Russell’s Theory of Logical Atomism and Metaphysical Problems It Solves

The 20^th century was a time of significant changes that influenced political, economic, social and spiritual spheres of human life and led to reinterpretation of the main values, birth of new ideas and new ways of perceiving the old things. Rapid progress caused the development of new human consciousness that perceived the world in a different way. Numerous philosophical movements depicted peculiarities of the spiritual life of renovated society. One of the leading movements of world’s philosophy of that time was analytical philosophy, which was represented by different doctrines, including the theory of logical atomism. In general terms, it may be characterized as the philosophy of mathematical logics. Logical atomism is based upon the idea that the cognizance of the world requires the identification of certain pieces of evidence originated from mathematical and logical-linguistic conclusions. Its main peculiarity is a detailed examination of the language aimed for interpretation of various philosophical points. In fact, all supporters of the theory of logical atomism supposed that the solution to any philosophical issue required logical analysis of the language that in fact was verbal representation of that problem. The most prominent representatives of this idea were B. Russell and L. Wittgenstein. Their assumptions framed the skeleton of the philosophy of logical positivism. In fact, they were the first thinkers who studied language as a basis of knowledge. In their works, these scholars paid special attention to the manner of utterances, their analysis and specification of their direct and symbolical meanings. Logical atomism by Russell is a philosophical doctrine that is anchored in the idea that the world entails a plurality of independent and discrete entities and effectively solves metaphysical problems of appearance, reality, and human knowledge relating to truths.

General Overview of the Theory of Logical Atomism

Bertrand Russell first presented the theory of logical atomism as a philosophical doctrine that essentially sees the world as a plurality of independent and discrete entities. Being a mathematician, he attempted to apply logical thinking to the interpretation of the world and human being. Obtained conclusions were presented to the public in the course of eight lectures entitled The Philosophy of Logical Atomism. According to Pears (1998), the primary value of Russell’s theory is the new way of the usage of basic mathematical concepts. The discipline has always been considered as self-discipline, but English philosopher proved that it is actually a section of logic. Moreover, Russell compared the basic structure of daily or “natural” language to the principles of mathematics and identified certain similarities between them. However, while natural languages share something common with mathematics, their nature is vaguer. For that reason, language is not suitable for regular philosophical analysis. According to Russell, the employment of mathematical logic would give philosophy a perfect tool for the extraction of the true value of a certain statement of any natural language (“Russell’s logical atomism,” 2005).

The theory begins with the assumption that human knowledge originates from sensory experience. According to Russell (2009), “Sense-data provide the primitive content of our experience, and for Russell (unlike the phenomenalists) these sense-data are not merely mental events, but rather the physical effects caused in us by external objects”. Each event takes place in private space of a separate individual and occurs immediately. Thus, the scholar claimed that different events have certain similarities and hence form a so-called public space from which even manifestation of certain sense may be said to occur. It means that sensory experience comprises both public and objective components.

In order to understand the concept of logical atomism, it should be analyzed from various perspectives. From metaphysical perspective, it represents the idea that the world exists in a number of entities that interconnect with each other and form certain facts. From the methodological point of view, logical atomism may be perceived as a certain kind of analysis that is performed in two steps when one attempts to identify a set of beliefs or scientific theory (“Logical atomism,” 2015). Furthermore, this entails the minimum and most basic concepts and vocabulary in which the other concepts and vocabulary of that domain can be defined or recast.

The scholar provides the following argumentation concerning the exact name of his doctrine, “The reason that I call my doctrine logical atomism is because the atoms that I wish to arrive at as the last sort of residue in analysis are logical atoms and not physical atoms” (Russell, 2009). Therefore, Russell claims that his logic is atomistic. Apparently, such definition presupposes it to be based on the opinion that the world comprises numerous separate parts. In fact, these parts are of concern to the analysis and are denominated as “logical atoms”. The theory presupposes the division of these components into two kinds. Hereby, some of these atoms are introduced as “particulars” and essentially represent “such things as little patches of color or sounds, momentary things” (Russell, 2009), while the others are presented as predications or relations. Hence, when the logic is applied in the interpretation of the notion of existence, it analyzes certain qualities of the things and relations that exist between them.

Russell presented logic of a new type that was much broader than the one proposed by Aristotle. The main difference between Russell and Aristotle’s logic is the idea that the logic of Aristotle was predominantly the logic of classes, and logic presented by Russell was the logic of utterances. Hence, the language itself was of concern to the logical analysis.

