Origin[ edit ] As mentioned above, the term "logical atomism" was first coined by Russell in These lectures were subsequently published in and in The Monist Volumes 28 and 29 , which at the time was edited by Phillip Jourdain. However, logical atomism has older roots. Russell and Moore broke themselves free from British Idealism in the s. His views on philosophy and its methods were heavily influenced by revolutionary nineteenth-century mathematics by figures like Cantor , Dedekind , Peano , and Weierstrass.
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Related Entries 1. Methodologically, logical atomism can be seen as endorsement of analysis, understood as a two-step process in which one attempts to identify, for a given domain of inquiry, set of beliefs or scientific theory, the minimum and most basic concepts and vocabulary in which the other concepts and vocabulary of that domain can be defined or recast, and the most general and basic principles from which the remainder of the truths of the domain can be derived or reconstructed.
Metaphysically, logical atomism is the view that the world consists in a plurality of independent and discrete entities, which by coming together form facts. According to Russell, a fact is a kind of complex, and depends for its existence on the simpler entities making it up.
The simplest sort of complex, an atomic fact, was thought to consist either of a single individual exhibiting a simple quality, or of multiple individuals standing in a simple relation. The methodological and metaphysical elements of logical atomism come together in postulating the theoretical, if not the practical, realizability of a fully analyzed language, in which all truths could in principle be expressed in a perspicuous manner.
The truth or falsity of an atomic proposition would depend entirely on a corresponding atomic fact. The other sentences of such a language would be derived either by combining atomic propositions using truth-functional connectives, yielding molecular propositions, or by replacing constituents of a simpler proposition by variables, and prefixing a universal or existential quantifier, resulting in general and existential propositions.
OKEW, Russell also at times suggests that analysis demonstrates that what we take to be essential or necessary properties of things and relations between things are the result of the logical forms the these things, properties and relations are logically constructed to have.
This suggests that there are no such connections between simple entities, that all atomic propositions are independent of each other, and that all forms of necessity reduce to formal logical necessity.
The next section discusses the origins of logical atomism in the break made by Russell and G. Moore from the tradition of British Idealism, and its development during the years in which Russell worked on Principia Mathematica. Moore rejected the main tenets of the dominant school of philosophy in Britain at the time to which both had previously been adherents , the tradition of neo-Hegelian Idealism exemplified in works of F.
Bradley and J. McTaggart, and adopted instead a fairly strong form of realism MPD, 9. It begins with a discussion of a distinction made by Bradley between different notions of idea. Instead, the relevant notion of idea is that of a sign or symbol representing something other than itself, or an idea understood as possessing meaning. Moore agreed with Bradley that it is not the mental occurrence that is important to logic.
However, the concept itself is independent of the ideas. When we make a judgment, typically, it is not our ideas, or parts of our ideas, which our judgment is about.
While propositions represent the content of judgments, according to Moore, they and their constituents are entirely independent from the judging mind. Some propositions are true, some are not. For Moore, however, truth is not a correspondence relationship between propositions and reality, as there is no difference between a proposition—understood as a mind-independent complex—and that which would make it true Moore , 5; Moore The facts of the world then consist of true propositions, themselves understood as complexes of concepts.
For his own part, Russell often described his dissatisfaction with the dominant Idealist and largely Monist tradition as primarily having to do with the nature and existence of relations. In particular, Russell took issue with the claim found in Bradley and others, that the notion of a fundamental relation between two distinct entities is incoherent.
Russell diagnosed this belief as stemming from a widespread logical doctrine to the effect that every proposition is logically of subject-predicate form.
In the period leading up to his own abandonment of idealism, Russell was already pursuing a research program involving the foundations of arithmetic see, e. This work, along with his earlier work on the foundations of geometry see EFG , had convinced him of the importance of relations for mathematics.
However, he found that one category of relations, viz. These relations are especially important in mathematics, as they are the sort that generates series.
The problem, according to Russell, is that for this reduction to hold, there must be a certain relation between the properties themselves. This relation among the properties would itself be an asymmetrical and transitive relation, and so the analysis has not rid us of the need for taking relations as ultimate. Moreover, according to some within this tradition, when we consider a, obviously we do not consider all its relations to every entity, and hence grasp a in a way that falsifies the whole of what a is.
BReal, 89; MTT, This position on relations allowed Russell to adopt a pluralist philosophy in which the world is conceived as composed of many distinct, independent entities, each of which can be considered in isolation from its relations to other things, or its relation to the mind. RA, 92; POM, , and it represents perhaps the most important turning point in the development of his logical atomism. Part I of POM is dedicated largely to a philosophical inquiry into the nature of propositions.
Russell took over from Moore the conception of propositions as mind-independent complexes; a true proposition was then simply identified by Russell with a fact cf. MTCA, 75— An entity occurs as concept when it occurs predicatively, i. In the proposition Socrates is human, the person Socrates the man himself occurs as term, but humanity occurs as concept.
In the proposition Callisto orbits Jupiter, Callisto the moon itself and Jupiter the planet occur as term, and the relation of orbiting occurs as concept. While Russell thought that only certain entities were capable of occurring as concept, at the time, he believed that every entity was capable of occurring as term in a proposition.
In the proposition Wisdom is a virtue, the concept wisdom occurs as term. His argument that this held generally was that if there were some entity, E, that could not occur as term, there would have to be a fact, i.
In particular, at both stages he would regard the simple truth that an individual a stands in the simple relation R to an individual b as a complex consisting of the individuals a and b and the relation R. Because Russell believed it impossible for a finite mind to grasp a proposition of infinite complexity, however, Russell rejected a view according to which the false proposition designated by All numbers are odd.
