What is the difference(s) between "poisoned with" and "poisoned by"?
This song is poisoned by unoriginal lyrics.
This song is poisoned with unoriginal lyrics/
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I As pertains to toxic substances, an expression of their agentive function in a given case of poisoning is apparently rendered by means of either preposition.
II The strong agentive connotations that suggests "by" make it, in my opinion, more suited to highlight a relation in which the poison itself, not being the true agent, is instead manipulated, insinuated, or caused to become effective, by the true agent. This principle is applied absolutely when the agent is a human being: "with" cannot be found. Here is an example which illustrates that and shows at the same time a useful consequence of the usage of both "by" and "with" described above.
In the realm of the figurative, whether this distinction is made consistently or not, or not at all, the use of both prepositions is common.
It seems, nevertheless, that in this domain,
1/ when the agent is external to the entity being poisoned, when it is not a part of it, merely acting upon it from an external situation, and
2/ when the agent is considered as a possibly impinging element and not as a normally co-occurring one,
the use of "by" tends to be preferable, and that, when these criteria are not satisfied, "with" does.
This first point (1/) tends to be verified in the literal sense of "poisoned", since in the context of the poisoning through the effects of pollution "with" is not found (ref.).
In the light of the last example in "2." above, this second point (2/) seems rather obvious; if we were to say "the purest intellectual pleasures are poisoned with bodily pain" we'd derive from it that bodily pain accompanies always the purest intellectual pleasures, which is not true. Instead, the preposition "by" manages in the import of the statement the understanding that the two phenomena are only incidental one to the other.
As the example in the question post is not the statement of a generality, "2/" is not relevant. One might choose "with" on the basis of "1/" but as well use "by"; to present the unoriginal lyrics as a poisoned part (with), or to infer possibly that the effect on the rest of the lyrics is detrimental, as the poison acts upon them (by), can be conveyed in any case by this sentence on the basis of added precisions, not to say that which preposition to use doesn't matter.