This paper raises some doubts about the claim that, on mastering a finite vocabulary and a finitely stated set of rules, we are prepared to produce and understand any of a potential infinitude of sentences. First, it is observed that it is not all that clear what it means to say that people are prepared to understand any of a potential infinitude of sentences. Second, doubts are raised about the assumption that understanding a sentence must be a matter of figuring out its meaning from an antecedent knowledge of the meanings of words.
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