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Discover LudwigSuggestions(1)
The phrase "a second principle" is correct and usable in written English.
It can be used when referring to an additional guiding rule or concept in a discussion or argument.
Example: "In addition to the first principle, we must also consider a second principle that governs our approach to this issue."
Alternatives: "another principle" or "a subsequent principle".
Exact(28)
And what do you think of a second principle?
During the infant's third month a second principle, called the discrepancy principle, begins to assume precedence.
And then there is a second thing, a second principle that we've got to go back and rediscover.
A second principle is that dead men cannot sue and may therefore be vilified to one's heart's content.
A second principle, sometimes called sudden death, was also considered and abandoned in the early days of competitive chess.
A second principle states that independence for Israel will be achieved only by bringing Jews to the land "and the removal of all hostile elements from the land".
Similar(32)
For her, feminism was a first principle.
Whereupon a first principle was established.
It should include a sixth principle: stubbornness.
"Business pacifism" became a first principle of the Gilded Age.
Chym. 2. To constitute; to make as a first principle.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com