- Can a Natural Language (like English for instance) describe anything?
- Are our thoughts limited by our language?
- If the number of words in a Natural Language is a finite set, can this set describe an infinite number of concepts, notions or ideas?
- Is there a core or reference set of vocabulary that can describe any concept?
What drove me to ask this question is my adoration to mathematics and its nature. Although any mathematical concept can in principle be formalized i.e. it can be expressed in terms of the axioms of set theory (ZFC), rarely the mathematicians do that. Instead they use natural language (English in particular) to describe and communicate mathematical concepts. So the following two questions came to my mind:
- Is natural language limited?
- Does natural language put constraints on the amount of mathematical discoveries that humans can make?
Steven Pinker has a nice presentation that touches upon this issue (particularly at the minute 20):