Russell’s Logical Atomism

Here’s a guide to Russell’s theory of Logical Atomism as introduced in his work- The Principles of Mathematics

Introduction to Russell

Bertrand Arthur William Russell (1872–1970) was an influential British philosopher and social critic. He made significant contributions to the fields of analytic philosophy and mathematical logic.

In this blog, the theory of Logical Atomism propounded by Russell (for which he partly credited Wittgenstein) will be discussed.

Overview of The Principles of Mathematics

In The Principle of Mathematics, Russell claims that mathematics and logic are identical, and that, in a strict, formal sense, everything can be reduced to logic. In other words, all experiences can be explained in terms of logical atoms. His atomistic philosophy is in direct contrast with monistic philosophy, as per which reality is believed to be single and indivisible.

What is Logical Atomism?

As per the theory of logical atomism, there is a perfect, one-to-one correspondence between an atomic proposition and an atomic fact (where the atomic proposition is an ‘atom’ of language). In other words, there is a corresponding atomic proposition for each atomic fact.

But what is an atomic proposition? An atomic proposition is that which asserts a certain quality as belonging to a certain thing. For example — Her hair is purple. In this proposition, the color purple is the quality being assigned to the person’s hair.

And what is an atomic fact? The simplest fact that signifies the possession of a certain quality to a specific thing is called an atomic fact.

So, when it is claimed that ‘language mirrors reality’, the proposition of the world being composed of simple and comprehensible facts is being referred to.

The Undeniable Data

To obtain truth, it is imperative that we first obtain undeniable data. The terms undeniable and true need to be distinguished here. Undeniable is a psychological term whereas true is not. To call something undeniable is to say that the thing being referred to will not be denied by anyone. This does not ascertain the thing as being true, but merely refers to the belief of people thinking of it as being true.

In the analysis of any theory, it should be kept in mind that it comes loaded with unavoidable subjectivity stemming from our own knowledge of the world. Then, if it appears to be true in our perception, we cannot go any further, as examining it outside of our mental capabilities is inconceivable.

Russell says that the so-called undeniable data of philosophy, that is claimed to be its starting point, is vague and ambiguous. He elucidates this with an example. If we state that there are x number of people in the room, the statement would appear undeniable. But when we attempt to define what a room is, who count as people, what it means for people to be in that room, and how one distinguishes between any of them, our reasoning will fall short, and our arguments might be, at best, circular. It is then that we realize how vague our statement was and how we didn’t actually know what we meant by it.

Sound philosophizing involves going from the vague and the ambiguous to the clear and precise. Analysis makes us realize that the vague and ambiguous is actually a shadow of what the truth is.

There is a risk of error when we attempt to transition from the vague and ambiguous to the clear and precise. The former could lose the undeniability it had when transformed to the latter. Also, the resultant latter might not even be true. These premises, which we use for building up certain systems, should not be confused with the premises for epistemology.

Way Back or Way Forward?

Russell pointed out that a great number of philosophical schools have a habit of tracing the roots of their premises further and further till they reach a point where they become inexact and vague. He called this a mistaken attempt to reach ‘primitive experiences’ instead of accepting our reflective capacity.

Emphasizing on the task of figuring out the nature of the world instead of merely studying its history, he stressed on the importance of not moving further back than we already are.

He praises the Cartesian system of doubting everything and only letting be those beliefs that are clear and distinct.

The World Contains Facts

Russell said that the world contains facts. Even though he doesn’t define them, he said that they determine the truth status of a proposition. To elucidate, if I say that it is sunny outside, my statement could be deemed false if the actual weather conditions are not reflected by it, as then, it would not be expressing a fact.

Russell also clarified how a single word is incapable of expressing a fact. For example, by itself, the word Hanks does not posit the existence of Hanks by the virtue of the word alone. Hence, the word Hanks cannot be understood to express the fact that Hanks exists. A fact requires a full sentence for its expression.

Characteristics of Facts

Facts are expressed by statements that assign certain properties or relations to and with certain things. The thing itself is not the fact, stressed Russell. Facts belong to the objective world, meaning that they are as much parts of the real world as physical objects like trees, birds and stones are. And their creation is not contingent upon our thoughts and beliefs. If we notice, most of the statements that we make express facts about the outer world (unless they are statements about psychological facts).

Types of Facts

General and particular facts: Russell clarified that particular facts like ‘This object is red’ are different from general facts like “All humans are mortal”. He stressed on the importance of both types of facts as they go hand-in-hand while attempting to describe the world.

Positive and negative facts: He briefly explained the distinction between these two — an example of a positive fact is “Faith is a choice” whereas an example of a negative fact is “Faith is not rational”.

On the Truth or Falsity of Facts

Russell stated that dualism of facts does not exist, i.e., there are no true or false facts, just facts. Qualities of truth or falsehood only apply to statements/propositions/judgements.

Symbols and Names

Russell called propositions symbols. A proposition can be called a complex symbol in the sense that it can be composed of parts that are in themselves symbols. For example — “Heat is a form of energy” is a sentence/complex symbol that contains multiple symbols.

Russell stressed upon the importance of understanding the theory of symbolism. If we fail to do so, we might mistake the properties of a symbol to be the properties of a thing. A confusion between the symbol and the thing being symbolized results in fallacies.

Russell stated that names are the right symbols to use for a person, and that sentences/propositions are the right symbols to use for facts. Sentences/propositions might be true or false, but such a duality does not exist for facts. It must be noted here that propositions are not names for facts, as the relation between a fact and a proposition is different from the relation between a name and the thing being named. Names are used for particulars. They can have only one relation with the thing they name.

Facts cannot be named. They can only be asserted, denied, desired, willed, wished or questioned. The thing that makes a proposition true or false cannot be put in the position of a logical subject.

Takeaway

As per Logical Atomism, language can be broken down into smaller parts by rigorous analysis. This process of breaking down a sentence into ‘logical atoms’ enables one to identify its underlying assumptions and thus better judge its truth or falsity.