independent complex. Theconstituents of the complex are the actual entities involved, andhence, as we have seen, when a proposition is true, it is the sameentity as a fact or state of affairs. However, because somepropositions are false, this view of propositions posits objectivefalsehoods. The false proposition thatVenus orbits Neptuneis thought to be a complex containing Venus and Neptune the planets,as well as the relation of orbiting, with the relation occurring as arelation, i.e., asrelating Venus to Neptune. However, itseems natural to suppose that the relation of orbiting could onlyunite Venus and Neptune into a complex, if in fact, Venus orbitsNeptune. Hence, the presence of such objective falsehoods is itselfout of sorts with common sense. Worse, as Russell explained, positingthe existence of objective falsehoods in addition to objective truthsmakes the difference between “truth” and“falsehood” inexplicable, as both become irreducibleproperties of propositions, and we are left without an explanation forthe privileged metaphysical status of truth over falsehood (see, e.g.,NTF, 152).

Whatever his primary motivation, Russell abandoned any commitment toobjective falsehoods, and restructured his ontology of facts, andadopted a new correspondence theory of truth. In the terminology ofthe new theory, the word “proposition” was used not for anobjective metaphysical complex, but simply for an interpreteddeclarative sentence, an item of language. Propositions are thought tobe true or false depending on their correspondence, or lack thereof,withfacts.

In the Introduction toPrincipia Mathematica, as part of hisexplanation of ramified type-theory, Russell described various notionsof truth applicable to different types of propositions of differentcomplexity. The simplest propositions in the language ofPrincipiaMathematica are what Russell there called “elementarypropositions”, which take forms such as “a hasqualityq”, “a has relation [inintension]R tob”, or “a andb andc stand in relationS”(PM, 43–44). Such propositions consist of a simplepredicate, representing either a quality or a relation, and a numberof proper names. According to Russell, such a proposition is true whenthere is a corresponding fact or complex, composed of the entitiesnamed by the predicate and proper names related to each other in theappropriate way. E.g., the proposition “a has relationR tob” is true if there exists acorresponding complex in which the entitya is related by therelationR to the entityb. If there is nocorresponding complex, then the proposition is false.

Russell dubbed the notion of truth applicable to elementarypropositions “first truth”. This notion of truth serves asthe ground for a hierarchy of different notions of truth applicable todifferent types of propositions depending on their complexity. Aproposition such as “(x)(x has qualityq)” which involves a first-order quantifier, has (orlacks) “second truth” depending on whether its instanceshave “first truth”. In this case,“(x)(x has qualityq)” would betrue if every proposition got by replacing the“x” in “x has qualityq” with the proper name of an individual has“first truth” (PM, 42). A proposition involvingthe simplest kind of second-order quantifier, i.e., a quantifier usinga variable for “predicative” propositional functions ofthe lowest type, would have or lack “third truth”depending on whether its allowable substitution instances have second(or lower) truth. Because any statement apparently about a class ofindividuals involves this sort of higher-order quantification, thetruth or falsity of such a proposition will ultimately depend on thetruth or falsity of various elementary propositions about its members.

Although Russell did not use the phrase “logical atomism”in the Introduction toPrincipia Mathematica, in many ways itrepresents the first work of Russell’s atomist period. Russellthere explicitly endorsed the view that the “universe consistsof objects having various qualities and standing in variousrelations” (PM, 43). Propositions that assert that anobject has a quality, or that multiple objects stand in a certainrelation, were given a privileged place in the theory, and explanationwas given as to how more complicated truths, including truths aboutclasses, depend on the truth of such simple propositions.Russell’s work over the next two decades consisted largely inrefining and expanding upon this picture of the world.

3. Russell’s Philosophical Method and the Notion of Analysis

Although Russell changed his mind on a great number of philosophicalissues throughout his career, one of the most stable elements in hisviews is the endorsement of a certain methodology for approachingphilosophy. Indeed, it could be argued to be the most continuous andunifying feature of Russell’s philosophical work (e.g., seeHager 1994). Russell employed the methodology self-consciously, andgave only slightly differing descriptions of this methodology in worksthroughout his career (see, esp.,EFG, 14–15;POM, 1–2, 129–30;RMDP, 272–74;PM, 59;IPL, 284–85;TK, 33,158–59;OKEW, 144–45;PLA, 178–82,270–71;IMP, 1–2;LA, 324–36, 341;RTC, 687;HWP, 788–89;HK,257–59;MPD, 98–99, 162–163). Understandingthis methodology is particularly important for understanding hislogical atomism, as well as what he meant by“analysis”.

The methodology consists of a two phase process. The first phase isdubbed the “analytic” phase (although it should be notedthat sometimes Russell used the word “analysis” for thewhole procedure). One begins with a certain theory, doctrine orcollection of beliefs which is taken to be more or less correct, butis taken to be in certain regards vague, imprecise, disunified, overlycomplex or in some other way confused or puzzling. The aim in thefirst phase is to work backwards from these beliefs, taken as a kindof “data”, to a certain minimal stock of undefinedconcepts and general principles which might be thought to underlie theoriginal body of knowledge. The second phase, which Russell describedas the “constructive” or “synthetic” phase,consists in rebuilding or reconstructing the original body ofknowledge in terms of the results of the first phase. Morespecifically, in the synthetic phase, one defines those elements ofthe original conceptual framework and vocabulary of the discipline interms of the “minimum vocabulary” identified in the firstphrase, and derives or deduces the main tenets of the original theoryfrom the basic principles or general truths one arrives at afteranalysis.

As a result of such a process, the system of beliefs with which onebegan takes on a new form in which connections between variousconcepts it uses are made clear, the logical interrelations betweenvarious theses of the theory are clarified, and vague or unclearaspects of the original terminology are eliminated. Moreover, theprocedure also provides opportunities for the application ofOccam’s razor, as it calls for the elimination of unnecessary orredundant aspects of a theory. Concepts or assumptions giving rise toparadoxes or conundrums or other problems within a theory are oftenfound to be wholly unnecessary or capable of being supplanted bysomething less problematic. Another advantage is that the procedurearranges its results as a deductive system, and hence invites andfacilitates the discovery of new results.

