The question is often asked: ”Is this genitive an objective or a subjective genitive?” I am going to suggest that this is an old-fashioned and unhelpful question, which can lead to questionable conclusions. It is based on the grammatical concepts of subject and object and it was asked long before people started to talk about semantics.
I am saying it is unhelpful, because it is too restricted. In terms of syntax there are three kinds of potential participants in a clause. They are best illustrated with a common ditransitive verb like ”give”. A gave B to C. A is subject, B is object and C is indirect object. In terms of semantics for ”give”, A would be the Agent, B the Patient and C the recipient. In semantics we operate with a bigger set of roles, including Experiencer, Location, Source, Goal, Direction, Instrument, Beneficiary, Recipient. Different theories of semantics operate with slightly different sets and the borderline between the roles are at times fuzzy.
Sometimes people ask about a phrase like ”the love of God”, is it a subjective or objective genitive? But quite often it is neither. In a clause like ”I love you”, it is more interesting to ask what are the semantic roles than what is subject or object. Is the subject an Agent? Is ”love” an action? Or a feeling or an attitude? It seems to me that the subject expresses the role of Experiencer. This semantic role is somewhere in-between Agent and Patient, probably closer to Patient. When I say ”I am in love”, or ”I love you” I am describing my feelings, not my actions. So, if the grammatical subject is Experiencer, what is behind the grammatical object? I would suggest the role to be a Goal or Direction. My love is directed towards ”you”. Similarly, in the phrase ”the love of God”, God might be the Direction (A loves God) or the Experiencer (God loves A) or the Source (love from God).
The Greek verb πιστεύω is usually translated by ”believe” or ”trust”. A few times it corresponds to ”entrust”. In the sense of ”entrust” it may take an accusative direct object and a dative indirect object in Greek (e.g. John 2:24, Luke 16:11), but it never has an accusative object in the common sense of ”believe, trust”. I suggest that the subject is best described as Experiencer and the ”object” for belief is the semantic Direction. The Direction can be expressed in different ways in the grammar. The most common Greek preposition used is εἰς, and this is understandable since εἰς indicates Direction. A quite rare preposition with πιστεύω is the Greek ἐν (Mark 1:15, John 3:15). In Koine Greek a prepositional phrase with ἐν is often equivalent to a simple dative, and we find that the ”object” for faith is often expressed in the dative, especially if it is a pronoun. This is understandable since the dative is often connected with the semantic roles of Direction, Goal and Beneficiary. It is common to have a mismatch between semantic roles and grammatical cases. One case may correspond to several roles, and one role may correspond to several cases or prepositions. Another preposition used with this verb is ἐπί (Matt 27:42; Luk 24:25; Acts 9:42, 11:17; 16:31, 22:19,; Rom 4:24,9:33, 10:11; 1Tim 1:16; 1Pet 2:6). Again, ἐπί with accusative often indicates Direction or Goal.
Now, when a noun is used rather than a verb, all semantic roles are made implicit and must be deduced from context. In order to indicate at least one of the roles, another noun or pronoun is often connected to the first noun by way of a genitive construction. The genitive in itself does not determine whether the second noun functions as Experiencer or Direction. In the case of a genitive pronoun, we find the following:
1st person singular: faith in me (Jesus speaking) – Rev 2:13, my faith – Rom 1:12
1st person plural: our faith – 1Jn 5:4 (once in NT)
2nd person singular: your faith – Matt 9:22 etc. (11 times in the NT)
2nd person plural: your faith – (24 times in NT)
3rd person singular: his faith – (Rom 4:5), faith in him – (Eph 3:12)
3rd person plural: their faith – (4 times in NT)
In each and every case the Direction for this faith is Jesus or God. Only two places do we have the pronoun in the role of Direction. That all the others are what is traditionally called ”subjective genitive” has nothing to do with the grammar or semantics, but is what is to be expected pragmatically. Faith is assumed in these contexts to be faith in Jesus and different people can have faith. In a few cases the role of Direction is explicit by way of a prepositional phrase, e.g. ἐν (1 Cor 2:5, Col 1:4), εἰς (1 Pet 1:21; Col 2:5) and πρός (1 Th 1:8), but it is rarely necessary to make this explicit.
