Formal logic is a set of formal "rules of logic" that have themselves been given names. For example, one "rule of logic" is the syllogism;
- Major premise: "All humans are mortal";
- Minor premise: "Socrates is a human";
- Conclusion: "Therefore Socrates is mortal".
Premises (or propositions) can contain evidences. Formal logic states the "law of logic" that if both the major premise and minor premise are true, then the conclusion is true.
The laws of formal logic can be named and listed, and are reliable. Indeed, if Socrates is a human and all humans are mortal, then we know that Socrates must be mortal. But what if we doubt that Socrates was a human? What if we doubt that all humans are mortals? Then the argument holds no force. Formal logic is only as good as its premises. In this case, the premises are that all humans are mortal and Socrates is a human. But formal logic cannot question its premises. If someone counters the argument by saying, "I don't believe all men are mortal. Enoch didn't die," the formal logician has to resort to informal logic if he wants to continue the argument. He has to argue that it's not reasonable to believe that Socrates was immortal.
Consequently, formal logic is a powerful tool, but is powerful only within a very limited realm: arguments in which both parties agree on the premises. And unfortunately, the parties to an argument rarely agree on their premises.
- God and Logic By Apologetics Information Ministry. October 20, 2009