Examples of this general procedure can be found throughoutRussell’s writings, and Russell also credits others with havingachieved similar successes. Russell’s work in mathematical logicprovides perhaps the most obvious example of his utilization of such aprocedure. It is also an excellent example of Russell’scontention that analysis proceeds in stages. Russell saw his own workas the next step in a series of successes beginning with the work ofCantor, Dedekind and Weierstrass. Prior to the work of these figures,mathematics employed a number of concepts,number,magnitude,series, limit,infinity,function, continuity, etc., without a full understanding ofthe precise definition of each concept, nor how they related to oneanother. By introducing precise definitions of such notions, thesethinkers exposed ambiguities (e.g., such as with the word“infinite”), revealed interrelations between certain ofthem, and eliminated dubious notions that had previously causedconfusion and paradoxes (such as those involved with the notion of an“infinitesimal”). Russell saw the next step forward in theanalysis of mathematics in the work of Peano and his associates, whonot only attempted to explain how many mathematical notions could be“arithmetized”, i.e., defined and proven in terms ofarithmetic, but had also identified, in the case of arithmetic, threebasic concepts (zero,successor, andnaturalnumber) and five basic principles (the so-called “Peanoaxioms”), from which the rest of arithmetic was thought to bederivable.

Russell described the next advance as taking place in the work ofFrege. According to the conception of number found in Frege’sGrundgesetze der Arithmetik, a number can be regarded as anequivalence class consisting of those classes whose members can be putin 1–1 correspondence with any other member of the class. According toRussell, this conception allowed the primitives of Peano’sanalysis to be defined fully in terms of the notion of a class, alongwith other logical notions such as identity, quantification, negationand the conditional. Similarly, Frege’s work showed how thebasic principles of Peano’s analysis could be derived fromlogical axioms alone. However, Frege’s analysis was not in allways successful, as the notion of a class or the extension of aconcept which Frege included as a logically primitive notion lead tocertain contradictions. In this regard, Russell saw his own analysisof mathematics (largely developed independently from Frege) as animprovement, with its more austere analysis that eliminates even thenotion of a class as a primitive idea (see the discussion of classesin Section 2.4 above), and thereby eliminates the contradictions (see,e.g.,RMDP, 276–81;LA, 325–27).

It was clearly a part of Russell’s view that in conducting ananalysis of a domain such as mathematics, and reducing its primitiveconceptual apparatus and unproven premises to a minimum, one is notmerely reducing the vocabulary of a certain theory, but also showing away of reducing the metaphysical commitments of the theory. In firstshowing that numbers such as 1, 2, etc., could be defined in terms ofclasses of like cardinality, and then showing how apparent discourseabout “classes” could be replaced by higher-orderquantification, Russell made it possible to see how it is that therecould be truths of arithmetic without presupposing that the numbersconstitute a special category of abstract entity. Numbers are placedin the category of “logical fictions” or “logicalconstructions” along with all other classes.

Russell’s work from the period after the publication ofPrincipia Mathematica of 1910 shows applications of thisgeneral philosophical approach to non-mathematical domains. Inparticular, his work over the next two decades shows concern with theattempt to provide analyses of the notions of knowledge, space, time,experience, matter and causation. When Russell applied his analyticmethodology to sciences such as physics, again the goal was to arriveat a “minimum vocabulary” required for the science inquestion, as well as a set of basic premises and general truths fromwhich the rest of the science can be derived. We cannot delve into allthe details of Russell’s evolving analyses here. However,according to the views developed by Russell in the mid-1910s, many ofthe fundamental notions in physics were thought to be analyzable interms of particular sensations: i.e., bits of color, auditory notes,or other simple parts of sensation, and their qualities and relations.Russell called such sensations, when actually experienced,“sense”. In particular, Russell believed that the notionof a “physical thing” could be replaced, or analyzed interms of, the notion of a series of classes of sensible particularseach bearing to one another certain relations of continuity,resemblance, and perhaps certain other relations relevant to theformulation of the laws of physics (OKEW, 86ff;RSDP, 114–15;UCM, 105). Other physicalnotions such as that of a point of space, or an instance of time,could be conceived in terms of classes of sensible particulars andtheir spatial and temporal relations (seeTK, 77;OKEW, 91–99). Later, after abandoning the view thatperception is fundamentally relational, and accepting a form ofWilliam James’s neutral monism, Russell similarly came tobelieve that the notion of a conscious mind could be analyzed in termsof various percepts, experiences and sensations related to each otherby psychological laws (AMi chaps. 1, 5;OOP chap.26; cf.PLA, 277ff). Hence, Russell came to the view thatwords as “point”,“matter”,“instant”, “mind”, andthe like could be discarded from the minimum vocabulary needed forphysics or psychology. Instead, such words could be systematicallytranslated into a language only containing words representing certainqualities and relations between sensible particulars.

Throughout these analyses, Russell put into practice a slogan hestated as follows: “Wherever possible, logical constructions areto be substituted for inferred entities” (RSDP, 115;cf.LA, 326). Rival philosophies that postulate anego ormind as an entity distinct from its mentalstates involve inferring the existence of an entity that cannotdirectly be found in experience. Something similar can be said aboutphilosophies that take matter to be an entity distinct from sensibleappearances, lying behind them and inferred from them. CombiningRussell’s suggestions that talk of “minds” or“physical objects” is to be analyzed in terms of classesof sensible particulars with his general view that classes are“logical fictions”, results in the view that minds andphysical objects too are “logical fictions”, or not partsof the basic building blocks of reality. Instead, all truths aboutsuch purported entities turn out instead to be analyzable as truthsabout sensible particulars and their relations to one another. This isin keeping with the general metaphysical outlook of logical atomism.We also have here a fairly severe application of Occam’s razor.The slogan was applied within his analyses in mathematics as well.Noting that sometimes a series of rational numbers converges towards alimit which is not itself specifiable as a rational, some philosophersof mathematics thought that one shouldpostulate anirrational number as a limit. Russell claimed that rather thanpostulating entities in such a case, an irrational numbershould simply bedefined as a class of rational numberswithout a rational upper bound. Russell preferred to reconstruct talkof irrationals this way rather thaninfer orpostulate the existence of a new species of mathematicalentity not already known to exist, complaining that the method of“postulating” what we want has “the advantages oftheft over honest toil” (IMP, 71).

In conducting an analysis of mathematics, or indeed, of any otherdomain of thought, Russell was clear that although the results ofanalysis can be regarded aslogical premises from which theoriginal body of knowledge can in principle be derived,epistemologically speaking, the pre-analyzed beliefs are morefundamental. For example, in mathematics, a belief such as “2 +2 = 4” is epistemologically more certain, and psychologicallyeasier to understand and accept, than many of the logical premisesfrom which it is derived. Indeed, Russell believed that the resultsobtained through the process of analysis obtain their epistemicwarrant inductively from the evident truth of their logicalconsequences (see, e.g.,TK, 158–59). As Russell putit, “[t]he reason for accepting an axiom, as for accepting anyother proposition, is always largely inductive, namely that manypropositions which are nearly indubitable can be deduced from it, andthat no equally plausible way is known by which these propositionscould be true if the axiom were false, and nothing which is plausiblyfalse can be deduced from it” (PM, 59; cf.RMDP, 282). It is perhaps for these reasons that Russellbelieved that the process of philosophical analysis should alwaysbegin with beliefs the truth of which are not in question, i.e., whichare “nearly indubitable”.

