(I’m catching up, so that’s why this is posted so far after the original.)
When I attempted this exercise I tried to think of how I use the word “arbitrary” and came up with a definition along the lines of “Something is arbitrary if its choice from a set makes no difference to the veracity of a particular statement”, i.e. arbitrary is a 2-part function, taking as input a choice and a statement, since without a statement to evaluate against calling something arbitrary to me just looks like membership.
But then I read on and realized that I was being too narrow in what I considered to be arbitrary. Perhaps from too much mathematical training, I didn’t even think of the common use as described above. This is an subtle kind of error to watch out for: taking a technical term that happens to have the same spelling and pronunciation as a non-technical term and trying to apply the definition of the technical term back to the non-technical term. The effect is either that you confuse other people because you use a technical term that looks like a non-technical one or you confuse yourself by misunderstanding what people mean when they use the term in a non-technical sense. This sort of thing becomes a bigger problem, I reckon, as you become more and more specialized in a field with lots of technical language.
(I’m catching up, so that’s why this is posted so far after the original.)
When I attempted this exercise I tried to think of how I use the word “arbitrary” and came up with a definition along the lines of “Something is arbitrary if its choice from a set makes no difference to the veracity of a particular statement”, i.e. arbitrary is a 2-part function, taking as input a choice and a statement, since without a statement to evaluate against calling something arbitrary to me just looks like membership.
But then I read on and realized that I was being too narrow in what I considered to be arbitrary. Perhaps from too much mathematical training, I didn’t even think of the common use as described above. This is an subtle kind of error to watch out for: taking a technical term that happens to have the same spelling and pronunciation as a non-technical term and trying to apply the definition of the technical term back to the non-technical term. The effect is either that you confuse other people because you use a technical term that looks like a non-technical one or you confuse yourself by misunderstanding what people mean when they use the term in a non-technical sense. This sort of thing becomes a bigger problem, I reckon, as you become more and more specialized in a field with lots of technical language.