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That would make scratch paper a potential "eggcorn," to use a term coined by linguists for a misconstrued word or phrase that gets reshaped with a new semantic motivation.
Whereas the second suggestion was semantic ("motivation on the cheap," one might say), this reply is in part metaphysical and requires substantial work in the philosophy of mind.
Some classifier-noun pairings are arbitrary, or at least appear to modern speakers to have no semantic motivation.
A sceptical position is that while particular restrictions might ultimately have a semantic motivation (or have had one historically), actual learners do not need to be aware of this motivation, and learn verbs' restrictions via solely pre-emption/entrenchment (e.g., Stefanowitsch, 2008).
Similar(56)
Since the same phrase can appear in various environments, the choice of the construction is bound with other semantic or pragmatic motivations.
Motivation: Although semantic similarity in Gene Ontology (GO) and other approaches may be used to find similar GO terms, there is yet a method to systematically find a class of GO terms sharing a common property with high accuracy (e.g. involving human curation).
The conceptual motivation behind strongly semantic information is that for a statement to yield information, it must help us to narrow down the set of possible worlds.
Motivation: On the semantic web, in life sciences in particular, data is often distributed via multiple resources.
The motivation was that semantic technologies can simplify data integration across multiple sources and support the logic to infer additional insights from the data.
(For a recent attempt to develop a Fregean semantics for propositional attitude ascriptions which avoids this sort of problem by integrating aspects of a Russellian semantics, see Chalmers (2011).) So, while there are powerful motivations for propositional semantic theories, each theory of this sort also faces some difficult challenges.
Many modern applications of description logics (DLs, for short), such as biomedical ontologies and semantic web policies, provide fresh motivations for extending DLs with nonmonotonic inferences a topic that has attracted a significant amount of attention along the years.
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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