# Justin Li

## Religion and Logic

2009-02-13

This post is actually less blasphemous than my other posts about religion.

Among my many objections against (some, not all) religious people, there is one I really can't stand: their use (or lack thereof) of logic.

Let me introduce the logic concepts first, then return to religion.

P->Q is read "If P, then Q". P and Q can be any statement; for example, if P is "it is raining" and Q is "the sidewalk is wet", then P->Q reads "if it is raining, then the sidewalk is wet". The proper name for this argument is modus ponens.

Elementary so far, right? The rules of logic allows us to define the contrapositive, \~Q->\~P. Since if P happens Q must happen too, Q not happening means P did not happen. Using the example above, this would read "If the sidewalk is not wet, then it is not raining". This also has a proper name, modus tollens.

More relevant to the point, logic does not allow us to draw the conclusion that Q->P. This fallacy is called affirming the consequent. This is a fallacy because it assumes P is the only thing which can cause Q. In our example, this would read "If the sidewalk is wet, then it is raining. However, the sidewalk could be wet from rain, but also from car washing, pipe leakage, or other things.

A similar fallacy is denying the antecedent, \~P->\~Q. It also stems from the assumption that only P can cause Q. Translated to English in our example, it reads "If it is not raining, then the sidewalk is not wet". Again, the side walk could be wet from other causes.

As a side note, if you do want to argue that given P->Q you know Q->P and \~P->\~Q, then you need to use the bi-implication, also known as the if-and-only-if. For example, P could be "it is 5 pm" and Q could be "it is 7 hours until midnight". All of the above arguments would be true, since only in the case of it being 5 pm could it be 7 hours until midnight.

Note that these rules say nothing about the inherent truth of P or Q, or whether it makes sense that P->Q. These rules are only saying that if P->Q is true, then certain arguments are valid. P could be "I am female" and Q could be "there's an apple on the table". Clearly P is false and these two statements have nothing to do with each together. It certainly does not mean that "if there's no apple on the table, then I am not female" (\~Q->\~P). The original implication, P->Q, is meaningless under this interpretation. Given a sensible P and Q, however, the rules stated above hold.

Now, let's bring this back to religion. A common statement might be that "if you believe in God, then you are a good person". I will ignore whether this implication is valid for the moment. What I want to focus on is how people, after saying that and getting agreement, would go on to say "if you don't believe in God, then you are not a good person." To make this even clearer:

1. P is "you believe in God"
2. Q is "you are a good person"
3. "If you believe in God, then you are a good person" (P->Q)
4. "If you don't believe in God, then you are not a good person" (\~P->\~Q) !!!

The problem is with the fourth line. As I pointed out in the logic section, \~P->\~Q is an invalid argument; it assumes only P can cause Q. And in this case, is believing in God the only cause of being a good person? Of course not. Many people who don't believe in God did great things. Even if everyone who was Christian is a good person, this argument would not hold.

Let's try something else. Here's a recent example:

1. P is "this movement is of God"
2. Q is "this movement will last"
3. P->Q is "if this movement is of God, then this movement will last" (Acts 5:39)
4. "If this movement lasts, then this movement is of God" (Q->P) !!!

Before you object, I know the Bible doesn't claim the last statement. This is just for demonstration purposes. This is the same idea as before, except this time the fallacy is affirming the consequent. Judaism, Hinduism, and Confucianism are all lasting movements, still active in the modern age, and yet they are not movement so of the Christian God. Confucianism, in particular, is not about God at all.

If you listen to religious rhetoric (or just any persuasive speech in general), you will find these logical fallacies all over the place. It makes me so frustrated when the speakers make them and go on like nothing is wrong.