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The phrase "a generalized conception" is correct and usable in written English.
It can be used when discussing an abstract idea or a broad understanding of a concept that is not specific or detailed.
Example: "In philosophy, a generalized conception of reality often leads to various interpretations and debates among scholars."
Alternatives: "a broad understanding" or "a general idea".
Exact(2)
The distinctive belief which is a generalized conception of events and of the members' relationships to them supplies the basis for the development of a distinctive and stable organization within the collectivity.
The idea of a generalized conception of space has been made prominent, in the belief that the properties and operations involved in it can be made to form a uniform method of interpretation of the various algebras".
Similar(58)
In a plural metatheory in which we have a theory of ordered pairs, one may adapt the generalized conception of an interpretation developed in Rayo & Uzquiano (1999) to provide a plural model theory in which one uses neither.
We then move to a more general conception of sequents as originally conceived, allowing a set of formulas to play the conclusion role rather than just a single formula, as well as to the associated idea of generalized consequence relations, emphasizing Carnap's motivation for making this generalization.
Reproductive traits (calving-first service interval, number of services per conception and total pregnancy rate) were analyzed with a generalized linear model (GENMOD procedure) with a Poisson distribution and log transformation (calving-first service interval) or a binomial distribution and logit transformation (pregnancy rate).
It's a generalized term.
2. a generalized instance.
And one is a generalized conspiracy count.
Lagrange and C.G.A. Mayer into a generalized statement.
A generalized mental arousal is thereby effected.
Leaper (n).: a generalized Knight.
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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