Since words are defined in terms of other words in dictionaries, leading to infinite loops, does it mean natural languages are meaningless?

Question

Since words are defined in terms of other words in dictionaries, leading to infinite loops, does it mean natural languages are meaningless? Are infinitely recursive definitions valid? If we visualize the relationship graph of a dictionary, where vertices are words and there is a directed edge X -> Y from word X to word Y if X appears in definition of Y, we would see that such a graph is full of cycles. So if you pick any word and try to fully capture its definition from the dictionary, you will be looping in the dictionary forever. In order to avoid that, you would need a DAG (directed acyclic graph) of definitions. Correct? Do you agree with this? If so, would that mean that all natural languages are bound to be meaningless and we should state our logical proofs in formal logic / mathematically?

Answer 1

Suppose I say that Tim is an X. Because you don't understand what I mean by 'X', you ask: "What's an X?" In reply I say, "an X is a Y". Because you don't understand what I mean by 'Y', you ask: "What's a Y?" Because I don't know of any other synonym for 'Y' besides 'X', and because I don't think it would be helpful for me to tell you that by 'Y' I mean 'X' if the reason why I used 'Y' in the first place was because you didn't know what I meant by 'X', I go, "Sorry man (or woman), I can't help you!" Does it follow from this that when I say that Tim is an X, that I don't understand what I'm saying? If not, it would seem that a word can be meaningful even there's no non-circular way of defining it, no?