When Russell spoke about the general philosophical methodologydescribed here, he usually had in mind applying the process ofanalysis to an entire body of knowledge or set of data. In fact,Russell advocated usually to begin with the uncontroversial doctrineof a certain science, such as mathematics or physics, largely becausehe held that these theories are the most likely to be true, or atleast nearly true, and hence make the most appropriate place to beginthe process of analysis.

Russell did on occasion also speak of analyzing a particularproposition of ordinary life. One example he gave is “There area number of people in this room at this moment” (PLA,179). In this case, the truth or falsity of this statement may seemobvious, but exactly what its truth would involve is rather obscure.The process of analysis in this case would consist in attempting tomake the proposition clear by defining what it is for something to bea room, for something to be a person, for a person to be in a room,what a moment is, etc. In this case, it might seem that the ordinarylanguage statement is sufficiently vague that there is likely noone precise or unambiguous proposition that represents the“correct analysis” of the proposition. In a sense this isright; however, this does not mean that analysis would be worthless.Russell was explicit that the goal of analysis is not to unpack whatis psychologically intended by an ordinary statement such as theprevious example, nor what a person would be thinking when he or sheutters it. The point rather is simply to begin with a certain obvious,but rough and vague statement, and find a replacement for it in a moreprecise, unified, and minimal idiom (see, e.g.,PLA, 180,189).

On Russell’s view, vagueness is a feature of language, not ofthe world. In vague language, there is no one-one relation betweenpropositions and facts, so that a vague statement could be consideredverified by any one of a range of different facts (Vag, 217).However, in a properly analyzed proposition, there is a clearisomorphism between the structure of the proposition and the structureof the fact that would make it true (PLA, 197); hence aprecise and analyzed proposition is capable of being true in one andonly one way (Vag, 219). In analyzing a proposition such as“there are a number of people in this room at thismoment”, one might obtain a precise statement which wouldrequire for its truth that there is a certain class of sensibleparticulars related to each other in a very definite way constitutingthe presence of a room, and certain other classes of sensibleparticulars related to each other in ways constituting people, andthat the sensible particulars in the latter classes bear certaindefinite relations to those in the first class of particulars.Obviously, nothing like this is clearly in the mind of a person whowould ordinarily use the original English expression. It is clear tosee in this case that a very specific state of things is required forthe truth of the analyzed proposition, and hence the truth of it willbe far more doubtful than the truth of the vague assertion with whichone began the process (PLA, 179–80). As Russell put thepoint, “the point of philosophy is to start with something sosimple as not to seem worth stating, and to end with something soparadoxical that no one will believe it” (PLA, 193).

4. Ontological Aspects of Russell’s Logical Atomism

4.1 Russellian Facts: Atomic, Negative and General

As we have seen, the primary metaphysical thesis of Russell’satomism is the view that the world consists of many independententities that exhibit qualities and stand in relations to one another.On this picture, the simplest sort of fact or complex consists eitherof a single individual or particular bearing a quality, or a number ofindividuals bearing a relation to one another. Relations can bedivided into various categories depending on how many relata theyinvolve: abinary ordyadic relation involves tworelata (e.g.,a is to the left ofb); atriadic relation (e.g.,a is betweenb andc) involves three relata and so on. Russell at times used theword “relation” in a broad sense so as to includequalities, which could be considered as “monadic”relations, i.e., relations that only involve one relatum. The qualityofbeing white, involved, e.g., in the fact thatais white, could then, in this broader sense, also be considered arelation.

At the time ofPrincipia Mathematica, complexes inRussell’s ontology were all described as taking the form ofn individuals entering into ann-adic relation.There he writes:

We will give the name of “a complex” to any such object as“a in the relationR tob” or“a having the qualityq,” or“a andb andc standing in relationS.” Broadly speaking, a complex is anything whichoccurs in the universe and is not simple. (PM, 44)

As we have seen, at the time of writingPrincipiaMathematica, Russell believed that an elementary propositionconsisting of a single predicate representing ann-placerelation along withn names of individuals is true if itcorresponds to a complex. An elementary proposition is false if thereis no corresponding complex. Russell there gave no indication that hebelieved in any other sorts of complexes or truth-makers for any othersorts of propositions. Indeed, he held that a quantified propositionis made true not by a single complex, but by many, writing,“[i]f φx is an elementary judgment it is true whenitpoints to a corresponding complex. But(x).φx does not point to a single correspondingcomplex: the corresponding complexes are as numerous as the possiblevalues ofx” (PM, 46).

Soon afterPrincipia Mathematica, Russell became convincedthat this picture was too simplistic. In the “Philosophy ofLogical Atomism” lectures he described a more complicatedframework. In the new terminology, the phrase “atomicfact” was introduced for the simplest kind of fact, i.e., one inwhichn particulars enter into ann-adic relation.He used the phrase “atomic proposition” for a propositionconsisting only of a predicate for ann-place relation, alongwithn proper names for particulars. Hence, such propositionscould take such forms as “F(a)”,“R(a,b)”,“S(a,b,c)” (cf.PM2, xv). An atomic proposition is true when it correspondsto a positive atomic fact. However, Russell no longer conceived offalsity as simplylacking a corresponding fact. Russell nowbelieved that some facts are negative, i.e., that if“R(a,b)” is false, there issuch a fact asa’s not bearing relationR tob. Since the proposition“R(a,b)” is affirmative, andthe corresponding fact is negative, “R(a,b)” is false, and, equivalently, its negation“not-R(a,b)” is true.Russell’s rationale for endorsing negative facts was somewhatcomplicated (see, e.g.,PLA, 211–15); however, onemight object that his earlier view, according to which“R(a,b)” is false because itlacks a corresponding complex, is only plausible if you suppose thatit must be afact that there is not such a complex, and sucha fact would itself seem to be a negative fact.

By 1918, Russell had also abandoned the view, held at least as late as1911 (seeRA, 94) that qualities and relations can occur in acomplex as themselves therelata to another relation, as in“priority implies diversity”. Partly influenced byWittgenstein, Russell now held the view that whenever a propositionapparently involves a relation or quality occurring as logicalsubject, it is capable of being analyzed into a form in which therelation or quality occurs predicatively. For example, “priorityimplies diversity” might be analyzed as“∀x∀y(x is prior toy⊃x is noty)” (PLA,205–06; for further discussion see Klement 2004).

