### Have you ever found yourself having a hard time responding to someone in an argument and not exactly knowing what the problem is?

Many times, the problem is that your opponent is making an assumption that you have not identified. And many times, it is this very assumption that is at issue. If you knew what it was, you could attack it and get on with your argument.

One of the main problems people face in debate—whether formal or informal—has to do with something their opponent is assuming but not stating. Often it is this assumption that is the real issue, but the person trying to argue against it is unaware of what it is.

In a logical argument, you have two premises (or assumptions) and one conclusion. In logic, this is called a “syllogism.” A classic example of a syllogism is the following:

Your conclusion is what you are trying to prove, and your two premises are your reasons for believing it. But in an actual discussion, you don’t use a logical syllogism; you use what Aristotle called a “rhetorical syllogism.” A rhetorical syllogism is an abbreviated argument—one in which you don’t state all your assumptions.

I was once in a debate about whether the Bible was reliable. My opponent contended that the Bible was not historically reliable because it was a religious book. This is a typical rhetorical syllogism:

But, again, this does not disclose the reasoning fully. There is something missing. A logic student would take his knowledge of arguments, and he would be able to back in to the missing assumption, revealing the debatable proposition. He would be able to look at what the argument does contain and derive what is missing.

The first thing he would do is identify the types of terms he has been given. Every argument contains three terms: a minor term, a major term, and a middle term. The minor term is the subject of the conclusion (in this case, “the Bible”); the major term is the predicate of the conclusion (in this case, “things that are historically unreliable”). The middle term is the term that appears in both premises, but not in the conclusion—the term by which the argument connects together the minor and major terms in the conclusion (in this case, “religious books”). Each one of these terms must appear twice.

A logic student would “mark” the terms so he knew which were which: “S” for the minor term, “P” for the major term, and “M” for the middle term. This would give him the following:

He would first note that, although S appears twice, the terms M and P do not. The missing premise, therefore, must contain the M and P terms. In other words, the missing premise is either “Historically unreliable books are religious books” or “All religious books are historically unreliable.” The logic student is armed with another piece of knowledge—how each of the 19 valid argument forms are structured (we won’t get into that here). He will see immediately that there is only one possibility in this case, which yields our missing statement:

In this particular case (a pretty self-evident one), many people could figure out the missing premise without knowing some of these things, but this is a pretty easy one. Many arguments are not so easy and require a more sophisticated knowledge of logic.

In the debate I was having, I asked my opponent if this was not his missing premise, which he agreed, in fact, it was. I then asked him, “How do you know this?” He went on about various reasons why religious books could be considered historically unreliable. But I said, “You have given me many reasons that I might be skeptical about these kinds of books, but in order to really know that all religious books are historically unreliable, wouldn’t you have had to test all of them yourself? Have you read them all? Do you know what they all claim? And can you tell me the ways in which they all come up short historically?” I was simply attacking the truth of his first, formerly missing, premise. Of course, he began backtracking quite a bit. And then I launched my logical attack: “Not only is the truth of your first premise questionable, but your argument itself has a severe logical flaw.”

“What is that?” he asked.

At this point, I observed that in order to know that all religious books are historically unreliable, you have to have analyzed all of them—including the one he made an assertion about in the conclusion: the Bible. I pointed out that in order to know that all these kinds of books were unreliable, he had to know that the Bible was unreliable first. But that was his conclusion!

In other words, he was assuming the conclusion in his first premise. He was assuming what he was trying to prove. This is a basic logical fallacy. You can’t assume the very thing you have set out to prove. That is, in fact, arguing in a circle.

But again, I could only point these things out because I was able to identify his basic assumption.

Originally published in *The Classical Teacher *Summer 2011 edition.