The Classification of Statements in Logic

In the previous post, we discussed generally which sentences qualify as statements in logic. In doing so, we established that statements are declarative sentences that have a truth value (i.e., they have the capacity to be either true or false). In this post we will discuss how statements are categorized, based on their contents, as either simple statements or compound statements.

Axiomatically enough, as its name suggests, a simple statement is a declarative sentence that pertains to a factual matter or claim thereby imbuing it with its truth value with respect to a single idea. And, by corollary, a compound statement is a declarative sentence that asserts a fact or claim with respect to multiple ideas. The common denominator between both types of statements is that they both carry truth values. The differentiator, however, between the two types of statements is that simple statements lack connectives whereas compound statements necessarily contain them.

It bears mentioning that the truth value of a statement is its quality that renders it capable of being tested for alignment with reality (i.e., with factual circumstances). In other words, truth value is the quality of a statement to be either empirically true or false (but neither both nor something in between). Accordingly, “finding the truth value” of a statement means analyzing it to ascertain whether it is true or false. It is the process of the testing the statement to ascertain whether it corresponds with external facts and circumstances.

Consider the following two statements:

• Albany is the capital city of New York State.
• If you eat less and exercise more, then you will lose weight.

Notice that each of the two foregoing statements contains truth values; they both have the capacity to be either true or false (but neither both nor anything in between). However, what is unique to each statement is the number of ideas that each contains. Whereas the former concerns itself with a single idea, the latter concerns itself with more than one idea that are combined together in a single statement. This is precisely what distinguishes simple statements from compound statements in logic.

As can be seen, compound statements are syntactically more complex than are simple statements. Therefore, it behooves us to study the syntax of compound statements in order to develop a firm grasp over them. Since philosophical language tends to be very rich, philosophical statements use many words to connect ideas. The words used to combine multiple ideas in a statement are called connectives. Since connectives are the lynchpin to compound statements, a lexical inquiry into the plain meaning of the ordinary English language word “connective” would be highly useful.

The word “connective” is comprised of the prefix “-con,” the base “nect,” and the suffix “-ive.” “Con-” is itself a variant of the prefix “com-” which means with, together, jointly, collectively etc. The base root “nect” means to tie, to bind, to join, to place beside etc. The suffix “-ive” functions to convert verbs and nouns into adjectives and it means akin to, having the quality of, tending to etc. Taken together, “connective’s” root-constructed meaning could be understood as something that tends to bring things or people together or something that has the quality of binding things together. So, based on the root-constructed meaning, “connective” could be thought of as a glue of sorts.

This is not far off the mark from “connective’s” contemporary dictionary definition which means something that connects or something that serves to connect. The ordinary English language word, “connective,” depending on its usage, functions either as a noun or as an adjective despite containing the suffix “-ive.”

Notwithstanding “connective’s” morphology and denotation, connective in the fields of philosophy and logic is a technical term, the definition of which is more specific than its ordinary, vernacular meaning. It means a word or term that joins or relates multiple ideas (i.e., statements) in such a way that the truth value of the resulting compound statement is determined by the truth value of each of its indivisible components. The centrality of connectives to compound statements and vice versa is such that either term cannot be defined without referring to the other.

The more important point to absorb is that in order to effectively analyze compound statements, one must be able to effectively disaggregate compound statements into its component parts. This, in turn, requires one to be equipped to identify the placement of the connectives in compound statements. This is necessary because without such identification one cannot accurately demarcate the component ideas resident in a compound statement. However, after precisely identifying the connectives, one can accurate disaggregate a compound statement’s component parts and then carefully analyze the implications of each component part.

The connectives used in logic generally fall into five categories: conjunction, disjunction, negation, conditional, and biconditional. We shall expound on each of these distinct forms of connectives and their implications to compound statements in a series of upcoming posts.