Since you’re trying to put numbers on something which many of us regard as being certainly true, I’ll take the liberty of slightly rephrasing your question.
How much confidence do I place in the scientific theory that ordinary matter is not infinitely divisible? In other words, that it is not true that no matter how small an amount of water I have, I can make a smaller amount by dividing it?
I am (informally) quite certain that water is not infinitely subdivisible. I don’t think it’s that useful an activity for me to try to put numbers on it, though. The problem is that in many of the more plausible scenarios I can think of where I’m mistaken about this, I’m also barking mad, and my numerical ability seems as likely to be affected by that as my ability to reason about atomic theory. I would need to be in the too crazy to know I’m crazy category—and probably in the physics crank with many imaginary friends category as well. Even then I don’t see myself as being in a known kind of madness to be that wrong.
The problem here is that I can reach no useful conclusions on the assumption that I am that much mistaken. The main remaining uncertainty is whether my logical mind is fundamentally broken in a way I can neither detect nor fix. It’s not easy to estimate the likelihood of that, and it’s essentially the same likelihood for a whole suite of apparently obvious things. I neglect even to estimate this number as I can’t do anything useful with it.
Since you’re trying to put numbers on something which many of us regard as being certainly true, I’ll take the liberty of slightly rephrasing your question.
How much confidence do I place in the scientific theory that ordinary matter is not infinitely divisible? In other words, that it is not true that no matter how small an amount of water I have, I can make a smaller amount by dividing it?
I am (informally) quite certain that water is not infinitely subdivisible. I don’t think it’s that useful an activity for me to try to put numbers on it, though. The problem is that in many of the more plausible scenarios I can think of where I’m mistaken about this, I’m also barking mad, and my numerical ability seems as likely to be affected by that as my ability to reason about atomic theory. I would need to be in the too crazy to know I’m crazy category—and probably in the physics crank with many imaginary friends category as well. Even then I don’t see myself as being in a known kind of madness to be that wrong.
The problem here is that I can reach no useful conclusions on the assumption that I am that much mistaken. The main remaining uncertainty is whether my logical mind is fundamentally broken in a way I can neither detect nor fix. It’s not easy to estimate the likelihood of that, and it’s essentially the same likelihood for a whole suite of apparently obvious things. I neglect even to estimate this number as I can’t do anything useful with it.