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The phrase "the standard conception" is correct and usable in written English.
This phrase is often used to describe a widely accepted belief, idea, or plan. For example, "The standard conception among physicists is that light is both a particle and a wave."
Exact(27)
From George Moore's The Untilled Field of 1903, the Irish story has shown a tendency to react against the standard conception of the Irish story.
Call this the standard conception of agency.
The standard conception is compatible, furthermore, with dual standpoint theories.
The standard conception of structure is either set theoretic or logical.
The standard conception of action provides us with a conception of agency.
No one forced the standard conception of "cool" onto a scientific endeavor.
Similar(33)
The critical notions constituting solids out of their plane sections and assigning weights to geometric figures were not formally valid within the standard conceptions of Greek geometry, and Archimedes admitted this.
Artists of the Post-Minimalist, Conceptual, and Performance movements rejected this standard conception of art and sought to make art based on an idea whose expression did not depend on the creation of a tangible object-- non-object-based art".
The broader and more standard conception of promoting an action by causing it simply has no foothold here, and if it did then the proposal would not correspond exactly with deontological intuitions.
This is important, because a standard conception of the transition from classical to relativistic physics is that although Einstein's theory of relativity supersedes Newton's theory, what we have is an improvement or generalization whereby Newton's theory is a special case of Einstein's (to a close approximation).
The contributions of Anscombe and Davidson have established a standard conception of action, and Davidson's work has provided the groundwork for a standard theory of action.
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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