There is a wonderful little book that I would blog if I were not so lazy called Walking the Tightrope of Reason. Robert Fogelin explores the paradoxes and problems associated with reason and logic. On the one hand, we are absolutely and unavoidably commited to the integrity of reason. On the other hand, we find that reason has a tendency to turn against itself and create incoherence when pursued unrestrained. In an early chapter entitled “Why Obey the Laws of Logic?” he makes the point that if we reject the law of non-contradiction, everything goes south fast:
The standard proof that everything follows from a contradiction depends on three seemingly unassailable principles. The first concerns conjunction. From the conjunction p & q we may infer p and we may also infer q. The second concerns disjunction: from p, we may infer p or q. The third principle also concerns disjunction and is a bit more complicated: from p or q, together with ~p, we may infer q. Given these three rules of inference, the proof of the spread principleâ€”the principle that everything follows from a contradictionâ€”is short and sweet:
p & ~p p The conjunction principle p ∨ q The first disjunction principle ~p The conjunction principle again q The second disjunction principle
Because q can be any proposition whatsoever, this proof shows that if we start with a contradiction, we can derive any proposition we please. In order to block this line of reasoning, at least one of the three inference rules that generate it must be rejected. This makes tough intuitive going, because each of these three inference rules seems wholly plausible on its face.†
This proof packs quite a punch. It shows that if you allow a contradiction to be “true,” then from that you can prove absolutely anything else. For example, from a single contradiction, every other contradiction can be proven. Thus, if you accept a contradiction, you are, in effect, granting the following permission:
In interpreting what I say, you may add the phrase “It is not the case that” to the front of any sentence I utter. Do this as you please, for it will in no way alter the significance of my discourse. ‡
So, the next time someone comes through here arguing that our logic doesn’t apply to God, I will agree with them that, indeed, our logic does apply to God, and direct them to this post to explain why I conclude from their statement the opposite of what they stated. If it is true that “our logic” does not apply to God, then we can stop wasting our time arguing at all. For that matter, we can stop believing things, or thinking that what we believe is important. Accepting a contradiction to save your theology strips your theology of rational meaning, so I recommend against it.
I think this proof provides quite a good reason to obey the laws of logic. What say you?
† Robert Fogelin, Walking the Tightrope of Reason, pg 174, footnote 21.
‡ Ibid. pg 36.