I'm discussed this before, but I'd like to address it in more detail. Nowadays there are prominent Christian apologists who say that if the Resurrection happened, then Christianity is true even if some things in the Bible are false. But I've never seen them spell that out.
Here's the most charitable interpretation of that basic approach. As I recall, back in the 70s, John Warwick Montgomery used to present a multistaged argument like this:
We don't have to begin with the inerrancy of Scripture. Rather, the Gospels are demonstrably historically accurate in general. The Gospels record the Resurrection of Jesus. If Jesus rose from the dead, then he must be divine. And the divine Jesus vouches for the historicity of the OT, as well as promising that the disciples will enjoy inspired recollection of everything he said. (I'm summarizing his argument from memory.)
This seems to be what gave rise to the current approach. And I think there's some merit to Montgomery's argument. Mind you, I don't quite agree with his argument as it stands, because the Bible doesn't treat the Resurrection as direct proof for the deity of Christ. Rather, the Bible typically says the Father raised Jesus from the dead.
Perhaps, though, we could modify the argument by saying the Resurrection is an indirect proof for the deity of Christ. It would be counterproductive for God to raise a false Messiah from the dead, since people would naturally take that as evidence of divine approval. The more so if the claimant predicted his resurrection, because that would be prophetic fulfillment.
If, therefore, Jesus claimed to be divine, if the Gospel narrators claim Jesus is divine, and if the Father raised him from the dead, then he must be divine. And I think there's a good potential argument there, although it has to be fleshed out.
However, that's not the kind of argument that the apologists I allude to are using. They've made a crucial change. Montgomery appealed to the Resurrection to prove the inerrancy of Scripture. By contrast, more recent apologists are doing just the opposite: they appeal to the Resurrection to prove the expandability of Biblical inerrancy. Yet there are major problems with that position:
i) If Jesus routinely appeals to the OT as unquestionably true, then you can't simultaneously affirm Jesus and disaffirm the Bible. That's incoherent, for they rise and fall together:
Let us examine then, first of all, His attitude to the historical narratives of the Old Testament. He consistently treats them as straightforward records of facts. We have references to: Abel (Lk. xi. 51), Noah (Mt. xxiv. 37-39; Lk. xvii. 26, 27), Abraham (Jn. viii. 56), the institution of circumcision (Jn. vii. 22; cf. Gn. xvll. 10-12; Lv. xii. 3), Sodom and Gomorrah (Mt. x. 15, xi. 23, 24; Lk. x. 12). Lot (Lk. xvii. 28-32), Isaac and Jacob (Mt. viii. 11; Lk. xiii. 28), the manna (in. vi. 31, 49, 58), the wilderness serpent (Jn. iii. 14), David eating the shewbread (Mt. xii. 3, 4; Mk. ii. 25, 26; Lk. vi. 3, 4) and as a Psalm-writer (Mt. xxii. 43; Mk. xii. 36; Lk. xx. 42), Solomon (Mt. vi. 29, xii. 42; Lk. xi. 31, xii. 27), Elijah (Lk. iv. 25, 26), Elisha (Lk. iv. 27), Jonah (Mt. xii. 39-41; Lk. xi. 29, 30, 32), Zachariah (Lk. xi. 51). This last passage brings out His sense of the unity of history and His grasp of its wide sweep. His eye surveys the whole course of history from ‘the foundation of the world’ to ‘this generation’. There are repeated references to Moses as the giver of the law (Mt. viii. 4, xix. 8; Mk. i. 44, vii. 10, x. 5, xii. 26; Lk. v. 14, xx. 37; Jn. v. 46, vii. 19); the sufferings of the prophets are also mentioned frequently (Mt. v. 12, xiii. 57, xxi. 34-36, xxiii. 29-37; Mk. vi. 4 (cf. Lk. iv. 24; Jn. iv. 44), xii. 2-5; Lk. vi. 23, xi. 47-51, xiii. 34, xx. 10-12); and there is a reference to the popularity of the false prophets (Lk. vi. 26). He sets the stamp of His approval on passages in Gn. i and ii (Mt. xix. 4, 5; Mk. x. 6-8.)
Although these quotations are taken by our Lord more or less at random from different parts of the Old Testament and some periods of the history are covered more fully than others, it is evident that He was familiar with most of our Old Testament and that He treated it all equally as history. Curiously enough, the narratives that proved least acceptable to what was known a generation or two ago as ‘the modem mind’ are the very ones that He seemed most fond of choosing for His illustrations.
ii) Likewise, Christianity can't be true if OT Judaism is false. To be true, Christianity must fulfill the OT. Christianity can't be true unless OT Judaism is true.
But Judaism can't be true if the call of Abraham is fictional, if the Akedah (Gen 22) is fictional, if the Abrahamic covenant is fictional, if the Joseph cycle (Gen 37-50) is fictional, if the call of Moses is fictional, if the Exodus is fictional, if the Davidic covenant is fictional, &c.
So where to these apologists draw the line? Their position is ominously similar to "progressive Christians" who say you can discount most of the reported miracles in Scripture. The only miracles you really must profess to be a Christian are the Incarnation and Resurrection.
iii) In addition, the Christian faith isn't based on bare events, but interpreted events. Not surprisingly, the NT contains extensive theological interpretation regarding the significance of the Resurrection. What's the divine purpose behind that event–as well as other events in the life of Christ (e.g. the Crucifixion)?