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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.<p>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.