Few people doubt that common sense is very effective in helping us to ``find the way.'' In the wilderness, even the most brilliant mathematician will not (and probably cannot) prove that he should keep away from a hungry lion. Common sense is simply crucial for his survival. However, when it comes to science, common sense seems to become a deadly enemy who one should fight against. For one thing, there is no place for common sense, it is widely believed, in pure mathematics. Everything must be rigorously logical! Since it is (classic) logic that is efficacious in mathematics, all ``exact'' sciences which talk mathematics should be strictly logical as well. But this view cannot be adequate.
It turns out that a crucial difference between logic and common sense is that logic is about truth but common sense (and indeed science) is about relevant information. Specifically, information about something must be capable of being memorized (it is representation which can be encoded and decoded in a systematic way). Therefore, information must rely on a system which is language-like. Thus the information about a fire does not have to be the fire itself. And the information of the danger associated with fire is not the danger itself.
In fact, if one realizes that common sense is thus mingled with language, one realizes that information alone may become a misleading concept. What is important is the relevance of a piece of apparently ``objective'' information. In fact, even a simple sentence like ``hungry lions are dangerous'' may not carry any objective information, strictly speaking. A hungry lion may not be dangerous for another hungry lion. It is certainly not dangerous for safari tourists who are in a well protected jeep, either. It is dangerous for an unarmed human or a sick zebra. In this regard, relevant information (and common sense) is always intentional. There must be someone or something who sees a piece of information as relevant. In this regard, it is hard to imagine a satisfactory framework of common sense without an adequate account of meaning5.1.
This motivates us to begin our account of common sense logic with a closer inspection of language.