a cultural and contextual truth

We like "scientific" statements because they are tidy. But they are not absolutely tidy, they are relatively tidy. Take the tidiest statement on my list:

The boiling point of water is 100°C.

If you are poaching eggs, the amount of sloppiness in that statement is acceptable. But suppose you were asked to measure the boiling point of water to within a millionth of a degree. Suddenly it becomes very difficult to decide what the truth is. Your instruments are too sloppy, your environment is too sloppy. Your definition of boiling is sloppy: "The experimenter saw some bubbles." Heck, your definition of water is sloppy. How much contamination? What proportion of heavy water? Laboratory supply companies do not sell "pure water." The standards for standard water are all approximate.

If you and b_b both make experimental measurements, you'll probably disagree. Yet water still has a boiling point. The fact that we can't perfectly apprehend the truth does not make us doubt that it exists.

The scientific workaround is a confidence interval. The ± symbol has little to do with water, and much to do with your contextual, culturally-informed, biased, local experience with water.

Boiling water is a simple case, where we have to require high precision in order to expose the sloppiness.

Choosing the best approximation for pi might be harder. What are we trying to optimize for, do we want more accuracy or ease of calculation? There might be a lot to discuss. But for a given set of values, some approximations will be better than others. It is absurd to conclude that there is no right answer because it is hard to find agreement.

Suppose I exhibit two actions. In my view, Action A is virtuous and Action B is evil. I choose extreme examples to make the point clear; we don't need expensive thermometers to make a judgment. I say, "Action A is better than Action B," do you agree? Does my statement have a truth value? You may have utilitarian values, or you may follow some kind of Kantian rule system, but I have selected exhibits such that we are pretty sure to agree.

If you deny that my statement has a truth value, if you say it's all relative, I don't see how you can do science or form beliefs. Saying "Water boils at 100±2°C" is equivalent to saying "It appears to me that water boils at 100±2°C." Your confidence is increased by wide agreement with the statement. You will say that detractors are probably mistaken.

If you do agree with me, the next step is to find some human society that has unusual mores. Someone in that society says that Action B is better. Does that mean there is no truth? I say no, I say that person is wrong. I am fairly certain that I am right, but I am very certain that only one of us can be right.