Russell used the phrase “molecular proposition” for thosepropositions that are compounded using truth-function operators.Examples would include, “F(a) &R(a,b)” and“R(a,b) ∨R(b,a)”. According to Russell, it is unnecessary to supposethat there exists any special sort of fact corresponding to molecularpropositions; the truth-value of a molecular proposition could beentirely derivative on the truth-values of its constituents(PLA, 209). Hence, if “F(a) &R(a,b)” is true, ultimately it ismade true by two atomic facts, the fact thata has propertyF and the fact thata bearsR tob, and not by a single conjunctive fact.

However, by 1918, Russell’s attitude with regard to quantifiedpropositions had changed. He no longer believed that the truth of ageneral proposition could be reduced simply to the facts or complexesmaking its instances true. Russell argued that the truth of thegeneral proposition “∀xR(x,b)” could not consist entirely of the various atomicfacts thata bearsR tob,b bearsR tob,c bearsR tob, …. It also requires the truth that there areno other individuals besidesa,b,c, etc.,i.e., no other atomic facts of the relevant form. Hence, Russellconcluded that there is a special category of facts he callsgeneral facts that account for the truth of quantifiedpropositions, although he admitted a certain amount of uncertainty asto their precise nature (PLA, 234–37). Likewise,Russell also positedexistence facts, those factscorresponding to the truth of existentially quantified propositions,such as “∃xR(x,b)”. In the case of general and existence facts,Russell did not think it coherent to make distinctions betweenpositive and negative facts. Indeed, a negative general fact couldsimply be described as an existence fact, and a negative existencefact could be described as a general fact. For example, the falsity ofthe general proposition “all birds fly” amounts to thefact that there exist birds that do not fly, and the falsity of theexistential proposition “there are unicorns” amounts tothe general fact that everything is not a unicorn. Obviously, however,the truth or falsity of a general or existence proposition is notwholly independent of its instances.

In addition to the sorts of facts discussed above, Russell raised thequestion as to whether a special sort of fact is requiredcorresponding to propositions that report a belief, desire or other“propositional attitude”. Russell’s views on thismatter changed over different periods, as his own views regarding thenature of judgment, belief and representation matured. Moreover, insome works he left it as an open question as to whether one needpresuppose a distinct kind of logical form in these cases (e.g.,PLA, 224–28;IMT, 256–57). At times,however, Russell believed that the fact thatS believes thata bearsR tob amounts to the holding of amultiple relation in whichS,a,R andb are all relata (e.g.NTF, 155–56;TK, 144ff). At other points, he considered more complicatedanalyses in which beliefs amount to the possession of certainpsychological states bearing causal or other relationships to theobjects they are about, or the tendencies of believers to behave incertain ways (see, e.g.,IMT, 182–83;HK,144–48). Depending on how such phenomena are analyzed, it iscertainly not clear that they require any new species of fact.

4.2 Logical Atoms and Simplicity

Russell’s use of the phrase “atomic fact”, andindeed the very title of “logical atomism” suggest thatthe constituents of atomic facts, the “logical atoms”,Russell spoke of, must be regarded as utterly simple and devoid ofcomplexity. In that case, the particulars, qualities and relationsmaking up atomic facts constitute the fundamental level of reality towhich all other aspects of reality are ultimately reducible. Thisattitude is confirmed especially in Russell’s early logicalatomist writings. For example, in “Analytic Realism”,Russell wrote:

… the philosophy I espouse isanalytic, because itclaims that one must discover the simple elements of which complexesare composed, and that complexes presuppose simples, whereas simplesdo not presuppose complexes …

I believe there are simple beings in the universe, and that thesebeings have relations in virtue of which complex beings are composed.Any timea bears the relationR tob thereis a complex “a in relationR tob” …

You will note that this philosophy is the philosophy of logicalatomism. Every simple entity is an atom. (RA, 94)

Elsewhere he spoke of “logical atomism” as involving theview that “you can get down in theory, if not in practice, toultimate simples, out of which the world is built, and that thosesimples have a kind of reality not belonging to anything else”(PLA, 270). However, it has been questioned whether Russellhad sufficient argumentation for thinking that there are such simplebeings.

In the abstract, there are two sorts of arguments Russell could havegiven for the existence of simples,a priori arguments, orempirical arguments (cf. Pears 1985, 4ff). Ana prioriargument might proceed from the very understanding of complexity: whatis complex presupposes parts. In 1924, Russell wrote, “I confessit seems obvious to me (as it did Leibniz) that what is complex mustbe composed of simples, though the number of constituents may beinfinite” (LA, 337). However, if construed as anargument, this does not seem very convincing. It seems at leastlogically possible that while a complex may have parts, its partsmight themselves be complex, and their parts might also be complex,and so on,ad infinitum. Indeed, Russell himself later cameto admit that one could not know simply on the basis of somethingbeing complex that it must be composed of simples (MPD,123).

Another sort ofa priori argument might stem from conceptionsregarding the nature ofanalysis. As analysis proceeds, onereaches more primitive notions, and it might be thought that theprocess must terminate at a stage in which the remaining vocabulary isindefinable because the entities involved are absolutely simple, andhence, cannot be construed as logical constructions built out ofanything more primitive. Russell did at some points describe hislogical atoms as reached at “the limit of analysis”(LA, 337) or “the final residue in analysis”(MPD, 164). However, even during the height of his logicalatomist period, Russell admitted that it is possible that“analysis could go on forever”, and that complex thingsmight be capable of analysis “ad infinitum”(PLA, 202).

Lastly, one might argue for simples as the basis of an empiricalargument; i.e., one might claim to have completed the process ofanalysis and to have reduced all sorts of truths down to certainentities that can be known in some way or another to be simple.Russell is sometimes interpreted as having reasoned in this way.According to Russell’s well known “principle ofacquaintance” in epistemology, in order to understand aproposition, one must be acquainted with the meaning of every simplesymbol making it up (see, e.g.,KAKD, 159). Russell at timessuggested that we are only directly acquainted with sense data, andtheir properties and relations, and perhaps with our own selves(KAKD, 154ff). It might be thought that these entities aresimple, and must constitute the terminus of analysis. However, Russellwas explicit that sense data can themselves be complex, and that heknew of no reason to suppose that we cannot be acquainted with acomplex without being aware that it is complex and without beingacquainted with its constituents (KAKD, 153; cf.TK,120). Moreover, Russell continued to use the label “logicalatomism” to describe his philosophy long after his epistemologyhad ceased to center around the acquaintance relation. (For furtherargumentation on these points, see Elkind 2018.) Indeed, Russelleventually came to the conclusion that nothing can ever beknown to be simple (MPD, 123).

