Pauline prophecy

i) The debate over the continuance or discontinuance of NT prophecy centers on Acts and 1 Corinthians, since those are the two NT books which have the most to say about NT prophecy. Ideally, it's best to interpret a writer's usage by his own usage. If we don't have a large enough sample, then we may have to turn to the NT generally, or the OT generally, or extrabiblical usage. But the best starting-point is the author's usage.

This is a bit challenging. The Bible doesn't contain a glossary. So we have to define terms by ostensible examples or informative descriptions. Paul's letters are occasional writings. It also depends on whether we're defining prophecy in terms of the psychological experience, or the end-result (e.g. words). But here are some efforts to get a bead on Paul's understanding of prophecy:

The criteria for identifying the presence of oracular material in early Christian literature are the following: (1) If a saying or speech is attributed to a supernatural being (i.e. to God, Jesus, the Holy Spirit, an angel, a deceased person, Satan, a demon, &c.)… (2) If a saying or speech consists of a prediction of the future course of events, or reflects knowledge of the past or present that the speaker could not be expected to know by ordinary sensory means. D. Aune, Prophecy in Early Christianity and the Ancient Mediterranean World (Eerdmans 1983), 247-48.

ii) This defines prophecy in terms of extrasensory knowledge of the past, present, or future–as well as sacred space (i.e. the "third heaven"). Extrasensory knowledge of external events in time and space. 

At this stage in the argument, Aune isn't confining himself to the NT. But he goes on to say, with specific reference to Paul:

With varying degrees of confidence, we suggest that the following passages contain oracular sayings: 2 Cor 12:9; 1 Cor 15:51-52; Rom 11:25-26; 1 Thes 4:16-17a; 1 Cor 12:3; 1 Cor 14:37-38; Gal 5:21; 1 Thes 3:4; 1 Thes 4:2-6; 2 Thes 3:6,10,12 (261).

Let's consider another example: 1 Cor 14:25:

The Lord knew (1 Cor 4:5; Prov 15:11) and could reveal by prophecy the secrets of hearts (2 Kgs 5:26; cf. Sir 1:30). C. Keener, 1-2 Corinthians (Cambridge (2005), 115. 

Cf. 1 Cor 4:5, where nearly identical language describes the eschatological judgment of God. Now he uses it to refer to the judgment that takes place in the present through the Spirit. G. Fee, God's Empowering Presence (Hendrickson 1994), 245n667.  

A second parallel statement [1 Cor 4:5] explains and intensifies what this means: he will expose the motives of people's hearts…The one who searches the hearts is almost an OT title for God (Pss 17:3; 26:2; 44:21; 139:23). R Ciampa & B. Rosner, The First Letter to the Corinthians (Eerdmans 2010), 174.  

iii) Using 1 Cor 4:5 to gloss 1 Cor 14:25, this involves extrasensory knowledge of a second party's private thoughts, and memories. But that also includes things they've done in the past, where they were the only witness to their own conduct or misconduct. Their "secret sins."

If these examples are representative, then Paul's understands the experience of prophecy to involve extrasensory knowledge of events that happen in time and space, as well as mind-reading–which is, by definition, extrasensory. And God is the source of this extrasensory knowledge. God is omniscient, and God can convey otherwise inaccessible information to human recipients. 

iv) Thus far, this refers to the prophetic experience. Prophecy can also denote the effect of the prophetic experience. In canonical prophecy, this is a two-stage process. In the first stage, God reveals information to the prophet. In the second stage, God inspires the prophet to communicate that information through the medium of the spoken or written word.

v) This, in turn, raises the question of whether both stages are always present whenever prophecy takes place. For instance, there are Scriptural instances where God sends revelatory dreams to pagans, viz. Abimelech, Pharaoh, Nebuchadnezzar, Pilate's wife. They had a prophetic experience. But when they told others what they dreamt about, their account wasn't verbally inspired (unlike the Biblical narrative of their experience).

That may be a salient distinction when we consider the question of prophecy in the church. Even if prophecy continues off and on throughout church history, that's not the same as verbal inspiration. You can have the first stage without the second.