There is a similar problem in Phil 3:19 were we have:
ὧν τὸ τέλος ἀπώλεια, ὧν ὁ θεὸς ἡ κοιλία καὶ ἡ δόξα ἐν τῇ αἰσχύνῃ
αὐτῶν, οἱ τὰ ἐπίγεια φρονοῦντες = Their end is destruction, their
the god is their belly, and they glory in their shame, with minds
set on earthly things.
2 Cor 4:4 says this:
ἐν οἷς ὁ θεὸς τοῦ αἰῶνος τούτου ἐτύφλωσεν τὰ νοήματα τῶν ἀπίστων
εἰς τὸ μὴ αὐγάσαι τὸν φωτισμὸν τοῦ εὐαγγελίου τῆς δόξης τοῦ Χριστοῦ,
ὅς ἐστιν εἰκὼν τοῦ Θεοῦ = In their case the god of this world/age
has blinded the minds of the unbelievers, to keep them from seeing the
light of the gospel of the glory of the Christ, who is the image of
the God.
In John 1:1 we have:
Ἐν ἀρχῇ ἦν ὁ Λόγος, καὶ ὁ Λόγος ἦν πρὸς τὸν Θεόν, καὶ Θεὸς ἦν ὁ Λόγος
= In [the] beginning was the word and the word was with the God and the word was God/god.
For completeness, let me quote John 1:6 -
Ἐγένετο ἄνθρωπος, ἀπεσταλμένος παρὰ Θεοῦ, ὄνομα αὐτῷ Ἰωάνης - There came a man sent from God, whose name was John.
Now, I do not intend to launch into a major treatise in the subject of the Greek article which has been thoroughly examine in many places, most notable (and competently) in Daniel Wallace, "Greek Grammar Beyond the Basics", which I highly recommend.
In the case we have at hand, the use of the article in these texts can be understood as follows:
- In Phil 3:9, the article is monadic - for some people their one and only (but still false god) is their stomach. This can be readily deduced because the exclusive class is explicitly stated as the the group of people who are enemies of the cross (v18) and who worship this false god.
- In 2 Cor 4:4, the article is again monadic as pointing to a single example in the class of the false god of the world/age - again readily deduced as the source of spiritual blindness (v4) in contradistinction to the true God of the universe who imparts spiritual eyesight (v6)
- In John 1:1 we again have an example of the article used to signify that "God" is monadic, AND, we have another example of Colwell's rule of grammar for the Greek article - see appendix below. In any case, both forms of "theos" denote the one and only true God.
Another example of "theos" without the article is John 1:6 which again, indisputably, denotes the One true God.
APPENDIX - Colwell's Rule of Grammar
The following quote is taken from an article by the esteemed NT linguist and editor, Bruce Metzger found here >> http://www.bible-researcher.com/metzger.jw.html
Some years ago Dr. Ernest Cadman Colwell of the University of Chicago
pointed out in a study of the Greek definite article that, “A definite
predicate nominative has the article when it follows the verb; it does
not have the article when it precedes the verb. … The opening verse of
John’s Gospel contains one of the many passages where this rule
suggests the translation of a predicate as a definite noun. The
absence of the article [before θεος] does not make the predicate
indefinite or qualitative when it precedes the verb; it is indefinite
in this position only when the context demands it. The context makes
no such demand in the Gospel of John, for this statement cannot be
regarded as strange in the prologue of the gospel which reaches its
climax in the confession of Thomas [John 20:28, ‘My Lord and my
God’].”
In a lengthy Appendix in the Jehovah’s Witnesses’ translation, which
was added to support the mistranslation of John 1:1, there are quoted
thirty-five other passages in John where the predicate noun has the
definite article in Greek. These are intended to prove that the
absence of the article in John 1:1 requires that θεος must be
translated “a god.” None of the thirty-five instances is parallel,
however, for in every case the predicate noun stands after the verb,
and so, according to Colwell’s rule, properly has the article. So far,
therefore, from being evidence against the usual translation of John
1:1, these instances add confirmation to the full enunciation of the
rule of the Greek definite article.