Positively Negative Claims

If you spend much time on the Internet around atheists, you will inevitably hear something like this:

The burden of proof is on the person making the positive claim.

The burden of proof in any conversation is actually on the person who wants to be in the conversation, but if we accept the above statement for the moment it brings up a very important point: negative claims often have positive implications.

Let me start with a trivial example: suppose I were to deny the claim that the prime numbers are infinite. It’s a negative claim so I have nothing to defend, right? Ah, but here’s the problem: the natural numbers have properties, and in particular, they are well ordered. If there are finitely many prime numbers, then there is a biggest prime number. Thus if my negative claim is true, so is a positive claim. My negatively is, therefore, convertible with a positive claim. If I merely said, “I’m not claiming anything, I just don’t believe the prime numbers are infinite”, I either believe that there is a largest prime number or I haven’t thought through what I’m saying. This latter option is what one often sees on the Internet. Basically, “I haven’t considered the claim and you can’t make me consider it”, though it’s never stated so baldly, for obvious reasons.

“But Math is different!” someone might say. If we’re unlucky, they’ll tell us that Math is empirically verifiable. If instead our objector actually knows something about Math he’ll probably say that Math is hypothetical and thus true in all possible worlds or that the properties of the numbers flow out of their definitions whereas real things have properties quite apart from whatever definitions we want to give them. This makes no difference, because real things still have properties, which is all that’s needed. Consider the following, very simplified example:

Everyone agrees with me that the color red exists. I deny that anything else exists but the color red exists.

(I know that in ordinary life you’d assume the fellow who said this was joking or insane, but for the sake of this post not being twenty pages long, please just play along. Examples which are uncontroversial because they were made up on the spot require far fewer disclaimers.)

This necessarily entails the claim that everything we perceive to exist is one or the other of the following:

  1. An illusion.
  2. Made up of the color red.

The negative claim that nothing but the color red exists will also be false unless the positive claim that cats, chairs, and sounds are all made up of the color red is also true. If it turned out that gravity was, for example, a force that attracts mass and not some shade of the color red, this negative claim would be false.

If our very hypothetical a-non-redist were to to actually discuss his claim instead of just use it to shut down all discussion by saying, “where’s your evidence?” like he’s a child’s doll with a cord in his back and only one recording, he would have to defend the positive claim that gravity is actually a shade of the color red. (Or he could maintain that getting fat is an illusion which doesn’t really happen, but unless he’s willing to argue circularly, he needs to make the case that it is an illusion.)

What is true of this silly example is also true of examples I wish were hypothetical, such as Materialism. The claim that there is nothing beyond matter and the forces so far elaborated by physics (or forces substantially similar) entails the claim that everything we experience is either an illusion or material. This is neither a tautology nor a self-refuting claim, so it is one which must be proven, not merely asserted.

Which is why when it is a mere assertion, it is typically asserted angrily. As the (purportedly lawyers’) saying goes:

When the law is on your side, argue the law. When the facts are on your side, argue the facts. When neither is on your side, bang on the table.


Occasionally one will hear a defense of how free will is an illusion which invokes experiments using  fMRI machines. Aside from these things not proving what they purport to prove even if they were conducted perfectly, consider that you can use an fMRI to prove that a dead salmon can read emotion in human facial expressions.

2 thoughts on “Positively Negative Claims

  1. What, not even a passing nod to my point that “The burden of proof is on the person making the positive claim” is a positive claim, which requires the person putting it forth to prove it, before he can expect anyone else to abide by it?


    1. I beg pardon. I was basically stipulating to the burden of proof being on positive claims in order to investigate the nature of claims themselves, and that they are about the real world, not purely in a vacuum. I take your point to be a more basic one which is really about the distinction between a philosopher and an ordinary man—philosophers investigate the things ordinary men take for granted. It is a vitally important point that philosophy begins with asking questions, but it is a different point than what I was going for, and I feared that if I brought it up people might go into that rabbit hole foot-first and break their legs (i.e. miss my point). But I promise I will talk about your point very soon!


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