Subjects and Predicates in Language and Logic

Grammatical terms mislead us; I’ve argued this case previously: Exhibit A and Exhibit B. Too often, non-linguists read too deeply into the names of terminology, drawing conclusions that conclude too much. As Exhibit C, I present a case study with the terms “subject” and “predicate”:

Recently, I was teaching a Critical Thinking course with a unit on class logic and set theory. Things were going swell—all Venn diagrams and syllogistic reasoning—until my unfortunate students stumbled into this textbook passage:

Categorical propositions, and indeed all English sentences, can be broken down into two parts—the subject and the predicate. These terms are shared by both grammar and logic, and they mean the same thing in both disciplines. The subject is that part of the sentence about which something is being asserted, and the predicate includes everything being asserted about the subject. (Writing Logically, Thinking Critically, by Sheila Cooper and Rosemary Patton, 7^th edition, p.161, emphasis mine)

Reviewing this passage with my students, I explained my nuanced position:

First, imagine students trying to get their brains around Cooper and Patton’s final sentence. Isn’t every part of every sentence a part about which something is being asserted? Is every part of a sentence a subject?

Where does Cooper and Patton’s claim originate from? I’ve got my hunch. The analysis that grammatical subjects/predicates are equivalent to the logical ones traces back to Aristotle. In an Aristotelian analysis, we see the sentence

1. Socrates is mortal.

(In this example sentence and others, the grammatical subject is colored blue, and the grammatical predicate, orange.)

analyzed such that “Socrates” is both the logical and grammatical subject, and something like “(is) mortal” is the logical and grammatical predicate. In set theory, this means that the individual “Socrates” belongs to the set of individuals that are mortal.

Aristotle’s analysis—one of the first recorded analyses of the semantics of human language—lags behind the state of the art by a couple millennium. In fairness, though, if we’re only analyzing tidy sentences like #1, the logical terms and the linguistic terms line up nicely. But when we analyze more complex sentences, things get messy.

Cooper and Patton’s analysis suggests that a grammatically active sentence and its passive counterpart have different meanings:

2. John hit Mary. (active)

3. Mary was hit by John. (passive)

In fact, #2 and #3 are logically synonymous—each holds true (or false) in exactly the same situations as the other. #2 and #3 differ crucially in their pragmatics. #2 is a more natural answer to

4. What did John do?

while #3 is a more natural answer to

5. What happened to Mary?

Cooper and Patton’s analysis hits another problem with sentences where the grammatical subject does not refer to an entity:

6. There’s a problem.

7. It rained.

In #6, “there” acts as filler material, occupying the grammatical subject position of what linguists call an existential construction. (This assumes a reading where #6 posits the existence of a problem, as opposed to the location of a problem). In #7, “it” is similarly used to fill the grammatical subject position of the meteorological verb “rain.”

As Cooper and Patton would analyze #6 and #7, the entity “there” would probably belong to the set of entities that “is/are a problem,” while the entity “it” would belong to the set of entities that “rained.” But these “meanings” don’t compute.

Cooper and Patton’s analysis grows even more problematic when we examine certain expressions of quantification:

8. Not everyone slept.

If you believe Cooper and Patton’s analysis, this sentence would mean that the entity “not everyone” belongs to the set of individuals who slept. Probably not the right semantic analysis. The sentence is better translated into set theory as follows: at least one person does not belong to the set of individuals that slept.

So what exactly is the relationship between the grammatical subject/predicate and the logical ones? Actually, a couple of these terms have gone obsolete, and we should examine each separately:

The grammatical subject: To linguists, this is a purely syntactic position, largely independent of semantics. In English, the subject is identifiable by a number of syntactic and morphological features. Most notably, it’s a noun-phrase in a pre-verbal position. Typically, the subject and verb agree in number. A number of other tests can pinpoint the grammatical subject of a sentence, but the two above are most reliable.

The grammatical predicate: amongst linguists, this term has long disappeared from usage. It still lingers in English textbooks, where its definition tends to be muddled. Some textbooks define it in negative terms—it’s every part of the sentence other than the grammatical subject. In practice, such a definition approximates what linguists might call a “verb phrase.”

The logical subject: the term “subject” isn’t really used in logic or set theory. (I’ve seen it in literary theory, but that’s a separate usage.) Semanticists and logicians tend to speak instead about individuals or entities.

The logical predicate: this term defies easy definition, but it’s used in set theory and predicate calculus (a logical language). A predicate is a semantic relation that applies to one or more arguments. A one-place predicate would be “(be) green.” A two-place predicate takes two arguments. For example, the two-place predicate  “hit” involves both at hitter and the entity being hit. Nouns, verbs, and adjectives all correspond to semantic predicates.

As teachers, we must remember that a human language like English differs fundamentally from a logical language. Human language is messy, littered with vagueness and ambiguity. With time, usage and meaning drifts. Humans misunderstand and re-interpret. To skirt these problems, logical languages are crafted. Terms in logical languages are supposed to be defined carefully. An expression of logical language carries one unambiguous, unchanging meaning. Writing teachers will always be puzzling over the meanings within student essays, but a computer program will never puzzle over how to interpret a particularly complex line of code.