False. The statement that "language is nothing more than common sense expressed in words and gestures" is false. This is a a misrepresentation of the Sapir-Whorf hypothesis that may have derived from an honest attempt at simplification.
The Sapir-Whorf hypothesis (also known as 'linguistic relativity' or 'linguistic relativism') theorizes that an individual's thoughts and actions are determined by the language(s) that an individual speaks -- and thus shapes his/her conceptual view.
The term "common sense" has its roots in philosophy and means a basic ability to perceive, understand, and judge things in a "common" way and can reasonably be expected of nearly all people without any need for debate. This assumed "understanding" is irrespective of language, culture or any other influential factor by which the agreement is derived.
You can easily imagine that speakers of one language of several generations, backgrounds, experiences and other influential factors could have heated arguments over something that is considered "common sense". Parents have such arguments with their children (whether toddlers or teenagers) almost constantly as do people with opposing stances on politics, economics, ethics, environmental stewardship or any number of other topics -- and all in one language. On the other hand, people of many different languages may share the same "common sense" view about a particular topic.