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.a cultural and contextual truth
Those sound like code words for "no truth at all."
Not at all. It is a statement that regards the nature of the truth, not the quality of it. I agree here. Everything in the physical world must be described in relative terms. There is no such thing as an independent quality. Thus all qualities are dependent upon the quality of the relationship by which a definition of state is to be made. I think this may be where we see things differently. I do not assert that a boiling point of water exists beyond the degree to which it may be measured. It's a fine point, but IMHO it is of crucial importance. We can plot the boiling point of water, at one atmosphere, we might say that water boils at exactly 100°C. Although useful for most experimentation, in actuality that definition mischaracterizes boiling for what it is. In truth, there is a point to which you become close enough to 100°C whereby you cannot physically discern where boiling actually begins. That is because boiling is a macro phenomenon that results from micro phenomena that are not perfectly relatable to 'boiling'. This is something that is true of all physical phenomenon, and there is often confusion when definitions are applied beyond their scope. Thus, we can say that water at one atmosphere boils at 100°C, and as far as we are concerned with boiling of water, it is correct and reproducable. However, to conclude that water does begin to boil at exactly 100°C (but that we cannot measure it) simply does not describe a physical reality. Pi is similar. There is no exact value for Pi. What we have are calculations that approximate the value of Pi. However, the universe makes no such calculations and no such value need exist, nor can it exist. Yes, your statement absolutely has truth value. It might be a truth rooted in cultural context rather than physical reality, but it absolutely has value. To me, it might be more valuable than a truth rooted in physical reality. The color green exists only because my nervous system has the capacity to interact with photons of a wavelength of ~500nm in a particular manner. Does that make trees any less green? No. Trees are green to me, and that can be a very important truth to me. That that truth of green is not shared by a dog, a rock, a blind person, or anything in the majority of the time since the Big Bang where there were no eyes to see it, it doesn't mean that it does not exist for me, or have meaning to me.Those sound like code words for "no truth at all."
But they are not absolutely tidy, they are relatively tidy.
The fact that we can't perfectly apprehend the truth does not make us doubt that it exists.
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.
I haven't yet decided if we strongly disagree, or we agree on a level deeper than I can fathom. Regardless, I conclude that you deny the following statement: For every real number q, it must be the case that q < pi, or q = pi, or q > pi. I conclude that, if I describe two circles that each have a radius of 1, you will not know if they have the same area.There is no exact value for Pi.
Would you say the same of the square root of two, or one-seventh, or thirteen?
I guess I should clarify, that in the language of mathematics pi can be said to have an exact value. However, it cannot be realized in a physical sense, that is, printed as an exact value in decimal form. Math can have absolute axioms, but the physical world has only approximations.Would you say the same of the square root of two, or one-seventh, or thirteen?