While there is significant evidence that Russell did believe in theexistence of simple entities in the early phases of his logicalatomist period, it is possible that, uncharacteristically, he heldthis belief without argumentation. In admitting that it is possiblethat analysis could go onad infinitum, Russell claimed that“I do not think it is true, but it is a thing that one mightargue, certainly” (PLA, 202). In his 1924 piece“Logical Atomism”, Russell admitted that “by greaterlogical skill, the need for assuming them [i.e. simples] could beavoided”. This attitude may explain in part why it is that atthe outset of his 1918 lectures on logical atomism, he claimed that“[t]he things I am going to say in these lectures are mainly myown personal opinions and I do not claim that they are more thanthat” (PLA, 178). It may have been that Russell wasinterested not so much in establishing definitively that there are anyabsolutely simple entities, but rather in combating the widespreadarguments of others that the notion of a simple, independent entity isincoherent, and only the whole of the universe is fundamentally real.According to Russell, such attitudes are customarily traced to a wrongview about relations; in arguing for the doctrine of “externalrelations”, Russell was attempting simply to render a world ofsimple entities coherent again. Others had argued that possessing aninner complexity in the form of “nature” was needed toexplain the essential properties of things or the necessaryconnections between them; as we shall see in Section 4.3 below,Russell believed that such apparent essential properties or necessaryrelations could typically be explained away.

As his career progressed, Russell became more and more prone toemphasize that what is important for his philosophical outlook is notabsolute simplicity, but onlyrelative simplicity. As earlyas 1922, in response to criticism about his notion of simplicity,Russell wrote:

As for “abstract analysis in search of the ‘simple’and elemental”, that is a more important matter. To begin with,“simple” must not be taken in an absolute sense;“simpler” would be a better word. Of course, I should beglad to reach the absolutely simple, but I do not believe that that iswithin human capacity. What I do maintain is that, whenever anythingis complex, out knowledge is advanced by discovering constituents ofit, even if these constituents themselves are still complex.(SA, 40)

According to Russell, analysis proceeds in stages. When analysis showsthe terminology and presuppositions of one stage of analysis to bedefinable, or logically constructible, in terms of simpler and morebasic notions, this is a philosophical advance, even if these notionsare themselves further analyzable. As Russell says, the only drawbackto a language which is not yetfully analyzed is that in it,one cannot speak of anything more fundamental than those objects,properties or relations that are named at that level (e.g.,LA, 337).

In a later work, Russell summarized his position as follows:

If the world is composed of simples—i.e., of things, qualitiesand relations that are devoid of structure—then not only all ourknowledge but all that of Omniscience could be expressed by means ofwords denoting these simples. We could distinguish in the world astuff (to use William James’s word) and a structure. The stuffwould consist of all the simples denoted by names, while the structurewould depend on relations and qualities for which our minimumvocabulary would have words.

This conception can be applied without assuming that there is anythingabsolutely simple. We can define as “relatively simple”whatever we do not know to be complex. Results obtained using theconcept of “relative simplicity” will still be true ifcomplexity is afterward found, provided we have abstained fromasserting absolute simplicity (HK, 259)

Russell concluded that even if there are no ultimate simples, nofundamental layer of reality that analysis can in principle reach,this does not invalidate analysis as a philosophical procedure.Moreover, at a given stage of analysis, a certain class of sentencesmay still be labeled as “atomic”, even if the factscorresponding to them cannot be regarded as built of fundamentalontological atoms (MPD, 165). Russell concluded that“the whole question whether there are simples to be reached byanalysis is unnecessary” (MPD, 123). From this vantagepoint, it might be argued that Russell’s “logicalatomism” can be understood as first and foremost a commitment toanalysis as a method coupled with a rejection of idealistic monism,rather than a pretense to have discovered the genuine metaphysical“atoms” making up the world of facts, or even the beliefthat such a discovery is possible (cf. Linsky 2003; Maclean 2018).Indeed, Russell continued to use the phrase “logicalatomism” to describe his philosophy in later years of hiscareer, during the period in which he stressed relative, not absolutesimplicity (RTC, 717;MPD, 9).

4.3 Atomic Propositions, Logical Independence and Necessity

Another important issue often discussed in connection with logicalatomism worth discussing in greater detail is the supposition thatatomic propositions are logically independent of each other, or thatthe truth or falsity of any one atomic proposition does not logicallyimply or necessitate the truth or falsity of any other atomicproposition. This supposition is often taken to be a central aspect ofthe very notion of “logical atomism”, perhaps largelybecause it is found explicitly in Wittgenstein’sTractatusLogico-Philosophicus, almost certainly the most important accountof a logical atomist philosophy found outside of Russell’s work.Wittgenstein claimed:

4.211 It is a sign of a proposition’s beingelementary that there can be no elementary proposition contradictingit. (Wittgenstein 1922, 89)

5.134 From an elementary proposition no other can beinferred. (Wittgenstein 1922, 109)

The lack of any logical relations between atomic propositions goeshand in hand with a similar view about atomicfacts; eachatomic fact is metaphysically independent of every other, and any onecould obtain or fail to obtain regardless of the obtaining (or not) ofany other.

This position also pairs well with a broader view on the nature ofnecessity: that all necessity reduces to features of logical form.There is nothing in theform of one atomic statement thatwould allow us to infer (or reject) another. Hence, if all necessaryconnections are a result of logical form, atomic facts must beindependent. If what appears to be a simple subject-predicatestatement is necessary, it must in fact have a more complicated formwhen analyzed, so that the necessity of the statement is explained byits form. Similar remarks might be suggested what appear to be simplenecessary relational statements. Wittgenstein, at least, explicitlyendorsed the position that all necessity is logical necessity (6.37).Some commentators also take the thesis that all necessity is logicalnecessity (Landini 2010, chap. 4; 2018), or the thesis thatdere modality is to be rejected in favor ofde dictonecessity (Cocchiarella 2007, chap. 3), to be key to Russell’slogical atomism as well.

Russell’s precise positions on these matters is not as clear asone might hope and nowhere does he treat them at any length. The fewpertinent remarks he does make are either somewhat ambivalent or seemto work against interpreting him as holding strong versions of thesetheses. For example, in 1914, in arguing that atomic facts aretypically known by direct empirical means rather than by inference, hewrote that “[p]erhaps one atomic fact may sometimes be capableof being inferred from another, though I do not believe this to be thecase; but in any case it cannot be inferred from premises no one ofwhich is an atomic fact” (OKEW, 48). Here, Russellexpressed doubt about the existence of any relations of logicaldependence between atomic propositions, but the fact that he left itas an open possibility makes it seem that he would not consider it adefining feature of an atomic proposition that it must be independentfrom all others, or a central tenet of logical atomism generally thatatomic facts are independent from one another. In 1936 he even went sofar as to mock Wittgenstein’s claims that atomic facts areindependent of one another, and that all deductions must be formal, byclaiming that “no one in fact holds these views, and aphilosophy which professes them cannot be wholly sincere”(LE, 319).

