Validity vs. soundness
In logic there's an important difference between validity and soundness. An argument is valid if it's possible for the premises to be true but the conclusion to be false. An argument is sound if both the premises and the conclusion are true.
- I either own a bicycle or a car.
- I don't own a bicycle.
- Therefore, I own a car.
The premises can both be true, that is, it's possible for me to own a car but not a bicycle. However, it's not necessarily true that, just because I don't own a bicycle I must own a car. Thus, this argument is valid but not sound.
It's worth noting that the premises of an argument don't even need to be true in order for an argument to be valid. For example:
- All toothpicks are made of metal.
- All metal objects are toasters.
- Therefore, all toothpicks are toasters.
While the argument is obviously absurd, the premises to support the conclusion, thus the argument is valid but not sound.
An example of an argument that is both valid and sound is this one:
- No moth is a spider.
- All spiders are arachnids.
- Therefore, no moth is an arachnid.
In this argument the premises logically support the conclusion, plus both the premises and the conclusion are true. Thus, this argument is both valid and sound.