If we look at those cases where no pronoun or genitive is involved, we find the same three prepositions (εἰς, ἐν and ἐπὶ) used to indicate the Direction role:
Acts 24:24 περὶ τῆς εἰς Χριστὸν Ἰησοῦν πίστεως about the faith in/towards Christ Jesus.
Rom 3:25 διὰ [τῆς] πίστεως ἐν τῷ αὐτοῦ αἵματι through (the) faith in his blood
Gal 3:26 διὰ τῆς πίστεως ἐν Χριστῷ Ἰησοῦ through the/our faith in Christ Jesus
2 Tim 3:15 διὰ πίστεως τῆς ἐν Χριστῷ Ἰησοῦ though a faith that is in/towards Christ Jesus
Heb 6:1 πίστεως ἐπὶ θεόν faith in God
We found with the verb form that the dative case was used more often than a prepositional phrase, and in the case of a noun plus genitive we find that a genitive is also more common than a preposition.
These cases are somewhat debated, because it is a matter of context whether the genitive indicates Experiencer or Direction or even Source. One would need to look carefully at the context, and I am only giving references here:
Mark 11:22 πίστιν θεοῦ – probably faith in God (possibly Source)
Rom 3:22 διὰ πίστεως Ἰησοῦ Χριστοῦ – probably through faith in Jesus Christ
Rom 3:26 πίστεως Ἰησοῦ – probably faith in Jesus
Rom 4:12 πίστεως τοῦ πατρὸς ἡμῶν Ἀβραάμ – the faith of our father Abraham
Rom 4:16 πίστεως Ἀβραάμ – the faith of Abraham
Gal 2:16 διὰ πίστεως Ἰησοῦ Χριστοῦ, καὶ ἡμεῖς εἰς Χριστὸν Ἰησοῦν ἐπιστεύσαμεν – through faith in Jesus Christ, and WE have come to believe in Christ Jesus.
Gal 3:22 ἵνα ἡ ἐπαγγελία ἐκ πίστεως Ἰησοῦ Χριστοῦ δοθῇ τοῖς πιστεύουσιν – so that the promise based on faith in Jesus Christ could be given to those who believe (in him)
Php 1:17 τῇ πίστει τοῦ εὐαγγελίου – probably a genitive of Source, the faith that is contained in and brought by the Good News
Php 3:9 μὴ ἔχων ἐμὴν δικαιοσύνην τὴν ἐκ νόμου ἀλλὰ τὴν διὰ πίστεως Χριστοῦ, τὴν ἐκ θεοῦ δικαιοσύνην ἐπὶ τῇ πίστει – not having a righteousness of my own which is based on (keeping) the law, but the (righteousness) that (comes) through (having) faith in Christ, the righteousness from God based on (us having) faith (in Christ)
Col 2:12 διὰ τῆς πίστεως τῆς ἐνεργείας τοῦ θεοῦ – through faith in the (powerful) operation/working of God
Rev 14:12 οἱ τηροῦντες τὰς ἐντολὰς τοῦ θεοῦ καὶ τὴν πίστιν Ἰησοῦ – those who keep/hold on to the commands of God and the/their faith in Jesus.
As can be expected, when the genitive refers to a person (like Abraham), the genitive indicates the Experiencer (”subjective genitive”), and where the faith is directed towards Jesus or God or an activity of God then we have the role of Direction.
Some people have argued that a ”subjective genitive” is possible in some of these constructions as long as we understand πίστις to refer to ”faithfulness” rather than ”faith”. Normally ”faithfulness, trustworthiness” is expressed by the adjective πιστός, but πιστός can occasionally also mean ”a believer” and πίστις can at times mean ”faithfulness”. There is one genitive construction where the context demands this sense, namely Rom 3:3:
εἰ ἠπίστησάν τινες, μὴ ἡ ἀπιστία αὐτῶν τὴν πίστιν τοῦ θεοῦ καταργήσει;
If some were unfaithful, surely their unfaithfulness does not obliterate God’s faithfulness. Here the contrast is between the unfaithfulness of people and the faithfulness of God, a common topic in the Old Testament. The faithfulness of God is not a common topic in the NT, because that is assumed to be a known fact. When the writer wants to remind the hearers of God’s faithfulness, the adjective πιστός is used. I have only found two places where the faithfulness of Jesus is being mentioned (Heb 3:2, Rev 1:5)