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Principles of Logical Atomism

Russell’s Principles

Constituting Bertrand Russell’s theory of logical atomism are three interworking parts: the atomic proposition, the atomic fact, and the atomic complex. An atomic proposition, also known as an elemental judgement, is a fundamental statement describing a single entity. Russell refers to this entity as an atomic fact, and recognizes a range of elements within each fact that he refers to as particulars and universals. A particular denotes a signifier such as a name, many of which may apply to a single atomic fact, while a universal clarifies and orders these particulars according to their interrelation. In Russell’s Theory of Acquaintance, awareness of these particulars and universals comes through sense data, such that one must become familiar with each element of an atomic fact in order to understand its full proposition. Every system consists of many atomic propositions and their corresponding atomic facts, known together as an atomic complex. Rather than decoding the complex in a top-down manner, or accepting a monistic form, logical atomism extracts and analyzes its propositions individually before considering their collective import.

Russell’s perspective on belief proved a point of contention between him and Wittgenstein, causing it to shift throughout his career. In logic, belief is a complex that possesses both true and untrue propositions. Initially, Russell plotted belief as the special relationship between a subject and a complex proposition, exempting it from the rules that govern other complex propositions where an internal fallacy disproves the whole. Later, he amended this to say that belief associates with universals and particulars directly, in keeping with his thoughts on the role of sense data. Here, the link between psychological experience - sense data - and components of logical atomism - universals and particulars - causes a breach in the typical logic of the theory; Russell’s logical atomism is in some respects defined by the binarism of metaphysics and analytical philosophy that is characteristic of naturalized epistemology. (Kitchner) - {Find Critique against Russell saying that the logical aspect of his theory wavered}

Of Russell’s work on logical atomism, the most controversial idea he proposed, following from his aforementioned Theory of Acquaintance and further elaborated in his Correspondence Theory of Truth, is that for every positive fact exists a parallel negative fact: a fact that is untrue. The Correspondence Theory maintains that every atomic proposition coordinates with exactly one atomic fact, and that all atomic facts exist. The Theory of Acquaintance says that for any given statement we understand - the statement taking the form of a proposition in logical atomism - we must be personally acquainted with each of its constituent parts. For example, in the positive statement, “the leaf is green,” we must be acquainted with the atomic fact that the leaf is green, and we know that this statement corresponds to exactly this one deduction. Continuing in this vein of thought, the complementary negative statement, “the leaf is not green” insinuates a falsehood that we are acquainted with, since we know the leaf is green, but also the necessary existence of this fact for the statement to stand. Regardless of whether the second statement is true or not, the connection between its proposition and the untrue fact must itself be true. Russell and Wittgenstein were concentrating on one central dogma that enables conclusions such as this to work, known as The Logically Perfect Language Principle. In essence, this principle permits the theories of logical atomism by establishing that all of reality exists as atomic proposition and fact, and that language can only signify reality. In Russell’s viewpoint, this necessitates the negative fact, whereas Wittgenstein kept to the conventional reasoning of “p” and “not-p” for defining his atomic propositions.

Wittgenstein’s Principles

In his Tractatus Logico-Philosophicus, Wittgenstein explains his version of logical atomism as the relation of proposition, state of affairs, object, and complex, often referred to as “Picture theory” (http://www.iep.utm.edu/wittgens/#H2). In view of Russell’s version, the propositions are congruent in that they are both unconvoluted statements about an atomic entity. Every atomic proposition is constructed from “names” that correspond to “objects”, and the interplay of these objects generate “states of affairs,” which are analogous to atomic facts. Where Russell identifies both particulars and universals, Wittgenstein amalgamates these into objects for the sake of protecting the truth-independence of his propositions; a self-contained state of affairs define each proposition, and the truth of a proposition cannot be proven by the sharing or exclusion of objects. In Russell’s work, his concept of universals and particulars denies truth-independence, as each universal accounts for a specific set of particulars, and the exact matching of any two sets implies equality, deviation implies inequality, and these act as qualifiers of truth. In Wittgenstein’s theory, an atomic complex is a layered proposition subsuming many atomic propositions, each representing its own state of affairs.

Wittgenstein’s handling of belief was dismissive, and reflects his abstainment from the epistemology that concerned Russell. Because his theory dealt with understanding the nature of reality, and because any item or process of the mind barring positive fact, i.e. something absolute and without interpretation, may become altered and thus divorced from reality, belief exists as a sign (semiotic) of reality but not reality itself. Wittgenstein was decidedly skeptical of epistemology, which tends to value unifying metaphysical ideas while depreciating the casewise and methodological inspection of philosophy that dominates his Tractatus Logico-Philosophicus. (Temelin) Furthermore, Wittgenstein concerned himself with defining the exact correspondence between language and reality wherein any explanation of reality that defies or overburdens these semantic structures, namely metaphysics, becomes unhinged. Ironically, Wittgenstein’s work bears the exact philosophical determinants that he openly admonished, hence his later abandonment of this theory altogether.

Third paragraph about Wittgenstein's N-operon (yet to write).