Logic
Logic is a subject matter that uses symbol systems to enumerate possibilities. Based on this assumption, any set of symbols that allows for the same possibility space can be thought of as the same language. This can be explained as the term: up to isomorphism in Category Theory.
Some of the directly related ideas can be found here:
Why study logic?
Logic has a unique position in the cognitive process of all systems. It is a kind of self-contained, or invariant foundation to help reason or compare against other things.
Interesting Dicussions
Readers can find some relevant discussions about Logic here (starting at 5'41", just click on the following image, it will jump to that time point.):
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