Logic

Hello everyone and welcome back to Deeper Waters where we are diving into the ocean of truth. We’ve been looking lately at what it means to become a thinking Christian and the next step to take is to learn something about thinking. That means logic. Logic doesn’t just mean right thinking. There are rules to thinking. There are a number of people who think that they are logical and they do not know the first thing about forming a syllogism.

Keep in mind this important truth. Logic is not a tool to discover truth per se. It is a tool to guide your thinking to see if something is true or false, but it itself cannot determine if something is true. It can determine if an argument is false if it is invalid, but that does not mean that the conclusion is false. I will demonstrate this with a few syllogism as I go along. Let’s start with the classic one.

All men are mortal.
Socrates is a man.
Socrates is mortal.

This is a valid syllogism and a true one. The important point with validity is that if a syllogism is valid in its form with true premises, then the conclusion MUST be true. The first sentence is called the major premise because it contains the major term, which will be the predicate in the conclusion. The second sentence is the minor premise as it contains the minor term, the subject of the conclusion. The term showing up in the premises but not the conclusion is the middle term.

Now let’s consider this syllogism.

All angels are rational.
Gabriel is rational.
Gabriel is an angel.

If you are a Christian, you could be quite tempted to immediately say that this syllogism is valid. We can agree with the conclusion, but the argument to get there doesn’t work. Want the proof? Take out Gabriel and put in your name and then tell me if you’re ontologically an angel. (I know some of you are really good people, and I don’t mean an angel in that way.) Gabriel could be the name of your next-door neighbor and while he is rational, he is not an angel.

The fallacy that has taken place is that of undistributed middle. A classic example of this was committed by a poster on Theologyweb with this syllogism. (To this day, he has not admitted it is invalid.)

All basketballs are round.
The Earth is round.
The Earth is a basketball.

The fallacy is called undistributed middle. In logic, there are four types of propositions.

A = All S is P.
E = No S is P.
I = Some S is P
O = Some S is not P.

A term is distributed if it refers to the entire class of which it speaks. In an A term, the subject is distributed. In an E term, the subject and predicate are distributed. In an I term, none of them are. In an O term, the predicate is. A rule is that the middle term MUST be distributed at least once.

Looking at the first syllogism, we find that rational is not distributed as rational is a predicate in both premises that are A premises. Therefore, the syllogism is invalid.

Note also that if you have a term distributed in the conclusion, it must be in the premises. Consider the following:

All snakes are reptiles.
No turtles are snakes.
No turtles are reptiles.

The problem is that reptiles is distributed in the conclusion, but it is not in the premise. Since this is the major term, it is the fallacy of illicit major. To do so with the minor term would be the fallacy of illicit minor.

This has been a brief look. We’ll discuss more tomorrow.