Definitions. Words being defined should be distinguished by italics (or perhaps boldface in a textbook context). When italics are used to indicate a word being defined, it is unnecessary to use "called" or "said to be"; the use of italics announces that this is the term being defined and replaces these words.
Many definitions are phrased as "An object has property italicized term if condition holds." We use just "if" even though subsequently it is understood that an object has the property if and only if the defining condition holds. The italicization alerts the reader to this situation. The convention can be justified by saying that the property or object does not actually exist until the definition is complete, so one does not yet in the definition say that the named property implies the condition.
This seems confused to me for a number of reasons---especially the justification for the convention: "the property or object does not actually exist until the definition is complete". What does that mean?
Definition. An object x is a firath if and only if x is a female giraffe.Obviously, firaths existed long before I defined "firath"! They just were not so-called.
But what I mostly don't like is that the "definition" schema appears to merely give a sufficient condition for falling under the definiendum. The following is not a good definition of "firath".
Definition. An object x is a firath if x is a giraffe.
Does his advice seem reasonable or not? Presumably, a lot of mathematicians are adhering to his grammar suggestions.