Semantics and the Number of English Sentences
How many English sentences are there? Infinitely many has long been the answer in the catechisms of the orthodox. And not without reason. 'This is the cat that caught the rat.' is an English sentence. So is 'This is the cat that caught the rat that stole the cheese.'. This is the cat with white paws that caught the rat that stole the cheese.' is unobjectionable as well. Since a clear cutoff point cannot be specified, it is tempting to resort to the three dots. We argue that the argument from the lack of a clear cutoff point to infinity is a bad argument; the set of English sentences may be a fuzzy set rather than a standard set. We also argue that the initial question suppresses several quite distinct questions. A theory constructed to account for formal relations between sentences might warrant the positing of infinite semantic structures. A theory constructed to account for human understanding probably would not. Furthermore the common claim that infinity is necessary if there are to be novel and creative uses of language is found to be entirely without substance.