Initial development of basic logical concepts that formed the starting point for analytic philosophy belongs to Russell’s theory and its philosophical interpretation. Continuing research work performed by Peano and Frege, the philosopher did not confine his investigation to the application of this method in mathematics. In fact, he was the first one to attract attention of philosophers to symbolic logic. The theory of logical atomism illustrates the application of the method of logical analysis to the theory of knowledge in general and extends the area of its solutions to philosophical problems. The main task of the analysis was defined as the investigation of objects of study not aimed at obtaining new genuine concepts about the world but rather clarifying the content of words and expressions that constitute knowledge.

Correlation between Language and Logics as the Crucial Point of Russell’s Theory

The fundamental statement of Russell’s theory is the assumption that the nature of reality can be analyzed in the light of language. Language influences logical thinking (Philosophy Pages, 2011). Apparently, by language he means vocabulary as well as syntax and claims that this influence is of the double nature since linguistic structures influence cognition and human consciousness influences linguistic components. Reality also exists in close connection to its verbal reflection in the system of language. Russell claims that “a perfect one-to-one correspondence exists between an “atom” of language (an atomic proposition) and an atomic fact; thus, for each atomic fact there is a corresponding atomic proposition” (“Logical atomism,” 2015). Moreover, several atomic propositions form an atomic molecule. In molecular propositions, its constituent parts are joined by means of connectors such as “or”, “and”, “if”. The truthfulness or fallibility of these propositions is dependent on the quality of its atomic components.

First, Russell makes a distinction between what he calls the atomic propositions and molecular propositions. The latter are constructed based on the former by adding certain connectors. The scholar believed that the analysis of these components “results in a logically perfect language consisting only of words that denote the data of immediate experience (sense data and universals) and logical constants, that is, words like “or” and “not” (Carey, n.d.). For example, the sentence “John and Mary are going to the movies” is the molecular proposition consisting of two atomic. Hence, any molecular statement can be decomposed into a set of atomic propositions and logical connectors.

The difference between atomic and molecular propositions is also in the relation with the interpreted reality. In case of being, truthful atomic statement refers to an atomic fact that contains particular and universal components. However, molecular sentences unite atomic propositions into the structures referred to as “compound sentences”. When these structures are true, molecular statements do not correspond to a sole fact or phenomenon but refer to a number of atomic facts (Carey, n.d.).

Mathematical logics confirm that the world comprises “facts”, and that all these facts are of atomic nature. It means that every fact can be described by certain atomic sentences. In nature, there is no molecular evidence because each molecular sentence can be translated or represented by a set of atomic propositions and logical connectives such as “and”, “or”, “if … then”, and others. These linking components do not possess any meaning themselves and serve exclusively as language tools that allow one to combine atomic sentences in different ways. According to Philosophy Pages (2011), their use possesses purely “syntactic” character.

Applying mathematical principles in the analysis of linguistic statements, Russell attempted to provide a sketch of the perfect language. The language is perfect as it reflects the structure of the real world. If the proposal with conventional natural language is translated by means of perfect logical language, the importance of this proposal becomes evident. In case this transformation does not cause the acquisition of subject-predicate form, it means that there does not exist such object that is directly related to the grammatical subject. The reason is that in the structure of the perfect language, each subject-term signifies some real object of the world, and each predicate-term represents some real characteristics of the object.

The concept of atomic proposition expresses the complex of entities and relations between them. It was suggested that the expression meaning or denoting an object can be understood either by direct introduction to the relevant subject or with its description. Introduction presupposes a direct reference to the named object as well as its visual and sensual presentation. When talking about description, one means verbal description of the subject with regard to its features. Bertrand Russell proposed clear differentiation between the names and descriptions of two different types of relationships between the characters and the subject to avoid confusion (“Russell’s logical atomism,” 2005). In addition, he noted that the description may be either definite referring to the individual specific subject or indefinite indicating simply a class of objects. New important discovery was made as a result of division of certain proper names and descriptions that according to Frege belonged to the same type. It was stressed that even an individualized description still does not point directly to the appropriate object since it obtains its meaning in abstraction from its carrier.

The theory elaborated by Russell offered a new interpretation of expressions. According to this theory, constituent parts of a proposition occur under two titles, namely “a term” or “a concept”.

An entity occurs “as term” when it can be replaced by any other entity and the result would still be a proposition, and when it is one of the subjects of the proposition, i.e., something the proposition is “about”. An entity occurs as concept when it occurs predicatively, i.e., only as part of the assertion made about the things occurring as term. (“Russell’s logical atomism,” 2005)

Russell emphasizes the symbolic nature of proposition. He stated that certain statement does not possess any meaning on its own and should be viewed as an incomplete symbol. Moreover, it can be comprehended and perform the function only being a part of expression. Therefore, entities tend to uphold the same positions as prepositions even when they are replaced. Differences only occur in case of predictability of the occurrence of the entity.

