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The phrase "on one understanding" is correct and usable in written English.
It can be used when discussing a specific interpretation or perspective of a situation or concept.
Example: "On one understanding, the policy could lead to significant improvements in efficiency."
Alternatives: "from one perspective" or "according to one interpretation."
Exact(7)
Logical principles that are valid on one understanding of these notions may not be valid on another.
On one understanding of this process, each of the resulting people has a good claim to be you.
On one understanding of "feeling" or "sensation" we include pains, nausea, tickles, suffocation, and thirst, which are distressing in some way.
On one understanding frequent among philosophers, consciousness is a certain feature shared by sense-experience and imagery, perhaps belonging also to a broad range of other mental phenomena (e.g., episodic thought, memory, and emotion).
On one understanding such talk is taken to be introducing the notion of a conscious mental event that is not a genuine perception but which is introspectively indiscriminible from a genuine perception of the world.
On one understanding, descended from the work of G. E. L. Owen and developed more fully by Jonathan Barnes and especially Terence Irwin, the endoxa are a compilation of views held by various people with some form or other of standing: "the views of fairly reflective people after some reflection", in Irwin's phrase.
Similar(53)
In the end, one's attitude to utopianism usually depends on one's understanding of progress, since progress is, as Wilde wrote, just "the realisation of utopias".
Moreover, the fact that one's own temporal stream of consciousness never completely coincides with that of another, whose sequence of events and intensity of experience inevitably differs from one's own, places limits on one's understanding of another.
Rendering "to each his due" hinges on one's understanding of what each deserves, and this cannot be correctly ascertained without taking into account the dignity and worth that are at the same time general qualities of all persons, and inseparable from the singularity of each of them.
Reflecting on one's understanding of, feelings about and experience with a particular incident 2 Surprise: a mismatch is assessed in the event when the outcome of task execution is unexpected (positive or negative) 2 Experiencing and acknowledging an unexpected outcome: is there a problem?
Reflect on one's understanding, feelings and experience of an incident A Pre-sensing possible risks with IP rights B Experiencing delay and redefinition of objectives Anticipating issues that are expected to emerge Sensing that present design is not going towork 2 Experiencing and acknowledging an unexpected outcome: is there a problem?
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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