"The cake was baked." Is "baked" a past participle or predicate adjective? [duplicate]
The word baked in "The cake was baked" definitely could be considered a participle, but it could probably also be consided an adjective, depending on how you interpret the sentence.
Your sentence is semantically ambiguous. It could either take an eventive interpretation (for example, if I am telling a narrative, and at the point in the narrative where the cake is baked, I say "The cake was baked") or a stative interpretation (for example, if I am telling somebody that I am looking for a cake that I have misplaced, and they ask "Was the cake baked, or unbaked?", and I reply "The cake was baked").
The eventive interpretation: "baked" is a participle
The word baked would definitely be considered a participle if the sentence is interpreted as having a dynamic meaning, because an -ed/-en word in an dynamic passive construction can never pass the usual tests for distinguishing departicipial adjectives from participles.
The stative interpretation: "baked" is an adjective, I think
But with the stative interpretation, I would say that the word "baked" seems to be an adjective.
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It seems possible to use it after the verb "seemed":
a) "The cake seemed baked."
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It can take the adjectival negative prefix un-:
b) "The cake was unbaked."
Sentence b) can have the meaning The cake was not yet baked. (The meaning part of this test is important: the homographic and homophonic "reversative" prefix un- does attach to verbs, so the existence of a form unbaked does not by itself establish that baked is an adjective.)
Honestly, sentences a) and b) sound a bit weird to me, but I would say that they are grammatical. It would be completely impossible to use a "verbal" passive participle in these constructions.
Interestingly, the word baked is actually used as an example of a word that can be used either as a "syntactic passive" or as an "adjectival passive" in a lecture by Peter Svenonius, "The Zero Level": see (1.2) "Syntactic passives" and (1.3) "Adjectival passives" on page 2, and (2.6) on page 6:
(2.6) a. We baked our department chair a cake.
b. The department chair was baked a cake.
c. The cake seemed baked.
d. *The department chair seemed baked a cake.
Svenonius also discusses the grammatical structure of passives, but that part is a bit over my head, so you'll have to read that lecture yourself if you want to understand all the explanations and arguments in it.
The theoretical analysis of the two different kinds of "passive" seems to be a complicated part of grammar, so it may depend on things like the validity of the "Lexicalist hypothesis" and what it means for a word to belong to a particular "part of speech" like verb or adjective.
The meaning of the word "passive"
The term "passive" may be understood to refer to both "verbal" passives and "adjectival" passives. However, it also seems to be used, at least sometimes and by some authors, with a more restrictive definition that excludes "adjectival" passives: see the following sentence from "The passive in English" by Geoff Pullum:
I still have not done full justice to this topic; in particular, I have not opened up the topic of the close relation between passives and predicative adjective constructions (phrases like uninhabited are rather clearly adjectival, since there is no verb *uninhabit, yet we can say Antarctica is mostly uninhabited by humans).