> but science can't prove or disprove anything, ultimately.

What? From where do we derive our knowledge of the natural world and universe? How do we know, for instance, that the Earth revolves around the sun and not vice versa? Are you implying that we don’t know that, or are you implying our knowledge of this fact is a divine gift?

Prove is a very strong word. Science is empirical, an endless journey of testing hypotheses, gathering data, forming theories, and examining gaps in understanding. We do have more or less incontrovertible evidence for the Earth revolving around the Sun, so it's not a problem to take that as fact. However, there are many things that we are much less certain of, such as the nature of dark matter. The closest to complete understanding would be having no evidence to dispute our theories. The separation of this state and the ability to prove things may seem inconsequential as I've described it, but concepts such as the existence of God and the basis of human rights aren't touchable by science.

So your argument is that science can’t prove anything because it can’t prove everything? Also you said science can’t prove or disprove, but it seems trivially easy to construct many things science could disprove. E.g. you could disprove that 5 N of force is not enough to accelerate a 1 kg sphere to exit velocity on Earth.

If we're to be exact, we can't prove that if I throw an object upwards with 5 N of force right now, the gravitational field won't suddenly shift (for some reason) and send it out of the atmosphere. If you reduce it to a mathematical construct (Newton's laws, the gravitational field stays within a margin of 0.00001, blah blah) then sure, you can prove that it's not possible. Of course, I would bet a million dollars that it won't happen when I try it, if I'm sure it's not a scam, but I can't be sure that everything will work out like some simulation. Science is based on observations. Some things we have observed and reasoned about enough that we feel really confident. Great! Some things we're less certain about. Some things are really hard to observe (social "sciences") in a controlled way. And some things are simply far beyond the purview of observation.

> If we're to be exact, we can't prove that if I throw an object upwards with 5 N of force right now, the gravitational field won't suddenly shift (for some reason) and send it out of the atmosphere.

Ok then let’s rephrase the statement to “Absent any sudden shifts in the gravitational field, 5N of force is not enough to bring a 1 kg sphere to escape velocity.” Science can prove that.

And if we can’t prove it, then we return to the question of rationality. When given an unknown, is it rational to assume anything about that unknown without verifiable evidence? I think not.

Ah, but you're overreaching. I agreed with you in the comment you replied to. However, your point about rationality isn't so clear cut in the case of religion. If a religious person tells me that the theory of evolution is just flat out wrong then yeah, I'm going to dismiss that as irrational. If a religious person tells me that people reincarnate or get sent to the afterlife based on their deeds, I personally won't agree but not because science can determine this in any capacity. That's not a matter of rationality anymore; it's faith. There's no evidence either way.

> That's not a matter of rationality anymore; it's faith. There's no evidence either way.

If there is no evidence either way, then it is only rational to reject any positive assertion. The reason is that negative assertions are infinitely more likely to be correct than positive assertions. As a motivating example, think of a number between 1 and 1,000. Now, which statement seems more likely to be true: “the number you thought of is 32” or “the number you thought of is not 32.” I have evidence of the number you thought of, but the negative assertion is much more likely.

Another way of thinking about it is this: each positive fact yields are near infinite number of negative facts. E.g. if you know a ball is green then you also know it’s not red and it’s not blue, etc. the converse isn’t true. When you know a negative fact, you learn very little. E.g. what else can you say after learning a ball is not blue.

There is no rational distinction between positive and negative assertions in the general case. A positive assertion to a statement is equivalent to a negative assertion for the inverse of the statement. Numbers don't count (ha) because we know facts such as "the set of integers is infinitely large". Your ball color example is just nonsense. You used green but then switched to blue for the negative assertion. Also, that's not how colors work. In the case of religion, you're going off your preconceptions and biases. A religious person could easily say the opposite. You would both be speaking nonsense by saying your bias is more rational.