Saturday, October 9, 2010

Epistemic Weight and the Excluded Middle.

or, The Joy of Double Negatives.

I would like to discuss a few mistakes of understanding that are often made as regards atheism, agnosticism and the epistemic basis for both.

To affirm any form of theism is to make what is called a positive claim: to believe that a certain thing is, and that it is a particular way. To deny theism is to make a negative claim: to not believe that a certain thing is, or is a particular way. We hold a lot more negative beliefs — I tend to prefer the term negative assumptions, as they are the epistemic default: implicit, innumerable and are not generally held with much passion or thought — than positive ones. We intuitively consider it the responsibility of the person making the positive claim to have reasons for it, because the negative claim is the default and because it is defined in such a way as not to need specific reasons in its favour.

Negative claims are often impossible to prove evidentially, unless they have definable, measurable positive consequences; and unless they are logical tautologies (such as "there are no blue things that are not blue") they are also impossible to prove logically: one can only hope to disprove them. However, because we accord them no epistemic weight in and of themselves, we are justified, not perhaps in affirming them, but in assuming, or accepting them. Only when the positive claim is successfully defended do we have reason to adopt it in preference to its corresponding negative.

This is the entire basis of the scientific method, which involves the presupposition of a null hypothesis — a negative assumption about which, because of observed evidence, there is some doubt — which the scientist attempts to disprove. It is also (along with the potential moral consequences of doing otherwise) the basis of the legal principle of the presumption of innocence. These two examples alone should show the inequality in epistemic weight between affirming a positive claim and defaulting to the negative by not affirming it, and the importance of recognising this inequality. This is also the reason that in binary computing logic, where true is represented as one, false is represented not as negative one but as zero.

This view removes the need to resolve the disagreement between a reasonable atheist and a reasonable agnostic, if we accept conventional logic and the traditional definitions of these terms. The agnostic who maintains that he does not actually not believe fails to recognise this piece of logic: it is impossible to doubt whether X while still believing that X, and to not believe that X is to make the negative assumption that not-X. The atheist who does not admit that he does not know for complete certain whether God exists is not following proper methods of inquiry any more than the theist who believes despite the complete lack of reasonably convincing evidence, because he is assigning epistemic weight to a negative claim.

To wit (which by the way is just as short as tl;dr, unless you point it out):
  • not to know entails not to believe; and
  • not to believe entails to refrain from assigning epistemic weight.


  1. I don't think that's correct. It's possible to believe and sometimes even prove negative statements; they're not mere absence of belief in the positive statement.

    For instance, in Euclidean geometry, there is no construction for trisecting an angle. We can make this claim, believe it (to varying degrees), even prove it. It is not mere lack of belief in the presence of such a construction; it is a positive belief in its absence.

  2. True, but as a mathematical proof this counts as an exception to the general case I'm talking about. I probably should have found a better example of analytic truth than "there are no blue things that are not blue".

  3. I would think that the trisecting example would be more typical of the general case, actually.

    There's nothing magical about negative statements; they're usually harder to prove, but that's just a tendency, nothing categorical. Universal statements are also hard to prove — does the same argument apply to them? If we say "All swans are black", how does that compare with "No swans are white"?

    In general, one has to carefully distinguish absence of evidence from evidence of absence, but that's no call to conflate the two categories!

  4. You can disprove "all swans are black" by finding a swan that is not black. You can disprove "no swans are white" by finding a swan that is white. Only in a world where "all swans are either black or white" is the second as easy as the first.

    To prove either statement, on the other hand, requires you to find every swan that exists. To have a positive belief in the absence of white swans, every single swan would have to be accounted for. Yes, this is theoretically possible, but why would you do it? To negatively assume it, we need only to have not come across (or have any other reason to believe there exists) a white swan.

    Similarly, you can be certain of the nonexistence of certain gods, because from their definition other things logically follow that we would observe if they existed, and we do not observe them. This again is a case of disproving the positive, and affirming the negative only as a consequence of doing so. But theologians are savvy to this and tend to define God in such a way that he is undetectable, failing to notice (or accept) that if he is undetectable then he is purposeless as far as this universe is concerned.

  5. No love for inductive reasoning? There's relatively little one can say about the real world without some form of inductive, weight-of-evidence, non-monotonic reasoning.

    In any case, though, both "all swans are black" and "no swans are white" can only be disproved, and both are adequately disproved by finding a single counter-example; that makes them pretty similar. It's the universal that makes them difficult to prove conclusively, not whether they're negative or positive. Of course, if we want equivalent examples, we have to use the more stilted "all swans are non-white" or "no swans are non-black" for one or the other proposition.

  6. And all negative assumptions are universals, either of the form "There is no X that is Y" or simply "There is no X".

    Inductive reasoning is fine; I'm talking about situations where there is an absence of evidence. The case of God is such a case — you can disprove a lot of gods, but the cleverer theologians define him so as to be undisprovable.

  7. Jumped here from Pancake Morning. Good stuff. Anyway, a null hypothesis is not a negative hypothesis, its is the lack of a hypothesis, that is, usually, there is no difference between two things. The alternative is always that there probably is a difference, which we usually set out to prove. When we find evidence for the alternative, that is a difference, we don't prove the alternative, but reject the null hypothesis that there is no difference. The obvious exception being Maths, in which we can actually prove things with certain axioms (ie so long as you have the same definitions of 1 and 2, 1+1=2 is proven).

    So an agnostic says that we can not know the existence of god (the alternative to 'no god') therefore we can not reject the null hypothesis, but that does not prove the non-existance of god. Just the lack of proof for god.

  8. True, but until the null hypothesis/negative assumption is disproved, we should assume it, yes?