Similarly, although Russell admitted that such a proposition as 1 is equivalent to a formal implication, i. This was perhaps in part due to the difference in grammatical structure, and perhaps also because the former appears only to be about numbers, whereas the latter is about all things, whether numbers or not. Instead, Russell thought that the proposition corresponding to 1 contains as a constituent the denoting concept all numbers. As Russell explained them, when denoting concepts occur in a proposition, the proposition is not about them but about other entities to which the denoting concepts bear a special relation.
So when the denoting concept all numbers occurs in a proposition, the proposition is not about the denoting concept, but instead about 1 and 2 and 3, etc. OD, 48— According to the new theory adopted, the proposition expressed by 1 was now identified with that expressed by a quantified conditional such as 2. Similarly, the proposition expressed by Some number is odd. One involves how it is that a proposition can be meaningful even if it involves a description or other denoting phrase that does not denote anything.
The proposition in question is false, since there is no value of x which would make it true. One is not committed to a nonexistent entity such as the King of France simply in order to understand the make-up of the proposition. Secondly, this theory provides an answer to how it is that certain identity statements can be both true and informative.
A proposition was understood to be a unity in this sense. However, Russell was aware already at the time of POM that the supposition there is always a class, understood as an individual entity, as the extension of every propositional function, leads to certain logical paradoxes.
The class w would be a member of itself if it satisfied its defining condition, i. Similarly, w would not be a member of itself if it did not satisfy its defining condition, i. Hence, both the assumption that it is a member of itself, and the assumption that it is not, are impossible.
It follows from this that the number of subclasses of the class of all individuals, i. Russell took this as strong evidence that a class of individuals could not itself be considered an individual. Likewise, the number of subclasses of the class of all classes is greater than the number of members in the class of all classes.
Russell spent the years between and searching for a philosophically motivated solution to such paradoxes. He tried solutions of various sorts. However, in the version adopted in the first edition of Principia Mathematica, Russell believed that a statement apparently about a class could always be reconstructed, using higher-order quantification, in terms of a statement involving its defining propositional function.
For example, it follows from this contextual definition of class terms that the statement to the effect that one class A is a subset of another class B is equivalent to the claim that whatever satisfies the defining propositional function of A also satisfies the defining propositional function of B. While it may seem that a class term is representative of an entity, according to Russell, class terms are meaningful in a different way.
Classes are not among the basic stuff of the world; yet it is possible to make use of class terms in significant speech, as if there were such things as classes. During the period in which Russell was working on Principia Mathematica, most likely in , Russell also radically revised his former realism about propositions understood as mind independent complexes.
The motivations for the change are a matter of some controversy, but there are at least two possible sources. The first is that in addition to the logical paradoxes concerning the existence of classes, Russell was aware of certain paradoxes stemming from the assumption that propositions could be understood as individual entities.
Unlike the other paradoxes mentioned above, a version of this paradox can be reformulated even if talk of classes is replaced by talk of their defining propositional functions. Russell was also aware of certain contingent paradoxes involving propositions, such as the Liar paradox formulated involving a person S, whose only assertion at time t is the proposition All propositions asserted by S at time t are false. Given the success of the rejection of classes as ultimate entities in resolving the paradoxes of classes, Russell was motivated to see if a similar solution to these paradoxes could be had by rejecting propositions as singular entities.
Another set of considerations pushing Russell towards the rejection of his former view of propositions is more straightforwardly metaphysical. According to his earlier view, and that of Moore, a proposition was understood as a mind independent complex. The constituents of the complex are the actual entities involved, and hence, as we have seen, when a proposition is true, it is the same entity as a fact or state of affairs.
However, because some propositions are false, this view of propositions posits objective falsehoods. The false proposition that Venus orbits Neptune is thought to be a complex containing Venus and Neptune the planets, as well as the relation of orbiting, with the relation occurring as a relation, i. However, it seems natural to suppose that the relation of orbiting could only unite Venus and Neptune into a complex, if in fact, Venus orbits Neptune.
Hence, the presence of such objective falsehoods is itself out of sorts with common sense. Whatever his primary motivation, Russell abandoned any commitment to objective falsehoods, and restructured his ontology of facts, and adopted a new correspondence theory of truth. Propositions are thought to be true or false depending on their correspondence, or lack thereof, with facts.
In the Introduction to Principia Mathematica, as part of his explanation of ramified type-theory, Russell described various notions of truth applicable to different types of propositions of different complexity. Such propositions consist of a simple predicate, representing either a quality or a relation, and a number of proper names. According to Russell, such a proposition is true when there is a corresponding fact or complex, composed of the entities named by the predicate and proper names related to each other in the appropriate way.
If there is no corresponding complex, then the proposition is false. This notion of truth serves as the ground for a hierarchy of different notions of truth applicable to different types of propositions depending on their complexity. A proposition involving the simplest kind of second-order quantifier, i.
Because any statement apparently about a class of individuals involves this sort of higher-order quantification, the truth or falsity of such a proposition will ultimately depend on the truth or falsity of various elementary propositions about its members. Propositions that assert that an object has a quality, or that multiple objects stand in a certain relation, were given a privileged place in the theory, and explanation was given as to how more complicated truths, including truths about classes, depend on the truth of such simple propositions.
Russell employed the methodology self-consciously, and gave only slightly differing descriptions of this methodology in works throughout his career see, esp.
Russell’s Logical Atomism