In many contexts, it is required for a noun phrase to be completed with an article or some other determiner. It is not grammatical to say just "cat sat on table"; one must say "my cat sat on the table". The most common situations in which a complete noun phrase can be formed without a determiner are when it refers generally to a whole class or concept (as in "dogs are dangerous" and "beauty is subjective") and when it is a name ("Jane", "Spain", etc.). This is discussed in more detail at English articles and Zero article in English.