Nevertheless, there a number of aspects of Russell’sphilosophical positions that lead to the conclusion that they coherebest withsome doctrine about the independence of atomicfacts or propositions. Russell did often speak about theconstituents of atomic facts as independently existingentities. He writes for example that “each particular has itsbeing independently of any other and does not depend upon anythingelse for the logical possibility of its existence”(PLA, 203). It is not altogether clear what Russell meant byspeaking of particulars or entities as being logically independent. Incontemporary parlance, typically, “logical independence”is used solely to speak of a relation between sentences, propositions,or perhaps facts or states of affairs. One possible interpretationwould be to take Russell as holding that any atomic fact involving acertain group of particulars is logically independent of an atomicfact involving a distinct group of particulars, even if the two factsinvolve the same quality or relation (see, e.g., Bell and Demopoulos1996, 118–19). This weakened version of the independence thesiseven has certain attractions over the stronger principle endorsed byWittgenstein. Most of the usual counterexamples given against thethesis that atomic facts or propositions are always independentinvolve simple properties that are thought to be exclusive. Consider,for example, what has come to be called the “color exclusionproblem”. The propositions “a is red” and“a is blue” do not seem to be independent fromone another: from the truth of one the falsity of the other canseemingly be inferred. However, the weakened version of theindependence principle, on which only atomic facts involvingdifferent particulars are independent, does not entail thatit is possible that “a is red” and“a is blue” may both be true.

It is likely that Russell’s contention that particulars areindependent from one another was connected in his mind with his viewson relations. In holding the view that relations among simpleparticulars are external, Russell saw himself as denying the view thatwhena bearsR tob, there is some part ofa’s “nature” as an entity that involves itsrelatedness tob. It might be thought that Russell’sdoctrine of external relations committed him at least to certainprinciples regarding the modal status of atomic facts (if not theindependence principle). According to certain ways of defining thephrase, what itmeans for a relation to beinternalis that it is a relation that its relatacould not fail tohave; anexternal relation is one its relata could possiblynot have. Russell then might be seen as committed to the view thatatomic facts (all of which involve particulars standing in relations,in the broad sense above) are always contingent. While this does notdirectly bear on the question of their independence, it wouldnevertheless commit Russell to certain tenets regarding the modalfeatures of atomic facts.

However, Russell himself warned against interpreting his position onrelations this way, writing, “the doctrine that relations are‘external’ … is not correctly expressed by sayingthat two terms which have a certain relation might not have had thatrelation. Such a statement introduces the notion of possibility andthus raises irrelevant difficulties” (BReal, 87).Complicating matters here are Russell’s own rather idiosyncraticand skeptical views about modal notions. Russell was dissatisfied withthe prevailing conceptions of necessity and possibility amongphilosophers of his day, and argued instead against necessity (orpossibility) as a fundamental or irreducible concept (seeNPpassim).

Despite Russell’s misgivings about modal notions, it is clearenough from Russell’s conception oflogic that logicalrelations between propositions would always obtain in virtue of theirform (IMP, 197–98;PLA, 237–39). Again,atomic propositions are of the simplest possible forms, and there iscertainly nothing in their forms that would suggest any logicalconnection to, or incompatibility with, other atomic propositions.

Perhaps the most illuminating remarks to be found in Russell’swork that would lead one to expect complete logical independence amongatomic propositions involve the claims he made about how it is thatone recognizes a certain class of purported entities as “logicalconstructions”, and the recommendations he gives about analyzingpropositions involving them. Russell writes:

When some set of supposed entities has neat logical properties, itturns out, in a great many instances, that the supposed entities canbe replaced by purely logical constructions composed of entities whichhave not such neat properties. In that case, in interpreting a body ofpropositions hitherto believed to be about the supposed entities, wecan substitute the logical structures without altering any detail ofthe body of propositions in question (LA, 326).

Russell did not define here what he means by “neat logicalproperties”, but it is possible to understand what he had inmind by way of the examples he gave. He cited as “neatproperties” of material objects that it is impossible for twomaterial objects to occupy the same place at the same time, and thatit is impossible for one material object to occupy distinct places inspace at the same time (LA, 329; cf.AMi,264–65;AMa, 385). Consider then the propositions“O₁ is located atp₁ att₁”, and “O₁ islocated atp₂ att₁”where “O₁” is the name of a physicalobject, “p₁” and“p₂” represent distinct locations inspace, and “t₁” the name of a certaininstant in time. Prior to analysis, such propositions appear to belogically incompatible atomic propositions. However, Russell explainsthat the logical necessities involved in cases such as these are dueto the nature of material objects, points and instants as logicalconstructions. At a certain point in time, a physical object might beregarded as a class of sensible particulars bearing certainresemblance relations to one another occupying acontinuousregion of space. It is therefore impossibleby definition forthe same physical object to occupy wholly distinct locations at thesame time. When analyzed, such propositions as“O₁ is located atp₁ att₁” are revealed as having a much morecomplicated logical form, and hence may have logical consequences notevident before analysis. We do not have here any reason to think thattruly atomic propositions, those containing names of genuineparticulars and their relations, are not always independent.

Russell strongly intimated that it is a part of the very nature oflogical analysis that if our pre-analyzed understanding of a certainphenomenon involves the postulation of entities with certainstructural or modal properties, one should seek to replace talk ofsuch entities with logical constructions specifically constituted soas to have these features by definition (PLA, 272–79;LA, 326–29). A logical construction would typically beunderstood as a sort of class; since discourse about classes wasregarded by Russell as a convenience, which would be eliminated in afully analyzed language in favor of speaking of their definingproperties and relations, by such a process Russell believed it ispossible to replace commitment to entities having “neat logicalproperties” with commitment to those that do not possess suchfeatures. Russell’s work on mathematics provides us with what hewould have taken as many examples of this phenomenon. If we take “3> 2” and “3 < 2” at face-value as expressing simpledyadic relations between simple entitiesnamed“2” and “3”, then these appear to be twoatomic propositions, one necessary, one impossible, which are notindependent of each other. But after analysis, “2” and“3” are revealed not to be names at all, and thenecessity, impossibility, and mutual incompatibility of thesestatements is rendered purely logical. Assuming that there is a finalterminus of analysis in absolutely simple entities and fully atomicfacts, one might suppose that here the logical necessities andrelationships between them would have completely disappeared.