Main Metaphysical Problems the Theory Was Supposed to Solve

Regarding the propositions, the philosopher by denoting objects discovered and attempted to solve two major problems. First, the theory solves the metaphysical problem of appearance and reality, which is a problem many people face. It has been shown that in some cases, two expressions that denote the same object are not necessarily identical. Therefore, these utterances are not always interchangeable and any substitution of one of them by the other one may cause the transformation of the original message. In fact, this issue has been demonstrated on the examples of the two phrases of identical meaning. Russell introduced the question “Is Walter Scott an author of the novel Waverly?” (“Russell’s logical atomism,” 2005). Since the answer is positive, it seems that the interchange of the two propositions “Walter Scott” and “the author of Waverly” will not provoke any changes of the content of the message. However, in that case, it becomes apparent that the king George IV who was asking a question wonders if Scott is actually the Scott. In fact, the propositions “the author of Waverley” and “Scott” are not identical, although it does not mean anything other than that person. In case it carried any other meaning, the whole phrase “Walter Scott is the author of Waverley” would be incorrect (“Russell’s logical atomism,” 2005).

Secondly, it solves the problem of the division of human knowledge into knowledge by acquaintance and knowledge by description. Notably, it was discovered that in certain cases, there may not be any mediocrity in verification of the message. One of the two propositions must be true, namely “A is B” or “A is not B”. For instance, no knowledgeable person can possibly recognize the statement “The present king of France is bald” as truthful one because in France, today there is no king. However, it cannot be treated as a mistake because in that case, the correct statement should be expressed as the opposite of the previously indicated one, “The present king of France is not bald” (“Russell’s logical atomism,” 2005). However, it is not appropriate as well. If one checks all the people who are bald and then those who are not and make lists of them, we will not find the present King of France in any of them.

Bertrand Russell concluded that the denial of the existence of something is always controversial and contradicts itself. In fact, if the expression “A is different from B” is true, then there must be certain differences between its components A and B. If it is false, it becomes evident that between A and B there is no difference, and it can be expressed in the following way, “The differences between A and B do not exist”. Hence, the problem lies in determination whether it is warrantable for a non-existent entity to be the subject of expression. After declaring the possibility of existence of certain thing, one could attribute the non-existence of something that is the subject of the statement and represents something real rather than nothing. In other words, statements about the non-existence of certain subjects contradict themselves.

In essence, the theory is always successful in solving these problems because it clearly discerns the kinds of knowledge that human beings possess in the process of trying to think about different things in the world. According to Carey (n.d.), with both descriptive and acquaintance knowledge, individuals are able to understand worldly matters from different perspectives. Moreover, the theory successfully solves the problem by appreciating the fact that matter that exists independently constitutes the world. The idea is reasonable as seen from the occupied world with varying states of matter such as solid and liquid.

Critics on the Theory of Logical Atomism

Russell suggested that in logically perfect language, each sign will correspond to a certain fact. Apparently, this will allow one to avoid any ambiguities and paradoxes. However, this point of view was criticized by “late” Wittgenstein and representatives of linguistic philosophy. The views of the later Wittgenstein on the nature and function of language is quite different from those that were expressed in the Tractatus Logico-Philosophicus. Thus, they are presented in the Philosophical Investigations.

First, the theory was criticized from the perspective of logic. Pears (1998) affirms that the doctrine of atomic propositions and facts was elaborated with the aim of bringing the ontological basis for a certain logical system, namely Principia Mathematica. However, human consciousness may use various kinds of logic, while the reality that the mind attempts to comprehend by the application of the logic is single. Hence, Russell’s logic is only one of the possible kinds of logic.

Critics of the theory claimed that if logic of Principia Mathematica was absolute (universal) value, Russell’s system could pretend to be named as a theory of truth. One could argue that logic and its language were formed under the influence of the structure of reality. Their main function is representation of the real world. Therefore, Pears (1998) indicates that knowing the structure of the language, one must be able to investigate the structure of the world on its basis. However, there are no means of insuring that the Principia Mathematica is absolute or universal logical system.

Wittgenstein admits that the simple atomic facts do not exist, and absolutely “simple” fact can be analyzed only in a relative sense. Mentioning anything “simple”, one has to always specify in relation to what does this “simple” exists, namely the context in which it is located. Carey (n.d.) stresses that a single word does not necessarily denote the same object. Thus, it can have a plurality of values ​​determined by the context. In fact, this situation was illustrated by the famous picture of rabbit and duck. Although the projection contour of the figure on the retina is constant, people can see the figure of a duck (right to left) or the rabbit (from left to right) taking into account the awareness of the semantic context of this image.

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