As was I, when I used the rail thin woman as an example.
I said, "If I say the ball is round, could it be true?" Without getting into all of the particulars of tolerances, which would be necessary to determine the precision of my statement, could my statement be true?
What do mean by "round"?
I considered discussing spheres, as you did, but instead raised the issue of tolerances without getting into them. Only God can make a perfect sphere. Men can theorize them, but can not make one. Man can, as best, come close.
I also considered talking about the colour of the ball, which took me into frequency of the colour & the lighting in which the colour is being seen in.
The word "round", in the way I used it has a certain range. It is an imprecise term that can be an accurate description of some kinds of objects, if indeed those objects are round. You wouldn't expect someone with a round face or a round belly to have a face or belly which is spherically shaped. A piece of furniture can be said to have round corners or edges. (there's an oxymoron for you) Range of "round" is determined by the kind of object it is being used to describe. Like the word "thin", it is a comparative word.
We can look at a ball and see that it looks like a sphere, but if we examine it up close then we observe tiny bumps on the surface; so we conclude that the ball is really not a sphere, even though it approximates one very closely.
Let's use something even closer to an actual sphere, a ball bearing manufactured in space. To the human eye it looks like a sphere. To human hands, using any standard measuring tools we have, it seems to be a sphere.
You mentioned tiny bumps on the surface & again, I have to ask what tolerance you're using. Now we're pulling out another group of measuring tools. If we find a single atom out of place, we're not dealing with a sphere. We're dealing with something which is round and it approximates a sphere.
Back to the statement that started this discussion, "A statement can be precise without being accurate, but it cannot truly be accurate without being precise."
All types of measurements come with a standard deviation, which will be described by a range. Precision is determined by the stringency of that standard, while accuracy is a relational term, like thin or round. Something could be described accurately without precision, but you wouldn't be able to determine how accurate that description is without something to compare it to. The more precise the thing it's being compared to is, the more you're able to determine accuracy.
Your statement requires one to fill in a variable with a value, even if the value is unknown.
However, keeping in mind what I wrote above, the terms "acute" and "obtuse" are precisely defined, i.e. there is no ambiguity in their definitions. So for example, if I were to tell you that an angle is acute, then you wouldn't know whether it is 20 degrees or 45 degrees or whatever, but you would know absolutely that it is greater than 0 degrees and less than 90 degrees.
The known value is a range. The term that I used in my first response in this particular tangent of this thread (slide fit) is also an expression of a range.
That is a very important observation. It says volumes about the the nature of God vs. the nature of Man. The mere fact that we are able to theorize about perfection, despite our inability to achieve it, is amazing to me.
The word "round", in the way I used it has a certain range. It is an imprecise term that can be an accurate description of some kinds of objects, if indeed those objects are round.
This is a circular statement; unfortunately, it just begs the question.
Let's use something even closer to an actual sphere, a ball bearing manufactured in space. To the human eye it looks like a sphere. To human hands, using any standard measuring tools we have, it seems to be a sphere.
These tools themselves have a degree of imprecision in their measurements. So we only know that this ball bearing approximates a sphere to within the tolerance of the measuring tools (in fact, the boundaries of this tolerance themselves are somewhat ambiguous).
All types of measurements come with a standard deviation, which will be described by a range. Precision is determined by the stringency of that standard, while accuracy is a relational term, like thin or round.
Not only are we using the word "precision" differently, but it also seems we're using the word "accuracy" differently. For an example of how I use the words in an empirical sense, see post 91.
Something could be described accurately without precision, but you wouldn't be able to determine how accurate that description is without something to compare it to. The more precise the thing it's being compared to is, the more you're able to determine accuracy.
That's why I'm saying that accuracy is meaningless without precision.
The term that I used in my first response in this particular tangent of this thread (slide fit) is also an expression of a range.
OK, let's go back to your slide fit:
A slide fit allows for movement. Picture a hinge. The pin & the dealybobs that move around it would have a slide fit. The term is used for some kinds of bearings.
Yes, there is a range involved. But the point I'm trying to make is that the range itself is precisely defined.