You'll find logicians who'll explain to you that "number theory" is some collection of theorems to do with Peano arithmetic. Almost exactly wrong, if designed to bring on an existential crisis in number theorists (is no one theorem more significant than another?) The counter-attack begins with the assertion that there are major planks of number theory, even if G. H. Hardy's conception of their "depth" isn't really tenable. But this is more a matter of "faith" than anything else. If people believe that there is a complete, detailed theory of Hasse-Weil L-functions to be had eventually, rather than there being inexplicable "junk" in that theory, I think they are usually appealing to some sort of traditional thinking, rather than the existence of an ultimate top-down theory (though there is a minority view, cf. comments of Weil in the introduction to Basis Number Theory).