Defeasible Reasoning Every argument begins with some assumptions, and proceeds by some sort of reasoning to a conclusion. If the reasoning is airtight, so that the conclusion has to be true whenever the assumptions are true, then the argument is said to be valid. Here is an example of a valid argument:
EXAMPLE 1A
Socrates is a man.
All men are mortal.
Therefore, Socrates is mortal.
This is a very old example known as a classical syllogism.
Valid arguments are important, especially in a field like mathematics, where the "proof" of a theorem is always a valid argument. But, just because the argument is valid, we cannot be sure that the conclusion is correct. Here is another example of a valid argument:
EXAMPLE 1B
If Princeton is in Greece, then Socrates is alive.
Princeton is in Greece
Therefore, Socrates is alive.
This argument is valid, and yet we know that the conclusion is false. The argument is worthless because it begins from wrong assumptions! This argument is still valid, but it is unsound. We say that an argument is unsound if either 1) it begins from assumptions that are known to be false or 2) it is invalid -- based on flawed logic.
But there is a middle ground. Many arguments begin from assumptions that are not known to be either true or false, but are thought probable, and proceed by arguments that are sometimes, but not always, correct, such as statistical arguments. Many real conversations have to rely on arguments of these kinds, arguments that are not airtight.
