I'm still not sure how I'm supposed to interpret this question. If you're asking whether I think "matter is made up of atoms" is an extremely useful working hypothesis for many many scientific purposes, then the answer is obviously "yes" with probability that only negligibly differs from 1. (ETA: Don't ask me how negligibly different, because I couldn't tell you. I am not enough of an ideal Bayesian that I can meaningfully attach probabilities with many significant digits to my beliefs.)
If you're asking whether the fundamental structure of matter is in fact discrete, I would assign that a probability of about 0.3. Quantum field theory is sometimes interpreted as a particle theory, but this seems wrong to me. It is best interpreted as telling us that the basic constituents of nature are continuous field configurations (or, to be more precise, linear superpositions of field configurations).
Particle number is not fixed in any workable relativistic quantum field theory. This strongly suggests that particles are emergent rather than fundamental. If you suppose that a a particle cannot be located at two disjoint regions in a single space-like hyperplane, then any relativistic quantum theory of a fixed number of particles predicts a zero probability of finding a particle anywhere (see here for the proof). So the only consistent particle QFT is one where there are no particles!
There's also the fact that an observer accelerating uniformly in a Minkowski vacuum will see a thermal bath of particles (the Unruh effect). If one can bring particles in or out of existence simply by a change of reference frame, then they shouldn't be part of one's fundamental ontology.
Of course QFT itself is in all probability not the right fundamental theory, so matter may still turn out to have discrete constituents.
the answer is obviously "yes" with probability that only negligibly differs from 1.
That's the general answer I'm aiming to evoke; I'm trying to get a better idea of just how big that 'negligibly' is.
How much confidence do you place in the scientific theory that ordinary matter is made of discrete units, or 'atoms', as opposed to being infinitely divisible?
More than 50%? 90%? 99%? 99.9%? 99.99%? 99.999%? More? If so, how much more? (If describing your answer in percentages is cumbersome, then feel free to use the logarithmic scale of decibans, where 10 decibans corresponds to 90% confidence, 20 to 99%, 30 to 99.9%, etc.)
This question freely acknowledges that there are aspects of physics which the atomic theory does not directly cover, such as conditions of extremely high energy. This question is primarily concerned with that portion of physics in which the atomic theory makes testable predictions.
This question also freely acknowledges that its current phrasing and presentation may not be the best possible to elicit answers from the LessWrong community, and will be happy to accept suggestions for improvement.
Edit: By 'atomic theory', this question refers to the century-plus-old theory. A reasonably accurate rewording is: "Do you believe 'H2O' is a meaningful description of water?".