Having argued that non-belief is probably the best
term to describe people who are not Christians (see here), it’s probably worth considering
whether disbelief is just belief in the negation or a distinct cognitive
standpoint. If we think that to not believe q = to believe not-q, then we
contend that If Jack believes p, then he automatically believes not-(not-p),
which is equivalent to believing p again.
But if not believing is a distinct cognitive standpoint, in at least some way independent of belief in negation, then it’s more akin, say, to how distrust is not identical to belief that someone is untrustworthy, or how dislike is not identical to belief that something is bad. On this view, one can believe p without actively disbelieving not-p. Under this condition the distinction of not believing constitutes a more robust, attentive, or attitude-laden response than simply believing the negation.
Logically: belief(p) → disbelief(not-p) – but whether in the case of rejecting Christianity that feels to the sceptic like it applies may be a matter open for debate with the beholder.
I think if I were to probe the sceptic and take it to its natural course, I’d conclude that whether disbelief is really just shorthand for “belief in the negation,” or whether it is a distinct cognitive standpoint in its own right, depends a lot on whether we are dealing with professed disbelief, unbelief or non-belief. And I wonder, if you asked most non-Christians, would they instinctively know straight way which of the three applies to them? For many, under the terms above, they may not have given it much thought.
If disbelief is simply the flip side of belief - nothing more than affirming not-p when one denies p - then the distinction I’ve drawn collapses neatly into classical logic. On that account, to believe Christianity is false just is to disbelieve it, and the psychological texture of that rejection is irrelevant. But I have argued before that disbelief is more like a worldview in itself, and is a more intentional state than mere logical complement, and far more than most sceptics would like to acknowledge.
Taken with my part one article, it seems quite a compelling case that disbelief occupies a firmer, more deliberate space than either unbelief or non-belief - not because logic requires it, but because lived cognition and behavioural values exhibit it. It’s not quite the same for, say socialists vs. capitalists, because in that case, once we understand human minds as packages of values, economic assumptions, moral priorities, and social aims, socialists are actually capitalists pretending not to be (see here).