What is a Statement?

Foundations of Logic

Becoming a good philosopher and logician starts with taking notice of, and becoming interested in, certain things which may seem obvious and mundane to, and are therefore taken for granted by, the majority of people. The concept of a statement, for instance. What is a statement? If you had to define it for yourself, what would you say it is? Maybe stop now for just a second and try to define it.

Now that you have considered the concept of a statement, consider also the following sentences:

1. How many roads lead to Rome?

2. Go therefore and make disciples of all nations.

3. The world is full of trousered apes.

4. “’Twas brillig, and the slithy toves did gyre and gimble in the wabe.”¹

One of these sentences is a statement, the other three are not. But which one is the statement, and what qualifies it to be so whereas the other three fail to meet the proper conditions?

The first distinction which may be important to make is that the terms sentence and statement are not equivalent. Though not equivalent in meaning, sentence and statement do have a relationship. Sentence has the relation of being a genus of the term statement and statement has the relation of being a species of sentence. A genus is a kind of umbrella category wheres a species is a sub-category of that same genus (e.g. if we take “human” as a genus then “male” and “female” would be species of that genus). Another way to put this is to say “All statements are sentences, but not all sentences are statements.”

The above-given four examples are all species of the category sentence, but only the third example is a statement. Let’s identify the other three species of sentences.

Sentence one is a question. Questions are sentences which typically request information. I say “typically” because there are those questions which are rhetorical in nature and are actually meant to imply a specific answer (e.g. “Do not all men breathe the same air?”).

Sentence two is a command. Commands are sentences which typically demand action from another person. I say “typically” because there are some instances where a person issues a self-command (e.g. “Do better, Jacob!”).

Sentence four is nonsense. Nonsense sentences are sentences which fail to convey any intelligible meaning. They cannot be decoded by more effort (such as one could do when confronted with a sentence written in a foreign language), there is no meaning to be found.

Turning our attention back to the third sentence we will find that it is, in fact, a statement. Statements are sentences which make a claim about something and that claim is, necessarily, either true or false. A statement is true if what it is claiming to be so, or not be so, corresponds with the way things actually are. A statement is false if what it is claiming to be so, or not be so, is not in accord (agreement) with the way things actually are.

Some statements may not be within our power to judge as to whether they are true or false because of our finitude as human beings. For instance, if a person claims “The star furthest from planet earth has a planet in its orbit which would be inhabitable for human beings” there is no way for anyone to either confirm or deny this statement based on available information. Nevertheless, it either is or is not the case that this is so. Even if no man knows, it still either is or isn’t the case.²

There are simple statements and there are compound statements. This is a simple statement. The first statement in this paragraph, however, was a compound statement because the word “and” is functioning as a conjunction which joins two simple statements together, namely, “There are simple statements” and “There are compound statements.” For now we are only going to concern ourselves with simple statements, but there are many important considerations in logic when it comes to how to handle compound propositions (a synonym for statements).

Let’s analyze the following clear and simple statement. “All men are mortal.” Every statement has a subject, a predicate, and a copula. Every statement also claims something about the quantity and quality of the subject.

In our sample statement (“All men are mortal”) the term “men” is the subject. The subject is that about which the statement is making a claim.

In our sample statement (“All men are mortal”) the term “mortal” is the predicate. The predicate is that which is being claimed to be so, or not so, about the given subject.

In our sample statement (“All men are mortal”) the word “are” is the copula. The copula is also referred to as “the verb of being” and it joins the subject and the predicate together. The copula determines the tense (past, present, future) of the statement and must be in agreement with the plurality or singularity of the subject of the statement (e.g. “The man is working” or “The men are working”). Forms of the copula include, but are not limited to, is, is not, are, are not, was, was not, were, were not, and will be or will not be.

In our sample statement (“All men are mortal”) the word “All” is the quantifier. It tells us the extent of what is being claimed concerning the subject. In this case the claim extends to the entire class of those who can rightfully be called “men.” All possible quantifiers can be logically reduced to one of four quantifying terms, namely, all, no, some, and some not.

The quantifiers all and no are universal in their extent. When these quantifiers are employed in a statement it means that the claim being made is about the entirety of the subject’s class.

The quantifiers some and some not are particular in their extent. When these quantifiers are employed in a statement it means that the claim being made is being applied to a limited number of those things which belong to the subject’s class. That number must be at least one or more of the subject class and less than the complete set of all members of the subject class.³

In our sample statement (“All men are mortal”) the qualifier is the word “are” (which is also the copula). The copula is always the qualifier as well as that which joins the subject and predicate together. The qualifier determines whether the statement is affirming or negating something (namely the predicate) about the subject.

Every simple statement has all of these parts, even if they are stated in irregular ways as colloquial (every day, normal) speech and writing tends to be. Non-standard-form statements can always be converted into standard form for easier analysis. Every compound statement is simply two or more simple statements which have been connected together by a conjunct (and, but, still, etc.), a disjunct (or), a hypothetical (If/then), or some by some other linguistic connector. Compound statements can always be broken apart and analyzed as simple statements when necessary.

Understanding the parts of simple statements is necessary to the work of Categorical Logic (also known as Aristotelian Logic, because Aristotle explained and codified this approach to logic in his works on logic known as the Organon). Categorical logic is concerned with analyzing the relationship between the terms (subjects and predicates) of two related simple statements so as to, in turn, draw necessary conclusions by inference.

Soon we will take a look at the four different kinds of categorical statements and there relations to one another and then we will consider the form of logical argumentation known as the syllogism.

1. From The Jabberwocky, by Lewis Carroll.

2. If truth and falsity depend upon being apprehended by a mind (which is an interesting question) then all propositions indeterminable to man remain either true or false because God is the objective knower of all things.

3. Nota bene, a statement claiming that “some men are mortal” makes a more modest claim than “all men are mortal,” but the statement “some men are mortal” does not make any claim against “all men” being mortal. Of necessity, if “all men” are mortal, then “some men” (being a sub-set of the whole) are also mortal.