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Similar things happen surprisingly often in companies.  Many intense arguments can be diffused by first being specific about what we agree upon.Just to add to this, one strategy from the rationalist community that I rarely see practiced is to 'taboo' certain words.  For example if two engineers are arguing about a solution not being scalable, taboo the word scalable.  They both re-explain their POV without using the word scalable at all.  It often works like magic and they quickly reach a shared understanding.