for all intensive purposes
The phrase is “for all intents and purposes.” There is nothing intensive about it.
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Wrong: For all intensive purposes, it’s done.
Right: For all intents and purposes, it’s done.
Intents and purposes. Two nouns, near-synonyms, doubled up for emphasis.
Where it comes from
The phrase is roughly 500 years old and started life in English law as to all intents, constructions, and purposes. It piles up near-synonyms on purpose, the way legal language does, to mean “in every practical sense, whatever the technicality says.”
Intensive means concentrated or thorough. It has never appeared in the phrase and contributes nothing to it.
Why it survives
This is an eggcorn—a misheard phrase reshaped into something that almost makes sense. Spoken quickly, “intents and” and “intensive” are nearly identical, and “intensive purposes” sounds like it could mean something serious.
It doesn’t. It’s just the wrong words, and in writing there’s nowhere to hide.
Now go use both nouns.