it is not obvious intuitively that one is “correct” and one is “not correct”.
There is no inherent meaning to a set of symbols scrawled on paper. There is no “correct” and “incorrect” way of interpreting it; only convention (unless your goal is to communicate with others). There is no Platonic Ideal of Mathematical Notation, so obviously there is no objective way to pluck the “correct” interpretation of some symbols out of the interstellar void. You are right in as far as you say that.
However, you are expected to know the meaning of the notation you use in exactly the same way that you are expected to know the meaning of the words you use. Not knowing is understandable, but observing that it is possible to not-know a convention is not a particular philosophical insight.
People guess the meanings of words and notations from context all the time. Especially when they aren’t specialists in the field in question. Lots of interested amateurs exist and read things without the benefit of years of training before hand.
Some things just lend themselves more easily to guessing the accepted-meaning than others. It is often a good idea to make things easier to guess the accepted-meaning, rather than to fail to do so, if at all possible. Make it hard to fail.
There is no inherent meaning to a set of symbols scrawled on paper. There is no “correct” and “incorrect” way of interpreting it; only convention (unless your goal is to communicate with others). There is no Platonic Ideal of Mathematical Notation, so obviously there is no objective way to pluck the “correct” interpretation of some symbols out of the interstellar void. You are right in as far as you say that.
However, you are expected to know the meaning of the notation you use in exactly the same way that you are expected to know the meaning of the words you use. Not knowing is understandable, but observing that it is possible to not-know a convention is not a particular philosophical insight.
People guess the meanings of words and notations from context all the time. Especially when they aren’t specialists in the field in question. Lots of interested amateurs exist and read things without the benefit of years of training before hand.
Some things just lend themselves more easily to guessing the accepted-meaning than others. It is often a good idea to make things easier to guess the accepted-meaning, rather than to fail to do so, if at all possible. Make it hard to fail.