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The Universal Negative: Can It Be Proven?

by Shawn Ferguson

Atheists and sceptics sometimes claim that it’s impossible to prove a universal negative. This, they assert, relieves them of the burden of proof when they claim that God does not exist. They think it’s a savvy move, leaving them with nothing to defend and placing the entire burden of proof upon the theist, who is clearly making a positive claim. This is a mistake on their part, because, apart from being false, in the end it does more damage to their cause than good.

 The first order of business is to define a universal negative. A universal negative in this context is any claim that something doesn’t exist. So, when the atheist claims that God doesn’t exist, this is a universal negative—it asserts that it is universally true that there is no being in existence matching the description of God—and need not, indeed cannot, be proven.

It should already be apparent that there’s a problem here for the claimant that it’s impossible to prove a universal negative: the claim is itself an unmistakeable universal negative. The claim just is that it’s universally true that there exists no universal negative that can be proven. So by its own principle, if true, the claim cannot be proven, and thus has little to attract our assent.

But let’s leave that objection aside for the moment and look at the claim a little more deeply. Is it true that there is no universal negative which can be proven? No. This is demonstrably false. Consider the claim that no circular triangles exist. This is a universal negative. It claims that it is universally true that there are no triangles in existence which are also circular, and here’s a proof for it:

1.       If an object does not have exactly three sides and three angles, then it cannot be a triangle.

2.       A circular object does not have exactly three sides and three angles.

3.       Therefore, a circular object cannot be a triangle.

This is a deductively valid argument with all true premises[i], thus guaranteeing the truth of the conclusion. A universal negative has just been proven. In fact, any universal negative can be proven to be true if it can be shown to lead to an internal contradiction, just as we did for the circular triangle.

Ironically, the very same atheists and sceptics who claim that a universal negative cannot be proven will often turn around and attempt to offer a proof of the universal negative that God does not exist; they do this in the form of the problem of evil and suffering. This argument is an attempt to show that the very idea of an all-loving, all-powerful God is incompatible with the existence of the evil and suffering which permeates our existence. The basic argument is that an all-loving God wouldn’t want to permit evil and suffering, and an all-powerful God could ensure that it wasn’t permitted; but it is permitted, clearly, so there mustn’t be a God who is both all-powerful and all-loving.

Of course, the argument doesn’t work, but that’s not our interest here. What we find interesting is that this attempted proof is an exercise in the very thing that is often said to be impossible: proving a universal negative. They can’t have it both ways. Either universal negatives are unprovable, and this argument is futile, or this argument is worthy of consideration, and universal negatives are provable after all.     

Again, let’s leave this argument aside for the moment and look at the issue from another angle. What we find lurking beneath the surface is another irony just waiting to be uncovered. When the atheist or sceptic claims that a universal negative cannot be proven, what they’re doing is tantamount to admitting that their belief that God doesn’t exist is unprovable, and thus without merit. If it cannot be proven that God doesn’t exist, then why should we believe such a claim? This fact wouldn’t give us reason to believe that God does exist, to be sure, but it would absolutely preclude any belief that God doesn’t exist. At best, in the absence of positive evidence for God’s existence (of which there is plenty), such a claim, if true, would leave us agnostic. Let’s state this plainly: if a universal negative cannot be proven, then all atheists (here defined as a person who believes that God does not exist) are irrational because they are necessarily going beyond the evidence.

But let’s leave this aside for the moment and examine the claim from yet another angle. What exactly is meant by proof in this context? If by proof is meant one hundred percent certainty, then it may be true that any universal negative that can only be argued for inductively cannot be proven[ii]. So to claim, for example, that there are no white crows would be unprovable, as any attempted proof of such a proposition would necessarily rely on inductive reasoning (for any being who isn’t omniscient). But if one hundred percent certainty is the standard, then it’s equally as true that any universal positive which relies on inductive reasoning for its proof cannot be proven either; the problem would be with induction, not with the negativity or positivity of the proposition in question. What’s more, all universal negatives have a universal positive as a counterpart. That there are no white crows can be implied by the positive statement that all crows are black. That God does not exist can be implied by the positive proposition that the material world is all that exists. But to prove such a universal positive would amount to a proof for its implied universal negative. So, if it’s true that universal negatives are unprovable, who cares? So are universal positives. And if universal positives can be proven, then so can many universal negatives.

Still more can be said. Why grant the assumption that all proofs must provide one hundred percent certainty in the first place? Why not define proof as making a proposition more likely than its negation? If we do this, we can indeed prove many things inductively, both universally negative and positive, with some degree of probability. Of course, this is a controversial issue, and many will cite Hume against me here (to which I would fire back a citation of Plantinga, but that’s a debate for another day), but the point is that a proof’s being one hundred percent certainty can’t just be taken for granted—it must be argued for. (Oddly enough, to argue that a proof must provide one hundred percent certainty will likely be self-defeating, unless the proof itself is one hundred percent certain).

So the claim that it is impossible to prove a universal negative has little going for it, and much going against it, as we have seen. The claim is self-defeating because it is itself a universal negative, which by its own standard cannot be proven if it’s true; it is demonstrably false, as is obvious by the fact that many universally negative statements can be proven false by simply demonstrating an internal contradiction; it precludes any consideration of the problem of evil, which is the atheists’ strongest objection to God’s existence, and an objection worthy of consideration; it amounts to an admission that the atheist is going beyond the evidence and holding his belief that God doesn’t exist irrationally; it fails to realize that just as many universal positives are unprovable with one hundred percent certainty as are universal negatives; and it relies upon a controversial definition of proof, which is likely indefensible.

[i] A deductively valid argument with all true premises is what logicians call a sound argument. A sound argument is one in which the truth of the premises guarantees the truth of the conclusion logically and inescapably (it’s valid), and in which the premises are all true.  
[ii]Inductive reasoning, as opposed to deductive reasoning, cannot guarantee the truth of a conclusion with one hundred percent certainty. It can, however, provide differing degrees of probability for the conclusion of an argument.