Lemma 2: I believe in belief.

'Believe' is one of those horrible brain-action words with half a dozen meanings that overlap and clash with one another and with the meanings of other brain words like 'think' or 'know'. I believe I'll have another beer. I believe in Father Christmas. I believe Floyd Mayweather is the greatest living boxer. I believe you. They are notoriously difficult to translate because the way they overlap and cover the broad spectrum of 'thinking' differs from one language to another.

It's also one of those awkward concepts that lives in the mind rather than in the 'outside world' and so can be difficult or impossible to test. If I said "I live in England" or "I have three legs" then these assertions would be fairly easy to verify. If I said "I believe in the tooth fairy" then ... well ... I might do. And if I were cunning and lacking in moral fibre, I could make it quite difficult for somebody outside my brain to prove that I don't believe in the tooth fairy. We can't read people's brains very easily. That's why nobody trusts psychiatrists.

Let's narrow the broad word 'belief' down a bit and apply it to my contrived test statements from earlier:

1) I believe in Elvis
2) I believe in King Arthur
3) I believe in Harry Potter

There are still two different meanings here. Statements (2) and (3) are most sensibly interpreted as "I believe in the existence of X". But Elvis's existence isn't controversial, so that probably isn't what we mean in statement (1). The most likely interpretation of (1) is "I believe in the capabilities or qualities of X". Elvis is perhaps an odd choice here. It is probably clearer with something like "I believe in the president".

God is an awkard case. Perhaps not surprisingly. (remember God? I said I'd sneak back up on God). The statement "I believe in God" can be interpreted as either or both of the above meanings.

"I believe in the existence of God" and "I believe in the capabilities or qualities of God". (where the second statement presumably implies the first). So whenever we address this statement, we need to make completely clear what we mean.

Oh ... and the title of the post "I believe in belief". You could argue that you cannot prove that anybody else believes anything, since belief happens inside people's heads where you can't see it. This is in the same realm as arguing that you cannot prove that anything outside your own head exists. Diverting if you're a 17th century French mathematician or a student sipping cheap instant coffee. Not nearly diverting enough for me to bother about it here. Belief exists. People believe stuff and they believe in stuff. I'm taking that as given.