Militate: to influence strongly. The word militate is intransitive and is usually accompanied by the preposition against.
For if it happened that an individual, even when asleep, had some very distinct idea, as, for example, if a geometer should discover some new demonstration, the circumstance of his being asleep would not militate against its truth.
—René Descartes Discourse on Method (1637)
Mitigate: to make less severe or less intense. The word mitigate is transitive and may affix itself directly to a noun.
The joys of parents are secret; and so are their griefs and fears. They cannot utter the one; nor they will not utter the other. Children sweeten labors; but they make misfortunes more bitter. They increase the cares of life; but they mitigate the remembrance of death. The perpetuity by generation is common to beasts; but memory, merit, and noble works are proper to men.
—Francis Bacon Essays, Civil and Moral (1909)
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