Logic for Theological Discussion (LTD): parts of an argument

One of the fundamental ideas in logic is that in an argument, you have two sorts of ideas (statements) being presented: a conclusion, and one or more premises.

The conclusion ought to be fairly self-evident in definition: that point which the whole of the argument is attempting to demonstrate to be the case.

The premises (and there is almost always more than one) are those phrases or sentences (also known as statements) which are asserted as reasons to believe the conclusion.

Now, let’s talk about truth and what is called “truth value” for a moment. whenever a sentence can be said to be true or false, that sentence has a “truth value”-- and the truth value is whether or not it is true or false. Some sentences cannot be said to be true or false. A question, for example, or an exclamation cannot be disputed as untrue. But a premise MUST be a sentence that can be said to be true or false.

However, it is technically incorrect to say that an argument is “true” or “false”. This is because there is more to whether an argument is a good one or not than simply the truth value of its statements. Rather, an argument can be said to be two things: valid (or invalid), and sound (or unsound).

Validity (whether an argument is valid or not) is based on form alone, not on content. I know what you’re thinking: “is it possible for an argument to have premises that are both true, and a conclusion that is true, and the argument still not be valid?” Good question-- and the answer is yes. In fact, any of the following are possible:

• A valid argument whose premises are true and conclusion is false.
• An invalid argument whose premises and conclusion are true.
• A valid argument whose premises and conclusion are false.
• A valid argument whose premises are false and conclusion is true.

Of course, it’s also possible to have a valid argument whose premises and conclusion are all true. When that is the case, we say that the argument is “sound.” (All other cases are examples of unsound arguments.)

Validity is a complex thing, and I won’t get into it in detail now. I may dedicate a post or two to it in the future. Let’s assume, for now, that the arguments presented are valid (which is a treacherous assumption in many cases).

The tricky part about soundness in arguments is that there is often one or more premises that are left out-- either because they are implied within the argument, they are unknown factors (either to the arguer or the listener), or because to state them outright would expose the argument as unsound. It is the last case that gets us into the most trouble when it comes to theological discussions.

For example, I overheard a discussion at General Assembly about the meaning of the phrase, “their wives must be women worthy of respect” in 1 Timothy 3:11. Of the two people discussing the matter, one (we’ll call him Fred) was convinced that a naked reading of the English as rendered in the NIV was plain in its meaning-- clearly, thought he, this verse means that the verse is speaking of the wives of Deacons, not women in general. The other fellow (who we’ll call Joe) thought that, since the English is a translation from another language, we must be careful to assume that a naked reading is always accurate; he also felt that the naked reading was problematic because of what is in the original Greek (specifically, that the word translated as “wives” can also mean simply, “women”). The dialogue went something like this:

Fred: Clearly, 1 Timothy doesn’t suggest that a woman may be a Deacon or Deaconess.
Joe: I’m not sure that we can say that with such certainty. Doesn’t that assume a lot of what the translation ought to be?
Fred: Like what?
Joe: Like, what about the fact that the word translated “wives” can also mean just “women”?
Fred: Don’t you think that the Bible is clear?
Joe: Well, I was reading a commentary by a scholar I trust, and he said it wasn’t so cut-and-dried.
Fred: Some have their opinions about what this verse means, but I for one don’t think we should undermine God.

So, here’s the argument as it was stated:

Premise 1: Some people have theories about what 1 Tim. 3:11 means. (Truth value= true)
Premise 2: We shouldn’t undermine God. (Truth value= true)
Conclusion: 1 Timothy does not suggest that a woman may be a Deacon or Deaconess.

So, assuming the argument is valid, is this argument sound, or unsound? Look at the argument in the original dialogue again; is there a missing premise?

I would argue that there is-- though my guess is that even Fred doesn’t realize that it is there. I think the argument really goes like this:

Premise 1: Some people have theories about what 1 Tim. 3:11 means. (Truth value= true)
Missing Premise: My opinion about what it means is the same as God’s opinion about what it means.
Premise 2: We shouldn’t undermine God. (Truth value= true)
Conclusion: 1 Timothy does not suggest that a woman may be a Deacon or Deaconess.

See the problem? Now, this argument (as presented in the “full” version) has lots of problems, including the use of several “fallacies” which we’ll get into next time. But I hope that, even in this brief example, it is becoming clear how arguments work and how the truth can be easily missed or even distorted.