The phrase "auxiliary assumption" is correct and usable in written English.
It can be used in contexts involving logic, mathematics, or scientific reasoning where a supporting assumption is made to facilitate analysis or argumentation.
Example: "In our proof, we will rely on the auxiliary assumption that the function is continuous over the interval."
Alternatives: "supporting assumption" or "additional assumption".
One auxiliary assumption one may question is the traditional link between quantification and existence.
(Shapiro remarks that this auxiliary assumption seems best to capture the sense of multiple realization stressed by proponents of the standard argument).
In the above Newton example one would have to use the auxiliary assumption that the trajectories of the particles are twice differentiable and that other forces except the gravitational forces can be neglected.
For example, ∃E tells us that if in the process of constructing a proof one has already derived ∃xα(x) and also β with α(a/x) as an auxiliary assumption then the inference to β is allowed.
And, again, this is as it should be, in line with Nicod's mention of "the absence of \(G\) [here, non-black as evidence] in a case of \(F\) [here, raven as an auxiliary assumption]".
If object \(a\) is assumed to have been taken among ravens so that, crucially, the auxiliary assumption \ k = raven(a)\) is made and \(a\) is checked for color and found to be black, then, yes, the latter evidence, \ black(a)\), HD-confirms that all ravens are black \((h)\) relative to \ k\).
Key terms are poorly defined, auxiliary assumptions abound, and the literature I'm familiar with that is cited as authoritative is, well, not good.
The solution methods of GIEs are obtained without any auxiliary assumptions such as the effective field hypothesis (EFH), which is implicitly exploited in the known methods of micromechanics.
Next, the BEM discretized problem of unsteady flow around flat wing equivalent to the original geometry is recast into the standard form of a continuous-time state-space model considering some auxiliary assumptions.
The method is based on a centering procedure of subtraction from both sides of a known initial integral equation their statistical averages obtained without any auxiliary assumptions such as, e.g., effective field hypothesis implicitly exploited in the known centering methods.
The method is based on a recently developed centering procedure where the notion of a perturbator is introduced and statistical averages are obtained without any auxiliary assumptions such as, e.g., effective field hypothesis implicitly exploited in the known centering methods.
