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The phrase "a middle term" is correct and usable in written English.
It is typically used in logic, philosophy, or mathematics to refer to a term that appears in both premises of a syllogism and is used to connect them.
Example: "In the syllogism, 'All humans are mortal; Socrates is a human; therefore, Socrates is mortal,' the middle term is 'human.'"
Alternatives: "a connecting term" or "an intermediary term".
Exact(8)
The border confounded racists who'd reduced the world to a basic binary but didn't know how to slot a middle term between white and black, acceptance and opprobrium.
Consider the higher order nonlinear differential equation with a middle term x ( n ) ( t ) + q ( t ) x ( n − 2 ) ( t ) + r ( t ) f ( x ( t ) ) = 0, (1).
Logic also relates things to one another by means of a middle term in the syllogism, which is logic's subject matter.
It had excluded theology — "a connected system of ideas, each qualified by the other, each serving as a middle term by which the rest are held together" (CD 164).
She holds that judgment involves the comparison of two ideas and that sometimes we lack an "intermediate idea" (a "middle term") in order to make a judgment (Astell 2002, 146 7, 172 3).
This means, first of all, that a genus-difference definition of a thing, which does not identify really distinct parts in it, cannot serve as a middle term in demonstration.
Similar(52)
So, too, is a middle-term goal tied to a fixed need, like paying for college.
We hope to be able to address this question in a middle-term perspective.
When PC12 cells were exposed to a middle-term duration (8 days) microgravity, a reduced neurite extension with respect to 1 g cultures was demonstrated as well [ 40].
A meta-analysis of 14 randomized controlled trials employing BPs after joint arthroplasty found that the protective effect of these drugs, probably modified by BP generation and the prosthesis location, could persist in a middle-term follow-up after surgery and for 18 to 70 months after drug discontinuation.
In his theory of inference, he distinguished between inference for oneself and inference for the other and laid down three criteria of a valid middle term (hetu that it should "cover" the minor premise (paksha), be present in the similar instances (sapaksha), and be absent in dissimilar instances (vipaksha).
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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