“Scholars have proposed a number of possible explanations for why Paul says Christ’s death and resurrection on the third day each take place ‘according to the Scriptures’ …. One of the most important ingredients for 1 Corinthians 15:3, however, is Isaiah 53.
As we shall see, Paul knows the passage, referring to it elsewhere. The suffering servant, as the only human instance of vicarious death ‘according to the Scriptures,’ is the closest model for Christ’s death. There are similarities in the structure of the formula as well as in the language of ‘death’ and ‘sins.’ […]
First chapter 53 must be read within the wider framework of the surrounding chapters in Isaiah. The people of Israel are hard-hearted and in a state of disobedience; they refuse to repent and be gathered to God [….]
Second, despite this, God undertakes to redeem them. he gives them words of comfort in chapter 40, he promises in chapter 44 (vs. 21) that he has not forgotten Israel, and he even insists that in the absence of repentance on Israel’s part, he will accomplish it himself (chap. 46).
Third, we see how this will happen. As these chapters (the 40s and 50s in Isaiah) go on, it becomes clearer that God is raising up a servant who is distinct within the nation: the servant is not just a way of talking about Israel as a whole but is an individual who is going to be instrumental in saving the people. This character is the one who suffers in chapter 53. He is cruelly forsaken by the nation as a whole, and yet the Israelites later come to realize that he had accomplished their salvation [….]
There is considerable debate in scholarly circles about whether there is a ‘center’ to Paul’s thought. Among those who think there is one, there is debate about what that center is …. We may not have a ‘center’ here in 1 Corinthians 15, but we do clearly have a statement that the gospel, consisting of Christ’s substitutionary death and his resurrection is primary in Paul’s proclamation.
This is what Paul means by saying that he passed it on to the Corinthians ‘first’ or ‘as of first importance’ in verse 3. It may be difficult to discover which concept occupied the center of a dead person’s brain, but Paul himself tells us that the gospel as summarized in 1 Corinthians 15:3-4 does have primacy in his preaching.”
–Simon Gathercole, Defending Substitution: An Essay on Atonement in Paul (Baker, 2015).