Russell later summarized the attitude of his logical atomist period bywriting that “it seemed to result that none of the raw materialof the world has smooth logical properties, but that whatever appearsto have such properties is constructed artificially in order to havethem” (IPOM, xi). While this is not exactly anendorsement of the claim that atomic facts are logically independentof one another, it is perhaps the closest sentiment one can find inhis philosophy. It is again perhaps better understood as anendorsement of a methodological maxim. If a certain stage of analysisseems to portray entities as having “neat” logicalproperties, i.e., necessary features or relations not explained bylogical form, this is a sign that more analysis is needed. Perhaps byanalyzing the statements further, “busting open” theapparent terms for these things to reveal more complicated logicalforms, what appear to be necessary connections between atomic factswill be shown actually to be logically necessary relationships betweennon-atomic facts owed to their logical forms (cf. Elkind forthcoming).Apparent non-logical necessities in a pre-analyzed doctrine could beseen as a sign it is rife for analysis. As with his views regardingsimplicity, later Russell denied that logical atomism required holdingthat logically independent atomic facts were actually discoverable,and indeed suggested this was never an essential part of what he (andeven Wittgenstein) had been proposing (RU 618).

5. Influence and Reception

Russell’s logical atomism had significant influence on thedevelopment of philosophy, especially in the first half of the 20thcentury. Many especially in Britain characterized their ownphilosophical views in contrast with his. Notably, for example, SusanStebbing proposed a view of relations she regarded as an intermediarybetween Russell’s doctrine of external relations and the idealistdoctrine of internal relations (see Kouri Kissel 2024). Nowhere isRussell’s influence more clearly seen than in the work of hispupil Ludwig Wittgenstein. Wittgenstein’sTractatusLogico-Philosophicus appeared in 1921; in it, Wittgensteinpresented in some detail a logical atomist metaphysics. (It should benoted, however, that there is significant controversy over whether, inthe end, Wittgenstein himself meant to endorse this metaphysics.) IntheTractatus, the world is described as consisting of facts.The simplest facts, which Wittgenstein called“Sachverhalte”, translated either as“states of affairs” or “atomic facts”, arethought of as conglomerations of objects combined with a definitestructure. The objects making up these atomic basics were described asabsolutely simple. Elementary propositions are propositions whosetruth depends entirely on the presence of an atomic fact, and otherpropositions have a determinate and unique analysis in which they canbe construed as built up from elementary propositions intruth-functional ways.

Partly owing to Wittgenstein’s influence, partly directly,Russell’s logical atomism had significant influence on the worksof the logical positivist tradition, as exemplified in the works ofCarnap, Waismann, Hempel and Ayer. This tradition usually disavowedmetaphysical principles, but methodologically their philosophies owedmuch to Russell’s approach. Carnap, for example, describedphilosophy as taking the form of providing “the logical analysisof the language of science” (Carnap 1934, 61). This originallytook the form of attempting to show that all meaningful scientificdiscourse could be analyzed in terms of logical combinations beginningwith “protocol sentences”, or sentences directlyconfirmable or disconfirmable by experience. This notion of a“protocol sentence” in this tradition was originallymodeled after Russellian and Wittgensteinian atomic propositions. Thenotion of a “logical construction” was also important forhow such thinkers conceived of the nature of ordinary objects (see,e.g., Ayer 1952, chap. 3). The view that scientific language couldreadily and easily be analyzed directly in terms of observablesgradually gave way to more holistic views, such as Quine’s (see,e.g. Quine 1951), in which it is claimed that it is only a body ofscientific theories that can be compared to experience, and notisolated sentences. However, even in later works growing out of thistradition, the influence of Russell can be felt.

Besides positive influence, many trends in 20th century philosophy canbe best understood largely as a reaction to Russell’s atomisticphilosophy. Ironically, nowhere is this more true than in the laterwritings of Wittgenstein, especially hisPhilosophicalInvestigations (1953). Among other things, Wittgenstein therecalled into question whether a single, unequivocal notion ofsimplicity or a final state of analysis can be found (e.g., secs.46–49, 91), and questioned the utility of an ideal language(sec. 81). Wittgenstein also called into question whether, in thosecases in which analysis is possible, the results really give us whatwas meant at the start: “does someone who says that the broom isin the corner really mean: the broomstick is there, and so is thebrush, and the broomstick is fixed in the brush?” (sec. 60).Much of the work of the so-called “ordinary language”school of philosophy centered in Oxford in the 1940s and 1950s canalso been seen largely as a critical response to views of Russell(see, e.g., Austin 1962, Warnock 1951, Urmson 1956).

Nevertheless, despite the criticisms, many so-called“analytic” philosophers still believe that the notion ofanalysis has some role to play in philosophical methodology, thoughthere seems to be no consensus regarding precisely what analysisconsists in, and to what extent it leads reliably to metaphysicallysignificant results. Debates regarding the nature of simple entities,their interrelations or dependencies between one another, and whetherthere are any such entities, are still alive and well. Russell’srejection of idealistic monism, and his arguments in favor of apluralistic universe, have gained almost universal acceptance, with afew exceptions. Abstracting away from Russell’s particularexamples of proposed analyses in terms of sensible particulars, thegeneral framework of Russell’s atomistic picture of the world,which consists of a plurality of entities that have qualities andenter into relations, remains one to which many contemporaryphilosophers are attracted.

