Sunday, December 16, 2012

The Importance of Logic

As I said in my last entry, just because an argument is unsound doesn’t mean that every objection will be a good one. Consider the following moral argument popularized by William Lane Craig:

  1. If God does not exist, then objective moral values and duties do not exist.
  2. Objective moral values and duties do exist.
  3. Therefore, God exists.

This argument doesn’t work (see my refutation of this moral argument) but on more than one occasion I’ve seen atheists who would say the conclusion (line 3) doesn’t follow from the premises (lines 1 and 2), when anybody with sufficient training in logic (a discipline of philosophy that even science-loving philosophy-haters would like) would have known better. Consider these two relevant rules of logic:

Transposition says that “If A, then B” is logically equivalent to “If not-B, then not-A.” Two statements being logically equivalent means it’s impossible for the two to have different truth-values, so that if one is true then the other must be true, and if one is false then the other must be false. Some examples of transposition in action:

  1. If A, then B
  2. If not-B, then not-A    (follows from 1 and transposition)
  3. If A, then B    (follows from 2 and transposition)

A famous rule of inference called modus ponens goes like this:

  1. If A, then B
  2. A
  3. Therefore, B

We can see the moral argument follows by using the following symbolization key:

  • G = God exists
  • O = objective moral values and duties exist

And using the rules of logic as follows:

  1. If not-G, then not-O
  2. O

  1. If O, then G    (follows from 1 and transposition)
  2. G    (follows from 2, 3, and modus ponens)

This isn’t to say that the moral argument I depicted is a good one; see my little series on the moral argument for a good refutation of it. But this does illustrate that just because the argument is unsound doesn’t mean that every atheist attack is a good one, and some critical thinking is advisable when looking at would-be objections to theistic arguments. Some objections to theistic arguments do work, but the same doesn’t necessarily go with every objection peddled on the internet.

Knowing some rules of logic would have prevented certain atheists from claiming that the conclusion doesn’t follow from the premises. I recommend that all atheists (and theists too) get some training in logic. You might think, “I’m an atheist; I already know logic!” Maybe you didn’t make the mistake of thinking the moral argument’s conclusion doesn’t follow from the premises, but consider these two examples borrowed from page 2 of Harry J. Gensler’s Introduction To Logic (2nd edition). Test yourself by trying to correctly answer the following two questions:

  1. If you overslept, you’ll be late. You aren’t late. Therefore:
    1. You did oversleep.
    2. You didn’t oversleep
    3. You’re late.
    4. None of these follows.
  2. If you overslept, then you’ll be late. You didn’t oversleep. Therefore:
    1. You’re late.
    2. You aren’t late.
    3. You did oversleep.
    4. None of these follows.

If you guessed (b) for the first one and (b) for the second one, then you made a mistake; (b) is right for the first one but wrong for the second one. Choosing (b) for the second one makes the fallacy of denying the antecedent:

  1. If A, then B
  2. Not-A
  3. Therefore, not-B
For example:
  1. If I have twelve fingers, then I have at least ten fingers.
  2. I do not have twelve fingers.
  3. Therefore, I do not have at least ten fingers.

As Gensler says in page 2 of his book, “Untrained logical intuitions are often unreliable.” Even if you didn’t make a mistake with this mini-quiz I gave, learning logic is highly recommended. There just isn’t enough logic happening among theists and even among some atheists. Gensler’s Introduction to Logic is in many ways an excellent book (e.g. in its comprehensiveness, covering inductive logic and paraconsistent logic), but has the disadvantage of giving less standard names to the rules of propositional logic when it introduces those rules; something similar could be said for quantificational logic (it calls “universal instantiation” “drop universal”). Daniel Bonevac’s Deduction: Introductory Symbolic Logic at least mentions the traditional named rules like modus ponens and includes material on counterfactual logic, but overall it is less comprehensive and less readable than Gensler’s Introduction To Logic. Given a choice I’d pick Gensler’s while looking up the traditional names of those logic rules.

If you don’t want to buy a book on logic (though I think reading books is highly recommended for both atheists and theists) there’s Stefan Waner and Steven R. Costenoble’s introduction to logic on the web. In any case, logic is important and I advise all readers to learn it. If it were up to me, logic would be part of K-12 standard education. The world could certainly use more of it.