GRB-Murray notes that the majority of commentators interpret Matthew 16:19 through the rabbinic uses of "binding" and "loosing." This appeal to the aforesaid utilizations of "loosing" and binding are supposed to buttress the Roman Catholic notion of a magisterial office that is able to make decisions which are subsequently ratified in heaven. But B-Murray writes that "the terms [loose and bind] were also applied to imposing or relieving the 'ban' on offenders, i.e., their exclusion from or readmittance to the synagogue" (John. GRB Murray. Page 383).
In the final analysis, B-Murray opts for understanding Matt. 16:19 in a forensic sense, so that we are to understand Peter being given the authority to forgive those who respond to the Gospel of Jesus Christ and condemn those whom he sees fit to condemn (those who do not respond favorably to the good news of God). But this conclusion is also by no means certain.
BAGD (page 178) indicates that one way to interpret DEW in Matt. 16:19; 18:18 is by appealing to the Aramaic uses already delineated heretofore. But this lexical source says that the rabbinic terms in question could mean "to forbid" or "to permit." And while certain scholars emphasize this aspect of the rabbinic terms, others see the binding and loosing of Matthew 16:18; 18:18 as somehow connected with magic practices (which admittedly seems highly doubtful in light of the GNT).
Before discussing the rabbinic background of Matthew 16:19, however, BAGD points out that Matt. 16:19; 18:18 may be understood from a Greek vantage standpoint (apart from invoking the rabbinic background). Matthew's language may well be reflecting the Greek declaration made about Prometheus: hOSA DHSEIEN hO ZEUS, TAUT' EXON 'HRAKLEI LUSAI (BAGD 178). So it is quite possible that we need not resort to the rabbinic tradition at all.
Interestingly, Spiros Zodhiates writes that "believers can never make conclusive decisions about things, but can only confirm those decisions which have already been made by God Himself as conclusive in the general context of his kingdom" (The Complete Word Study: New Testament. Page 60). Zodhiates' words appear to be supported by Deuteronomy 1:17, where we are told that the OT judges were not to be influenced by man because "the judgment belongs to God." Jehoshaphat similarly reminded the judges of his time that they were
judges for Jehovah (2 Chron. 19:6, 7). Christian "judges," therefore, can
only allow or forbid what has already been permitted or forbidden in heaven.
God does not follow the dictates of mere men on earth; they submit themselves
to his judicial decisions. Put another way--heaven dictates to earth, not earth to heaven