Granville Sharp Rule

 Granville Sharp proposed a grammatical rule in 1798 regarding the Greek article. He restricted this rule to a very specific construction. Two substantives (same case but can be nouns, adjectives, participles) are joined by καί and the article precedes the first substantive only. Both nouns must be singular, refer to personal entities, and be improper.

When all these requirements are met, the two nouns refer to the same person. They have equal identity.

οὐχ οὗτός ἐστιν ὁ τέκτων, ὁ υἱὸς τῆς Μαρίας καὶ ἀδελφὸς Ἰακώβου "Is not this the carpenter, the son of Mary and brother of James" Mark 6:3

ἀναβαίνω πρὸς τὸν πατέρα μου καὶ πατέρα ὑμῶν καὶ θεόν μου καὶ θεὸν ὑμῶν "I ascend to my father and your father and my God and your God" John 20:17

Those who have analyzed each construction that matches Granville's restrictions have confirmed that every occurrence contains multiple substantives that have the same referent.

This is significant for some key passages like Titus 2:13 and 2 Peter 1:1, where the deity of Jesus is confirmed by using this construction. Some object that "god" is a proper name, but this is simply not the case. Proper names can't be pluralized.

So what happens when people start applying this rule to constructions that don't follow Granville's limitations? They can reach erroneous conclusions. Don't try to make the rule do more than intended.

If proper names are joined by "and," it doesn't matter. They always refer to unique individuals.

If plural nouns are joined by "and," the groups could be identical (see Rev 1:3), but more likely the groups are either distinct (Matt 3:7), or one group is a subset of the other (Matt 9:11; Mark 2:16). In these cases, though, the groups are still related to one another. They either act in unison, or they are part of the same socio-economic circles, etc. We just can't say they are equal unless context allows it.

Impersonal nouns joined by "and" rarely (maybe one instance) have the same referent. More likely, the nouns are referring to distinct entities, or one noun is a subset of the other. Again, the fact that two nouns are joined by a single article indicates some sort of relationship, though. 

Some texts are interesting to debate and wonder how close that relationship is, but concluding that the referents are identical is unlikely unless the nouns meet Granville's limitations.

Cf Wallace, Greek Grammar Beyond the Basics, 270-90, for a more exhaustive explanation and examples from biblical and extrabiblical sources.