In this article, I'd like to look at Daniel Wallace's explanation of independent adjectival participles that function as substantives on pages 268 to 271 of his book Basics of New Testament Syntax, particularly as they relate to verbal aspect.
Here are some important quotes from Wallace's book regarding verbal aspect and independent adjectival participles.
"[The adjectival force] tends to dilute the strength of the aspect." (p 268)
"When a participle is substantival, its aspectual element is more susceptible to reduction in force." (p. 268)
"For a structural clue, the student should note the article: If it stands before a participle and functions as a modifying article (normal use), then that participle must be adjectival." (p. 269)
"Just because a participle is adjectival or substantival, this does not mean that its verbal aspect is entirely diminished. Most substantival participles still retain something of their aspect." (p. 270)
As Wallace said, sometimes participles are substantive (i.e., functioning in the capacity of nouns). When they do this, they are proceeded by the article and MUST be adjectival (see the quote above on p. 269). How can it function as a noun and be adjectival at the same time? I will try to demonstrate this below.
Wallace gives a few examples of articular present and aorist participles that function as substantives (p. 271):
"Luke 1:45 μακαρία ἡ πιστεύσασα = blessed is she who believed
"John 3:16 πᾶς ὁ πιστεύων = everyone who believes
"John 6:39 τοῦτο δέ ἐστιν τὸ θέλημα τοῦ πέμψαντός με = now this is the will of the one who sent me"
Next, I'd like to do a little analysis to demonstrate that these types of participles are indeed adjectival and then show how they can function in the capacity of nouns as substantives.
Let's take an example from the parable of the sower in Matthew 13:37-49, since there we meet both an articular present participle (v. 37) and articular aorist participle (v. 39) that act as substantives.
First, let's do the articular present participle of verse 37 by rendering it as adjectival.
Ὁ σπείρων = "The sowing [one]."
Ὁ σπείρων τὸ καλὸν σπέρμα = "The sowing-good-seed [one]."
Ὁ σπείρων τὸ καλὸν σπέρμα ἐστὶν ὁ υἱὸς τοῦ ἀνθρώπου· = "The sowing-good-seed [one] is the Son of man."
Now, let's convert it so that it acts as a substantive.
"The sowing-good-seed [one] is the Son of man." ≈ (almost equals) "The sower of good seed IS the Son of man."
Now let's do the articular aorist participle of verse 39 but adapt it to the sentence used for the articular present participle above.
Ὁ σπείρας = "The sowed [one]."
Ὁ σπείρας τὸ καλὸν σπέρμα = "The sowed-good-seed [one]."
Ὁ σπείρας τὸ καλὸν σπέρμα ἐστὶν ὁ υἱὸς τοῦ ἀνθρώπου· = "The sowed-good-seed [one] is the Son of man."
Again, let's convert it so that it acts as a substantive.
"The sowed-good-seed [one] is the Son of man." ≈ (almost equals) "The sower of good seed IS/WAS the Son of man."
What about verbal aspect? Remember that Wallace said that the aspect tends to be diminished in participles, but this is especially true for these articular participles that acts as substantives. Therefore, it would be a mistake to emphasize verbal aspect in these types of participles.
Wallace also notes the following:
"Many nouns in Hellenistic Greek, for instance, were participles in a former life" and that "the constant pressure from the adjectival side finally caved in any remnants of verbal aspect." (p. 268)
"A general rule of thumb is that the more particular (as opposed to generic) the referent, the more of the verbal aspect is still seen." (p. 271)
This last quote is important because it means that gnomic (i.e., generic truth statements) will have more strongly diminished verbal aspect.
Wallace does paradoxically say on p. 271 when giving his example of John 3:16 that a substantive can function as gnomic and continual at the same exact time! How can a word express two contrary concepts at the same exact time? That doesn't sound possible to me. In fact, Wallace had already said earlier on p. 268, "But if they are already gnomic, we would be hard-pressed to make something more out of them—such as a progressive idea." So, why the exception for John 3:16? Wallace hints that his decision is due to theological bias. He thinks present tense verbs that are soteriologically significant should be interpreted as expressing continual action (presumably to bolster the idea that a believer must "endure to the end" to be saved). But this is really an abuse of the Greek language, and I think Wallace would have done better to keep his bias out of his textbook. And it is not as if Wallace didn't know he was incorporating the bias. He already commented on p. 268 that the present participle in πᾶς ὁ βλέπων γυναῖκα in Matthew 5:28 (which has a similar gnomic structure as πᾶς ὁ πιστεύων εἰς αὐτὸν in John 3:16) cannot be fit into the mold of continued action. We know that both Matthew 5:28 and John 3:16 are gnomic because of the use of the adjective πᾶς, indicating that they are both generic truth statements.
But for the sake of argument, let's assume for a moment that πιστεύω is an action verb (as opposed to a stative verb) and that ὁ πιστεύων in John 3:16 expresses continual action (as opposed to being gnomic). What can we prove from this? First off, the continual action would still be diminished if what Wallace said above is true. So, I don't think it should be emphasized in translation or interpretation by using the present continuous (i.e., "everyone who is believing"). But more importantly, again for the sake of argument, let's assume verbal aspect is strengthened and continual action is just as strong as it is in present indicatives. What would this tell us? Not much at all. It would still tell us nothing in regard to how long the action continues, much less guarantee that the action would "endure to the end" (Matthew 24:13). Simple common sense tells us that this is true, and it can be deduced from what Smyth and Monro wrote in their respective grammars. The continual action of the present tense can be fulfilled and terminated in as little as two seconds. Continual action by itself tells us nothing about the length of that continual action.
Interpretations should be based on grammatical, contextual, historical, and lexical considerations. This should go with out saying, but it is a serious problem when New Testament scholars are influencing grammatical considerations based on their theological biases.