2. Atomic Sentences

We are familiar with the construction and expression of ideas and argument in our everyday lives.  We understand that making an argument involves connecting ideas together in a particular way, and we know that we need to take care with how we express those ideas to convey our point.  But we are complex beings, and we may come up with ideas and arguments that are long, obscure, indecipherable, or nonsensical.  Our introduction to logic comes by way of taking a systematized approach to analyzing the expressions that people make in the context of presenting a position or argument.  If we were able to find some way of analyzing arguments that produces reliable results about the ‘state’ or ‘quality’ of those arguments, then we would have a tool that would allow us to determine what constitutes a good argument, or, perhaps more importantly, why some arguments are problematic.

Atomic Sentence

The term atomic sentence is used to describe an idea that can either be true or false.  For our purposes, atomic sentences make up the most basic building blocks for the argument we will be analyzing in the text, hence the ‘atomic’ component:  the most basic unit involved in our logical system is a proposition or idea that can either be true or false.  Note that atomic sentences are not limited in terms of length or complexity of the words used to articulate the idea.  Instead, the atomic sentence represents the portion of an argument that may be truth or false in principle.  Note that, for our purposes, the ‘boundary’ of an atomic sentence is determined by the presence of logical operators.

Examples:

The sky is blue.

This is an example of an atomic sentence:  this is an idea that may be true or false in principle.  Importantly, we are not yet concerned with whether the idea is true in the real world; instead, we are simply recognizing that an atomic sentence is one statement, one idea that may be assigned a truth value of TRUE or FALSE.

How are you?

This is not an atomic sentence precisely because this statement cannot be clearly assigned a truth value of either a TRUE or FALSE.

Sit down!

Similarly, this is not an atomic sentence because this statement is not articulating an idea that may be true or false in some possible world.  Instead, this statement is a command.

She told me to sit down.

This is an atomic sentence because this idea may be assigned a truth value that reflects the state of some possible world.

Typically, atomic sentences involve the articulation of a subject and a predicate that represents the state of some possible world.  While we will be exploring a more complicated account of atomic sentences when we explore first order logic later in the text, we can think of atomic sentences as the most basic ‘holders’ of a truth value.

We will use capitalized letters (A, B, C, and so forth) to represent atomic sentences in our logical system.  Importantly, an atomic sentence represents one (and only one) statement that is capable of being true or false.