# Disjunctive Syllogism

The disjunctive syllogism is a form of deductive reasoning that goes as follows:

1. Either p is true, or q is true.
2. p is false.
3. Therefore, q is true.

This is a deductively valid form of reasoning because, given that p and q are the only alternatives, and p is false, q has to be true. The conclusion follows necessarily from the premises in virtue of the form of the argument.

This form of reasoning is useful when we have a small set of hypotheses, because we can use it to narrow down which one is true. For example, in a murder trial, we might know that the only people at the scene of the crime were Alex and Bob. So, we could reason as follows.

1. The murderer was either Alex or Bob.
2. Alex is on video camera in a different room at the time of the murder, so he can’t be the murderer.
3. Therefore, the murderer was Bob.

Importantly, this requires us to actually have a good reason to believe that Alex and Bob were the only people at the scene of the crime. If there is evidence that there might have been a third person at the scene of the crime, then our argument commits the fallacy of the false dichotomy, because there is a third possibility, namely that the murderer was this third person. This may create “reasonable doubt” in the jury’s mind about whether Bob was the murderer, depending on the other facts.

However, alternative hypotheses cannot be generated arbitrarily. There has to be some reason to take a hypothesis seriously before it becomes an objection to our argument. For example, the defense attorney can’t say “maybe a Martian was the murderer” – that is a doubt, but it is not a reasonable one, and so does not undermine our argument.