Universal negatives and excluded middles
Published: 5 May 2013 (GMT+10)
The logic of biblical creation
Daniel T. from Australia writes:
You mention on your site a few times that it is not possible to prove a universal negative (a quick search for ‘universal negative’ on your site yields a few pages if you need references). I note that it is even fundamental to a few proofs of yours, such as the one I was considering—that “no antitheist can show that there is no possible good reason for allowing evil, since that would be a universal negative”. I really like this idea, and it would be a great rebuttal for the classic “problem of evil”, but in the spirit of 2 Timothy 2:15, I did a bit of searching and found that some things can indeed be proven not to exist. For example, a pair of numbers p and q such that (p/q)2 = 2. So if this holds true for mathematics, does it not also hold true for the more general case? Can it still be said that a possible good reason for allowing evil cannot be found, since there are things which can be proven not to exist? And if so, why? I would like to accept your argument but I feel unconvinced and would greatly appreciate a little explanation of why we can make this claim!
CMI’s Dr Jonathan Sarfati responds:
Dear Mr T.
That is a fair question. The answer is that things that are true in mathematics often don’t apply in the material world. Another example is induction, using the following logic:
- If something can be shown to be true for number x; and
- If something is true for x then it’s true for x+1
- Therefore, it is thus true for all natural numbers above x.
Similarly, we can show (by reductio ad absurdum) that there is no rational number that can be squared to give 2. But there is not the slightest analogous proof that God could have no possible good reason for allowing evil.
In short, the relationship between abstract numbers is not the same as that between concrete quantities.
I hope this helps, and gives you confidence that you can use this argument.
Graham D. from Australia writes, with comments from CMI’s Dr Jonathan Sarfati interspersed.
Hi. This is an inquiry about statement of faith number one.
“The scientific aspects of creation are important, but are secondary in importance to the proclamation of the Gospel of Jesus Christ as Sovereign, Creator, Redeemer and Judge.”
I have some questions and concerns:
1) What do you mean by this? Because from what I, and possibly many others (including Christians) can see, is that your ministry is primarily concerned with origins (biological etc). Just a quick observation of the Featured Articles archive would confirm this. In fact, a fairly recent featured article inferred that ancient Egyptian cosmetics was evidence against evolution: The biomedical properties of ancient Egyptian black eye makeup.
What matters is what our statement of faith says, and our practice as shown by the above-referenced articles, not perceptions. The article you cite comes under “The scientific aspects of creation are important.”
2) What makes you think that disproving evolution is evidence for creation? It seems as if you think creation is actually an alternative to evolution and thus you are committing the fallacy of creating a false dichotomy.
It’s a matter of simple logic, called the disjunctive syllogism: either things were made or they were not. If you have a third alternative, please let us know, as well as explain why the law of excluded middle is somehow abolished. You might also want to admonish your fellow evolutionists, from Darwin to Dawkins, who try to use alleged evidence against creation as evidence for evolution (cf. Rats! A toothless argument for evolution). My old article on logic explains this more: Disjunctive syllogism.
3) How is believing in a young or old Earth essential to salvation?
How is knocking down a straw man helpful? See Can Christians believe evolution? A better question would have been: what is wrong with trying to mix evolution and billions of years, and it’s answered in many places such as Did God create over billions of years? and Response to the evolution appeasers.
I have befriended about 20 old-earth Christians who find no problem in living with science and theology. Most of whom regularly practice their faith and apply it in their lives.
The young earth Christians who work for CMI and who have earned doctorates in science likewise have no problem in living with science and theology. But what do you care? Compare ‘Useful idiot’—who, me? and Dawkins on compromising churchians.
Bonus question: You guys don’t actually believe in dragons do you?
What is a dragon? See for example Crouching Tiger, Hidden Dinosaur?
Jonathan Sarfati, Ph.D., F.M.
Evolution + science → falseness! Falseness - science → evolution !
Creation + truth → science ! Science + truth = creation !
With regard to the claim that it is impossible to prove the non-existence of something, or a universal negative, I must respectfully disagree. According to my research, we can prove the non-existence of a thing if it is logically self-contradictory.
For example, we know the statements “there are no married bachelors” or “there are no square circles” are true since a married bachelor or a square circle are logically self-contradictory. And I don't think anyone would believe that self-contradictory things can exist.
Likewise, the atheist can prove “there is no God” if he were to show that the concept of God is logically self-contradictory. And of course, no-one has been able to do that. Or, he could prove that “there is no reason for God to allow evil” if he were to show that the concept of God allowing evil is self-contradictory.
Keep up the awesome work,
That is not what ‘universal negative’ means. This is a statement (or implied statement), ‘No As are B’ or the equivalent ‘All As are not-B’. It does not mean a logical contradiction (see also If God can do anything, then can He make a being more powerful than Himself? What does God’s omnipotence really mean?).
And we are still waiting for an atheist to demonstrate either that the concept of God is self-contradictory, or that a good God allowing evil is self-contradictory. “There is no reason for God to allow evil” really is an example of a universal negative.