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"New" approaches to exegesis emerge constantly, while old ones are revamped.
The titles or names of exegetical methods convey minimal information. Evaluate exegetical methods by these criteria:
Subject: who typically employs this exegetical method?
Scholar with five ancient languages? Pastor? Student?
Object: what does the exegesis study?
Language? Theology? Social history?
Goals: what does the method's final project (the exegesis) hope to do?
Win an academic argument? Enrich a sermon?
Audience: for whom is the exegesis produced?
Late-career professors? Kindergartners?
To start out, consult an overview of exegetical methods like the following:
A Handbook to the Exegesis of the New Testament by Stanley E. PorterTheoretical and practical. Introduces various definitions of exegesis. Discussed methods include: textual criticism; linguistic analysis; genre criticism; source, form, and redaction criticism; discourse analysis; rhetorical and narratological criticism; literary criticism; and canonical criticism. Also includes "applications" section.