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The phrase "a first cause of" is correct and usable in written English.
It can be used in discussions about philosophy, metaphysics, or causality, particularly when referring to the initial cause of a series of events or phenomena.
Example: "Many philosophers argue that there must be a first cause of the universe, which is often identified as a divine being."
Alternatives: "an initial cause of" or "a primary cause of".
Exact(3)
Indeed al-Kindi argues for a first cause of being precisely by arguing for a first cause of oneness, and asserting that "bringing something to be" means imposing unity of a certain kind.
(Κ repeats other material, ΜΝ argue against Academic theories of forms and numbers); Lambda considers God, primarily as a first cause of motion, whereas for Avicenna the First Principle is a cause of being.
And one is justified in this because rational agency can only operate by seeking to be the first cause of its actions, and these are the prescriptions, and so on, of being a first cause of action.
Similar(57)
The harsher sanctions regime is a third cause of hunger.
A second cause of queues in product development is batch size.
A second cause of panic is the special character of the situation in which people find themselves.
A third cause of problems is the fact that acquisitions although a quick route to growth require full payment up front.
A third cause of homoplasy, reversal, is not covered here.
A second cause of overshoot results from the definition of the depth-of-error to be removed.
A third cause of overshoot arises from any tilt of the part in the machine coordinate frame.
A third cause of the British celebrity shortage is that the culture (in Britain as well as in the U.S). has become more focused on the Everyman who performs on so-called "reality" television.
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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