Bibliography

Works By Russell

Secondary Literature

• Austin, J.L., 1962.Sense and Sensibilia, ed. G. J.Warnock. Oxford: Clarendon Press.
• Ayer, A.J., 1952.Language, Truth and Logic, 2nd ed., NewYork: Dover. (First edition 1936.)
• Baldwin, Thomas, 2003a. “Logic and PhilosophicalAnalysis,” in Baldwin 2003b, pp. 417–23.
• Baldwin, Thomas (ed.), 2003b.The Cambridge History ofPhilosophy 1870–1945, Cambridge: Cambridge UniversityPress.
• Bell, John and William Demopoulos, 1996. “ElementaryPropositions and Independence,”Notre Dame Journal of FormalLogic, 37: 112–24.
• Bostock, David, 2012.Russell’s Logical Atomism,Oxford: Oxford University Press.
• Bradley, F.H., 1883.The Principles of Logic, 2 vols.Oxford: Oxford University Press.
• –––, 1893.Appearance and Reality,Oxford: Oxford University Press.
• Carnap, Rudolf, 1934. “On the Character of PhilosophicProblems” in Rorty (1967), pp. 54–71.
• Cartwright, Richard, 2003. “Russell and Moore1898–1905,” in Griffin 2003b, pp. 108–27.
• Cocchiarella, Nino, 1987.Logical Studies in Early AnalyticPhilosophy, Columbus: Ohio State University Press.
• –––, 2007.Formal Ontology and ConceptualRealism, Dordrecht: Springer.
• Elkind, Landon, 2018. “On Russell’s LogicalAtomism” in Elkind and Landini 2018, pp. 3–37.
• –––, forthcoming. “Russell‘s LogicalAtomism and Modality” in S. Lebens, F. MacBride, andGraham Stevens (eds.),The Oxford Handbook of BertrandRussell, Oxford: Oxford University Press.
• Elkind, Landon and Gregory Landini, eds., 2018.The Philosophyof Logical Atomism: A Centenary Reappraisal, Basingstoke:Palgrave Macmillan.
• Griffin, Nicholas, 1991.Russell’s IdealistApprenticeship, Oxford: Clarendon.
• –––, 2003a. “Russell’s PhilosophicalBackground,” in Griffin 2003b, pp. 84–107.
• Griffin, Nicholas (ed.), 2003b.The Cambridge Companion toBertrand Russell, Cambridge: Cambridge University Press.
• Hager, Paul, 1994.Continuity and Change in the Development ofRussell’s Philosophy, Dordrecht: Kluwer.
• –––, 2003. “Russell’s Method ofAnalysis,” in Griffin 2003b, pp. 310–31.
• Hochberg, Herbert, 1978.Thought, Fact and Reference: TheOrigins and Ontology of Logical Atomism, Minneapolis: Universityof Minnesota Press, 1978.
• Hylton, Peter, 1990.Russell, Idealism and the Emergence ofAnalytic Philosophy, Oxford: Clarendon.
• –––, 2008.Propositions, Functions, andAnalysis: Selected Essays on Russell’s Philosophy, Oxford:Oxford University Press.
• Klement, Kevin, 2004. “Putting Form Before Function: LogicalGrammar in Frege, Russell and Wittgenstein,”Philosopher’s Imprint, 4: 1–47.
• –––, 2009. “Russell, His Paradoxes andCantor’s Theorem,” in 2 parts,Philosophy Compass,5 (January), doi:10.1111/j.1747-9991.2009.00270.x anddoi:10.1111/j.1747-9991.2009.00271.x
• Kouri Kissel, Teresa, 2024. “Susan Stebbing andRussell’s Logical Atomism,” inBertrand Russell,Feminism and Women Philosophers in his Circle, L. D. C.Elkind and A. M. Klein (eds.), Cham: Palgrave Macmillan,pp. 191–206.
• Landini, Gregory, 1998.Russell’s Hidden SubstitutionalTheory, Oxford: Oxford University Press.
• –––, 2007.Wittgenstein’sApprenticeship with Russell, Cambridge: Cambridge UniversityPress.
• –––, 2010.Russell, New York:Routledge.
• –––, 2018. “Logical Atomism’sNecessity”, in Elkind and Landini 2018, pp. 39–67.
• Linsky, Bernard, 2003. “The Metaphysics of LogicalAtomism,” in Griffin 2003b, pp. 371–92.
• Livingston, Paul, 2001. “Russellian and WittgensteinianAtomism,”Philosophical Investigations, 24:30–54.
• Lycan, William, 1981. “Logical Atomism and OntologicalAtoms,”Synthese, 46: 207–29.
• Maclean, Gülberk Koç, 2018. “Logical Atomism inRussell’s Later Works” in Elkind and Landini 2018, pp.69–90.
• Monk, Ray and Anthony Palmer (eds.), 1996.Bertrand Russelland the Origins of Analytical Philosophy, Bristol: Thoemmes.
• Moore, G.E., 1899. “The Nature of Judgment,”Mind 8, pp. 176–93, reprinted in Moore 1993, pp.1–19.
• –––, 1901. “Truth and Falsity,”reprinted in Moore 1993, pp. 20–22.
• –––, 1993.Selected Writings, ed. T.Baldwin. London: Routledge.
• Pears, David, 1967.Bertrand Russell and the British Traditionin Philosophy, London: Collins.
• –––, 1985. Introduction to B. Russell,ThePhilosophy of Logical Atomism, Chicago: Open Court.
• Quine, W.V., 1951. “Two Dogmas of Empiricism,”Philosophical Review, 60: 20–43.
• Rodríguez-Consuegra, Francisco, 1996.“Russell’s Perilous Journey from Atomism to Holism1919–1951,” in Monk and Palmer 1996, pp.217–44.
• Rorty, Richard (ed.), 1967.The Linguistic Turn, Chicago:University of Chicago Press.
• Sainsbury, R.M., 1979.Russell, London: Routledge.
• –––, 1980. “Russell on Constructions andFictions,”Theoria 46, pp. 19–36.
• Simons, Peter, 2003. “Logical Atomism,” in Baldwin2003b, pp. 383–90.
• Skyrms, Brian, 1993. “Logical Atoms and CombinatorialPossibility,”Journal of Philosophy, 90:219–32.
• Stevens, Graham, 2005.The Russellian Origins of AnalyticalPhilosophy: Bertrand Russell and the Unity of the Proposition,London: Routledge.
• Urmson, J.O., 1956.Philosophical Analysis: Its DevelopmentBetween the Two World Wars, Oxford: Clarendon Press.
• Warnock, G.J., 1951. “Metaphysics in Logic,”Proceedings of the Aristotelian Society, 51:197–222.
• Wittgenstein, Ludwig, 1922.TractatusLogico-Philosophicus, London: Kegan Paul.
• –––, 1958.PhilosophicalInvestigations, Oxford: Basil Blackwell.

Academic Tools

	How to cite this entry.
	Preview the PDF version of this entry at theFriends of the SEP Society.
	Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO).
	Enhanced bibliography for this entryatPhilPapers, with links to its database.

Other Internet Resources

• Bertrand Russell Research Centre
• Bertrand Russell Archives
• Bertrand Russell Society
• Russell: The Journal of Bertrand Russell Studies
• Writings by Bertrand Russell
• Encyclopaedia Brittanica Online: Analytic Philosophy

Related Entries

analysis |descriptions |facts |Frege, Gottlob |logical constructions |Moore, George Edward |Ockham [Occam], William |Principia Mathematica |propositional function |propositions |Russell, Bertrand |sense data |simplicity |Vienna Circle |Wittgenstein, Ludwig |Wittgenstein, Ludwig: logical atomism