Philosophy of Being and Knowledge

Philosophy of Language

Logical Atomism

Another foundational figure in analytic philosophy was the English philosopher Bertrand Russell (1872-1970), known for his active public engagement (Russell was a driving force behind the founding of the Pugwash Conferences on Science and World Affairs in 1955, based on the Einstein-Russell Manifesto). In 1950, Russell was awarded the Nobel Prize in Literature. From 1910 to 1913, he co-authored, with Alfred North Whitehead, the three-volume work Principia Mathematica, which significantly impacted the development of mathematics and logic. Russell's philosophical stance is commonly referred to as logical atomism. This doctrine was further developed by his student and collaborator, the Austrian philosopher Ludwig Wittgenstein (1889-1951). Wittgenstein’s work is typically divided into two periods: the early or Vienna period, during which he expanded on the ideas of logical atomism, and the later or Cambridge period, when he laid the groundwork for the philosophy of ordinary language. The similarity, or even identity, between Russell’s and Wittgenstein’s ideas is attributed to their collaborative development of these concepts. Despite being Russell’s student, Wittgenstein inspired Russell’s own notions of logical atomism.

Logical atomists contended that philosophical problems which remain unresolved over time are not due to the inherent complexity of the subject matter but rather to the inadequacy of language. To overcome these problems, language must be purified, necessitating the establishment of a criterion to determine which propositions to discard and which to retain. This criterion is the truth value. In logic, truth value refers to the truth or falsity of a proposition. There are three forms of thought: concepts, propositions, and inferences. Concepts themselves cannot be true or false, meaning they lack truth value. Similarly, inferences can be correct or incorrect, but not true or false. Only propositions can be true or false; thus, truth value is a characteristic of propositions.

According to Russell, the object of knowledge is what propositions describe. For instance, the proposition "The table is rectangular" describes the fact that the table is rectangular. It does not describe the table or the rectangle itself, but rather the relation between them. The relationship between objects conceived in a proposition, Russell called atomic facts. A specific table is an atom of reality, meaning a singular and independent entity. This table has a certain property, and this property is expressed through a proposition. The fact of the presence of a property in an object is an atomic fact. However, atomic facts can only be discussed when referring to individual things, not general cases. For example, the proposition "All Ukrainians have read Shevchenko’s works" does not express an atomic fact, whereas "This man has read Shevchenko’s works" does express an atomic fact. The distinction between these propositions is that the latter can be verified, and its truth value established through verification, while the former cannot be directly verified. To verify the first proposition, it must be broken down into atomic propositions concerning each individual Ukrainian, checked, and then the data combined. Thus, the fact that all Ukrainians have read Shevchenko’s works is molecular, consisting of many atomic facts. Atomic facts are described by atomic propositions. An atomic proposition is one that describes an atomic fact and can be verified based on this fact. They are suitable for use in philosophy and language. Problems arise with propositions that do not express any atomic fact. For example, there is no atomic fact that can be studied to determine whether the proposition "Love will save the world" is true or not. This poetic statement is appropriate in poems or novels, but when such utterances enter the realm of science, they create numerous problems; thus, science must be cleansed of such statements. Wittgenstein explained that atomic propositions reflect atomic facts, and thus language is a mirror of reality. This doctrine of Wittgenstein is articulated in the Tractatus Logico-Philosophicus and is known as the "picture theory."

An important aspect of logical analysis of language and set theory is Russell's Paradox. Russell posited that all sets can be divided into two categories: closed and open. An open set is one that is not an element of itself. For instance, the set of tables is not a table itself and thus does not include itself, and the set of people is not a person. A closed set is one that is an element of itself. For example, if all sets are combined, a set of sets is created, but this set of sets is a set, hence an element of itself. If there are open and closed sets, then one can speak of a set of open sets and a set of closed sets. The problem arises when trying to determine whether the set of open sets is itself open or closed. If the set of open sets is open, then it is an element of itself. But a set that is an element of itself is closed. Therefore, the set of open sets is closed. However, the set of closed sets contains only closed sets; if the set of open sets is part of the set of closed sets, it is open. Thus, the set of open sets is neither open nor closed. This is the essence of Russell's Paradox.

Russell proposed a solution to this paradox, known as the theory of types. Each proposition belongs to a specific type. For instance, "A car is a type of transport" and "A car is a noun" belong to different types: the former discusses objects, while the latter discusses language (meta-language). Problems arise when the distinctions between types are not observed, and language about objects is mixed with language about language. If type differences are ignored, the two propositions can be conflated into the statement "A noun is a type of transport." Such errors can be avoided by using language about objects for objects and language about language for meta-language. The theory of types led to a distinction in analytic philosophy between language and meta-language, that is, language about language.