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Hi, How could we tell if a participle in what looks like a past perfect progressive tense is a participle part of the tense or an adjective of a past perfect tense construction?

The cook had been making cake all day until he was called by the head chef to do other tasks. -- looks to be a good past past perfect progressive tense.

The student had been finishing up on his composition when a knock on the door put a stop to it. -- looks to be an adjectival phrase with past perfect before it.
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Hi,
How could we tell if a participle in what looks like a past perfect progressive tense is a participle part of the tense or an adjective of a past perfect tense construction?

The cook had been making cake all day until he was called by the head chef to do other tasks. -- looks to be a good past past perfect progressive tense.

The student had been finishing up on his composition when a knock on the door put a stop to it. -- looks to be an adjectival phrase with past perfect before it.

#2 doesn't look adjectival to me. It looks the same as #1.

How would you assess this version?
The cook had been making cake all day when a knock on the door put a stop to it.

Best wishes, Clive
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The problem of disambiguating a participle that is part of a verb phrase from a participle that is an adjective is not related at all to the past perfect tense. Any time you have the verb to be in any tense, the same problem can occur.
You seem to be focusing on present participles.
As a general rule -- but it is not 100% accurate -- an animate subject will lead you to think of the -ing word as part of a verb phrase. (That's the case with both of your examples.)
An inanimate subject is often a signal that the -ing word is an adjective. The present participle in the latter case is often from a verb of psychological state -- a word that expresses a human reaction to a situation.

Examples of present participles as adjectives: amusing, annoying, confusing, disgusting, embarrassing, exciting, horrifying, irritating, maddening, perplexing, revolting, sickening, surprising, troubling, upsetting.
The play [is / was / had been / will be / ... ] [amusing / exciting / perplexing].
The food [is / was / had been / will be / ... ] [disgusting / sickening].
The sight of all that blood [is / was / ...] [horrifying / troubling].
The present participles of some of these verbs are occasionally used as parts of verb phrases with human beings as direct objects:
The yapping dogs [are / have been] [annoying / upsetting] your mother. Take them outside.
Her unusual behavior was clearly [embarrassing / irritating] the guests.
Peter [is / was] always surprising his wife with expensive gifts.
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Note how the presence of a direct object makes the participle part of a verb phrase:
His actions were embarrassing. (were embarrassing : linking verb and adjective)
His actions were embarrassing the women. (were embarrassing : verb phrase)
CJ
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Comments  
Had and been are both helping verbs. Helping verbs must help action verbs. In this sentence, had and been are helping the present participle making, which is an action verb. Because making is a present participle, it must have helping verbs to help it.
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HI. Although it seems to be a thread that was started a long time ago, I found your explanation to be very good.

Could you help us by telling (showing?) us how we could distinguish whether a past participle is part of the verb (that is the verb "to be", I think) or is a past participle acting as an adjective?
AnonymousCould you help us by telling (showing?) us how we could distinguish whether a past participle is part of the verb (that is the verb "to be", I think) or is a past participle acting as an adjective?
Whereas the confusion with the present participle is between an adjective and part of a progressive verb form, the confusion with the past participle is between an adjective and part of a passive form, so the problem reduces to differentiating between a true passive and an adjectival construction that looks like a passive.

See Passive voice vs Adjective for an explanation of two kinds of "true passives" and three kinds of "adjectival passives". Note that there is a part on how to determine if a past participle is an adjective.

CJ