The concept of distribution in the Syllogism

What follows is the transcript from the following video :
https://www.udemy.com/course/introduction-to-logic01/learn/lecture/26199074/

Today we’re going to present in this short video, what the distribution is and how it matters in a syllogism. Remember a syllogism is made of three propositions, two premises, and one conclusion. Now the parts of a propositions are the quantifier, the subject, the copula and the predicate. A quantifier is ‘all’ our, ‘some’, the subject is the subject.

So, the subject is the term, the copula is the verb (the link between the subject and the predicate) and the predicate is the other term. For example, ‘all human beings are mortal’. All is the quantifier, human beings the subject, are the copula, mortal the predicate. What matters now in this analysis, is that you focus on the subject and the predicate because they are the terms in this proposition and the terms are those you have to watch for when you decide about distribution or undistribution. What is distribution? The definition of distribution is as follows: a term, either a subject or a predicate is distributed, if it refers to the whole class it names. In the proposition, all human beings are mortal, the term, ‘all human beings’ is the subject that is distributed to the entire class it to names. So, the name of this class is all human beings. And when I say ‘all’, I refer to the entire class, to all the members of this class. The subject of the proposition, therefore, ‘all human beings are mortal’ is the distributed subject.

Next is, of course, in the same proposition the predicate ‘mortal’, which although it names a class, it does not reflect onto the whole of the class, it does not refer to the entire class. In fact, for example, it does not cover the animals, which are also mortal. Therefore, the predicate in this proposition is not distributed, right.

We can look at the definition of undistribution: a term is undistributed if it refers not to the whole class it names, but to only a part of the class, as we have seen in ‘all human beings are mortal. ‘Mortal’ is the undistributed term. It does not refer to the entire class it names.

The four types of categorical proposition.

We have seen already in the previous videos that we have 4 types of categorical propositions: A type, E type, I and type O. A – universal affirmative ‘all human beings are mortal. E – universal negative, ‘no dogs has wings’, I particular affirmative, ‘Some is called Socrates’. O – particular negative ‘This man is not Socrates’, ‘Some men is not Socrates’. These are the four types of propositions.

How the concept of distribution and undistribution applies to those terms of those propositions so we can [00:04:00] draw the following tables. First table, we look at the subject as a preposition. Remember we have to look either at the subject, either are to the predicate. First we look at the subject, the subject of a name preposition is distributed.

The subject of an E proposition is distributed. The subject of the I proposition is undistributed; the subject of a O prophecy is undistributed and consequently, what we look at is the predicate of the proposition. And we see that the predicate of an A proposition is undistributed – the predicate, remember, the predicate of a E proposition is distributed.

The predicate of a I proposition is undistributed. The predicated of an O proposition is distributed. With these two tables, you can have a clear visualization of the distribution for the subject and for the predicate, according to which proposition you’re dealing with: an A proposition, an E proposition, an I proposition or an O proposition.

And now why this concept of distribution and undistribution is important? Because of the first rule of the Syllogism. The first rule to define, to determine, to decide of a valid syllogism says: rule one, the middle term must be distributed at least once. So, you have to understand what the distribution means to apply the first rule.

You have to look at the middle term. And the middle term is the term that occurs in the major and in the minor premise. And you look at it and you see if it’s distributed; it must be distributed at least once. The second rule is that a term that is distributed in the conclusion must be distributed in one of the premises.

This is also important. So, these two rules to decide of a valid syllogism, okay, require that you understand the concept of distribution. You look at the term that you have to consider; in this case, you have to see if the subject of an A proposition, or the predicate of A proposition and so on. With the tables I have provided here, you can look quickly at them. You have to understand what distribution means.

When a term names a class, it must refer to the entire class; if the term names a class, but does not refer to the entire class, then there is no distribution.

Okay. Thank you very much for watching this video. I hope this has been useful to you because the concept of distribution is important to decide of the validity of a syllogism.

Okay. Thank you. Until the next video, enjoy learning and don’t forget to live. Thank you.