Part I: Lesson

“Not every sentence is true or false; a prayer, for instance, is a sentence but it is neither true nor false. Let us set aside these other cases, since inquiry into them is more appropriate for rhetoric or poetics; our present study concerns affirmations”

Aristotle, De Interpretatione (Irwin and Fine, 1996)

As mentioned in an earlier lesson, logic is composed of terms, propositions, and syllogisms. In this lesson we will be talking about propositions and the parts of which they are made. 

To review, propositions (what Aristotle here calls an “affirmation”) can be thought of as a sentence that can either be true or false. There are three parts to every proposition: 

• Subject – The categorematic term that the proposition is about, or the category of thing(s) to which a property is being ascribed in the proposition. 
• Predicate – The property which is being ascribed to the subject in the proposition. This also takes the form of a categorematic term.  
• Copula – The linking verb which does the job of ascribing the predicate to the subject; generally speaking, this will take some form of the verb “to be” in english, however strictly speaking this is not always the case.

Not all propositions start in a nice “subject-copula-predicate” form, however. Take the propositions:

1. All trees have trunks.
2. Plato stands 10 feet tall.

In these two examples, the copula takes the forms of the verbs “have” and “stands”. We can reformulate these types of propositions to make the copula explicit. Doing so will allow us to better understand which categories the subject term and the predicate term represent. 

For propositions of the first sort, it must be understood that the verb taking the appearance of the copula is actually part of the predicate. From our example before, the proposition can be reformulated along the lines of this realization to show its true form. 

1. All trees are things that have trunks.

Now it is explicit that the subject designates the category “trees” and that the predicate designates the category “things that have trunks”.  Specifically, all members of the former category are also members of the latter category. In other words, the proposition says that all members of the category “trees” have the property of having a trunk, which is the property exclusive to all members of the category “things that have trunks”.  From our second example above we get:

2. Plato is a thing that stands 5-feet tall

It is now explicit that the two categories being compared are “Plato” and “things that are 10-feet tall”. We are saying that the only member of the first category (Plato himself) is a member of the latter category. Specifically, Plato has the property of being 5-feet tall, which is only a property common to all members of the category “a thing that stands 5-feet tall.” Therefore, Plato is a member of the category “a thing that stands 5-feet tall.” 

 All non-standard forms of the copula can be rephrased this way. Why? Well, everything is a thing, literally! In other words, the category “things” contains everything, including the members of whatever category is designated by any possible subject. Since we can predicate “thing” of literally anything, making it explicit in a predicate does not change the meaning of the original proposition.

For both cases, it is important to paraphrase the assertions stated in ways that will reveal the true form of the copula. This is important because propositions compare categories, which should be made explicit in their formulation.