Faith and Science: Symbolic Logic

Almost all of today’s class was spent using logical equivalences and rules for inference in their symbolic form to verify the validity of various arguments. One of my favorites was the following:

If the Mosaic account of cosmogony (the account of the creation in Genesis) is strictly correct, the sun was not created till the fourth day. And if the sun was not created till the fourth day, it could not have been the cause of the alternation of day and night for the first three days. But either the word “day” is used in Scripture in a different sense from that in which it is commonly accepted now or else the sun must have been the cause of the alternation of day and night for the first three days. Hence it follows that either the Mosaic account of the cosmogony is not strictly correct or else the word “day” is used in Scripture in a different sense from that in which it is commonly accepted now.

We label the various statements that make up this argument by $$M, C, A, D$$. Thus the argument takes the form:
$$\begin{array}{ll} 1.& M \Rightarrow \ \sim C \\ 2. & \sim C \Rightarrow \ \sim A \\ 3. & D \vee A \\ \therefore & \sim M \wedge D \end{array}$$

The proof goes like this:
$$\begin{array}{lll} 4. & M \Rightarrow \ \sim A & \mbox{from 1,2 by Hypothetical Syllogism}\\ 5. & A \vee D & \mbox{from 3 by Commutativity}\\ 6. & \sim \sim A \vee D & \mbox{from 5 by Double Negation} \\ 7. & \sim A \Rightarrow D & \mbox{from 6 by Material Implication}\\ 8. & M \Rightarrow D & \mbox{from 4,7 Hypothetical Syllogism} \\ 9. & \sim M \vee D & \mbox{from 8 Material Implication}\end{array}$$

Next time, a colleague from the Division of Mathematics and Sciences will take over for a couple classes, helping us to understand the scientific method cycle and the historical development of modern science.

4 thoughts on “Faith and Science: Symbolic Logic”

1. I disagree with your argument.

You are assuming a definition of day something like: “The alternation of darkness and light caused by the sun in a 24-hour period.” Thus your definition implies your conclusion–either “day” meant something else, or the biblical account is false.

The text of Scripture does not agree with your definition. If we remove the phrase “caused by the sun” from the definition of “day,” the passage is consistent.

Def: A day is the alternation of darkness and light in a 24-hour period.
The sun was not formed until day four.
Thus the sun “could not have been the cause of the alternation of day and night for the first three days.”

Using that definition (based on Genesis 1:4-5), there is no inconsistency with a literal interpretation of the biblical account.

2. I don’t deny your claim. I point out that you are disagreeing with one of the premises of the argument and not the logic. We simply wanted to verify that if you accept 1-3, then the conclusion must follow.

It is a very important thing that I have been teaching the students is to find exactly the point at which you disagree. Is it with one of the premises or is there a flaw in the logic. Here, the logic is sound, so if you disagree with one of the conclusions you must necessarily disagree with one of the premises.