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The phrase "the two premises" is grammatically correct and can be used in written English.
It refers to the two main statements or claims that serve as the basis for an argument or reasoning. Example: "The two premises of the argument were weak and lacked evidence, making the conclusion unreliable."
Exact(26)
The two premises which attracted the greatest attention were those of Judge Seabury & Gypsy Rose Lee, at 154 & 153 E. 63rd St.
Using role stress, a specific type of work stressor commonly found among frontline employees, this study was designed to confirm which of the two premises best encompasses the role stress-alcohol use relationship among front-of-house restaurant servers in the United States.
In such arguments as "All C are B and no B are A, so no C are A," the truth of the two premises requires the truth of the conclusion in virtue of the manner in which the predicates B and A are distributed with reference to the classes specified by C and B, respectively.
The two premises can, however, be challenged.
This forces the focus onto the two premises.
Since the predicates in the two premises express different properties, Leibniz's Law has no application.
Similar(34)
The problem is, the two premise realizations may be quite different.
That's philosopher's jargon, that is to say, given the three premises, the conclusion really does follow.
The interesting question is, "Are the three premises true?" And they've got to all be true.
The four premises have been knocked through to create one impressive eating space: there are black marble floors with spangly bits in some rooms, and walls painted shades of peach and burnt umber.
Now the three premises ~(A&B), A and B entail a contradiction.
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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