I wrote earlier about the deductive argument; an argument which claims that if its premises are true, then its conclusion must be true. I also wrote about fallacies; ways that arguments can go wrong. Today I’d like to write about four ways that deductive arguments can go right.
One form of valid deductive argument is called Modus Ponens. It looks like this:
- If P, then Q.
- Therefore, Q.
This is clearly valid. Here’s an example:
- If pointless suffering exists, then an all-good, all-powerful, all-knowing God does not exist.
- Pointless suffering exists.
- Therefore, an all-good, all-powerful, all-knowing God does not exist.
Keep in mind that though this argument is logically valid, it might not be sound. One or both of its premises might be false. For example, the theist might deny (2) and argue that all suffering which exists does have a purpose, though often we are not capable of understanding that purpose.
A Modus Tollens argument looks like this:
- If P, then Q.
- Therefore, Not-P.
- If God exists, then objective moral facts exist.
- Objective moral facts do not exist.
- Therefore, God does not exist.
Once again, though the form is valid the premises may be highly debatable.
A valid dilemma argument works as follows:
- Either P or Q.
- If P, then R.
- If Q, then R.
- Therefore, R.
A famous example is the Euthyphro dilemma, applied to monotheism:
- Either what is moral is moral because it is commanded by God, or God commanded it because it is moral.
- If what is moral is moral because it is commanded by God, then classical theism is false (because God’s morality would thus be arbitrary, which classical theism denies).
- If God commanded what is moral because it is moral, then classical theism is false (because God would thus be subject to an external moral system, but according to classical theism God is not subject to anything).
- Therefore, classical theism is false.
This is a valid argument, but of course it might not be sound. The atheist, for example, would deny premise (1).
Simplification is so obviously valid it is barely worth mentioning. It works like this:
- P and Q.
- Therefore, P.
- Socrates is a man and Socrates is a mortal.
- Therefore, Socrates is a man.
Brilliant! You’re a master logician now!
There are other valid forms of argument, for example the reductio ad absurdum and various forms of syllogism. We will discuss them later.