Monday, February 12, 2007

Zanchius: Logic gone awry - Part II

Immanual Kant said, "Fallacious and misleading arguments are most easily detected if set out in correct syllogistic form." [Quoted in Copi and Cohen, "Introduction to Logic," 10th ed., p. 256.]

Kant was certainly correct, and it is just this procedure that I hope to apply to the argument of Zanchius in respect of Romans 8:32. In part I, I made a critique of the logic of Jerome Zanchius in the argument he used to reach the conclusion that Christ did not die for every man. He committed a fairly egregious error in logic, which shows that he was capable of making such errors. I say that to prepare the reader's mind to accept that Zanchius might have made a similar error in his analysis of Romans 8:32. Some readers will be strongly tempted to try to rehabilitate Zanchius as if his logic were not really flawed — as if it were all just a big misunderstanding. No; Zanchius could — and did — commit logical errors of the most obvious kind.

Here is Zanchius's comment on Romans 8:32 (which is in the paragraph following the paragraphs I criticized in part I:

In the same chapter Paul asks, "He that spared not His own Son, but delivered Him up for us all [i.e., for all us elect persons], how shall He not, with Him, also freely give us all things?" i.e., salvation and all things necessary to it. Now, it is certain that these are not given to every individual, and yet, if Paul says true, they are given to all those for whom Christ was delivered to death; consequently He was not delivered to death for every individual.

This is a two-step argument, consisting of two categorical syllogisms. The second argument is a good and powerful one, and I'll set it out first.

All died-for are regenerated,
Some men are not regenerated;
Therefore some men are not died-for.

I use the term "died-for" as a short way of expressing "those for whom Christ died." I use the term "regenerated" as referring to those men who are given salvation and all things necessary to it — who one day come to faith. This is a valid argument, and if the premises are true, then the conclusion must be true. I suspect many have been convinced of the truth of limited atonement by this argument. We can analyze this argument using Venn diagrams. The major premise looks like this:

We add a cross to the diagram to represent the minor premise, "some men are not regenerated."

The cross must go somewhere outside the "regenerated" circle (as required by the minor premise) and somewhere outside the "died-for" circle as required by the major premise (the major premise shaded out as empty all the area within the "died-for" circle that is outside the "regenerated" circle). The only place the cross can be placed is in an area that indicates that there are some men (at least one man) who is outside the "died-for" circle, and thus Zanchius's syllogism is confirmed. There is at least one man (probably Judas — and many more beside) who is not died-for.

The conclusion follows ineluctably from the premises. Where does Zanchius get these premises from? The minor premise is universally believed to be true — at least by conservative Christians. But what of the major premise? That premise comes from the first argument in the two-step chain of argumentation.

This premise is contained in the clause, "and yet, if Paul says true, they are given to all those for whom Christ was delivered to death...." The word "if" indicates to us that Zanchius has reached this conclusion as the result of a previous argument. (If such and such is true, then such and such proposition follows.) Zanchius claims to get the proposition from the apostle. But since the verse does not contain this proposition explicitly, it must come as the result of an argument.

So what is this step-one argument? Here it is, taken from Zanchius's paragraph, paraphrased and set down in syllogistic form:

All elect are died-for,
all elect are regenerated;
therefore, all died-for are regenerated.

Before we turn to the Venn diagram, let's confirm that we have represented Zanchius accurately. The first premise (it is actually the minor premise) says "all elect are died-for." This comes from Zanchius's statement, "He that spared not His own Son, but delivered Him up for us all [i.e., for all us elect persons]...." To paraphrase, Christ was delivered up for all us elect persons. Or — even shorter — all elect are died-for.

The second (major) premise comes from Zanchius's statement, ""how shall He not, with Him, also freely give us all things?" i.e., salvation and all things necessary to it." As a paraphrase we could say, "He will regenerate all elect," or "all elect are regenerated," which is our minor premise.

As one last minor housekeeping matter, we should reverse the order of the first and second premises to put the major premise first. (The major premise contains the predicate of the conclusion.) So the final form of the argument is:

All elect are regenerated,
all elect are died-for;
therefore, all died-for are regenerated.

Let's look at the Venn diagram. The major premise, "all elect are regenerated looks like this:

Now we add the minor premise, "all elect are died-for:"

We are left with a diagram showing that all the elect are both died-for and regenerated. But look at that diagram. Somehow Zanchius arrives at the conclusion from this argument that all died-for are regenerated. How does he do that? Look at that big old space of died-for folks who are outside of the elect and regenerated circles. Zanchius's argument is a complete flop — again.

Argument 1 being a big flop, argument 2 (which was sound up til now) becomes a big flop as well. Even if we interpret Romans 8:32 in the way Zanchius wants us to, the logic doesn't work out favorably for his argument.

As before, we've seen the diagrams, but it is also useful to consider a parallel argument to illustrate the fallacy. So here is a parallel argument:

All bananas are yellow,
all bananas are sweet,
therefore, all sweet things are yellow.

As ridiculous as that looks, it is the very argument Zanchius used as the first step of his two-step argument. The only difference is in the terms used. Just to round things off, let's illustrate the valid step-two argument:

All sweet things are yellow,
Some candy is not yellow;
therefor some candy is not sweet.

The step-two argument is perfectly valid; the problem lies in the false major premise that was taken from the conclusion of the fallacious step-one argument.

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