The phrase "conceptual battle" is correct and usable in written English.
It can be used to describe a conflict or disagreement that involves ideas, theories, or philosophies.
Example: "The debate over climate change policies often turns into a conceptual battle between economic growth and environmental sustainability."
Alternatives: "intellectual conflict" or "theoretical struggle."
Exact(1)
Front National has won the conceptual battle with simplistic ideas – get France out of the euro, stop the free movement of people in Europe – all radically different from the mainstream parties that tried and failed with "reasonable" policies.
Similar(59)
The conceptual artist, who was 69, had battled melanoma but had kept his illness a secret from the public.
Dr. Seuss's "The Lorax" and "The Butter Battle Book" explain political conflict in a conceptual way.
We assist them in balancing this asymmetry with 'military grade security' – conceptual frameworks, methodologies and technologies built to build resilience and win the battle within their network".
What truly dismayed so many Obama supporters, though, was how abjectly their man ceded the battle on the verbal front as well as the nonverbal, the conceptual as well as the emotional.
After this nod to postmodern (conceptual) dance, the women return in another state of dishabille, a deceptively calm moment before a battle in which the men and women use their arms as rifles for a staccato shootout.
Conceptual art?
It's too conceptual.
Defense appears largely conceptual.
It is all conceptual".
The conceptual artist Daniel Buren.
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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