Frege introduced the distinction between sense and reference to account for the information conveyed by identity statements. We can put the point like this: if the meaning of a term is exhausted by what it stands for, then how can 'a =a' and 'a =b' differ in meaning? Yet it seems they do, for someone who understands all the terms involved would not necessarily judge that a =b even though they judged that a =a. It seems that 'a =b' just says something more than the trivial ’a = a' - it seems to contain more information, in some sense of 'information'. So either we have to add something to explain this extra information, or sever the very plausible links between meaning and understanding. This is what some writers have called 'Frege's Puzzle' It is undeniable that there is a phenomenon here to be explained, and it was Frege's insight to see the need for its explanation. But how should we explain it? Frege's idea was to add another semantic notion - Sinn, or Sense -— to account for the information conveyed. Sense is part of the meaning of an expression: it is the 'cognitive value' of the expression, or that ’wherein the mode of presentation is contained' (Frege 1957 p.57). Sense has a role to play in systematically determining the meanings of complex expressions, and ultimately in fixing the contents of judgements. It is the senses of whole sentences — Gedanken or Thoughts - which are candidates for truth and falsehood, and which are thus the objects of our propositional attitudes. Of course, introducing the notion of sense in this way does not, by itself, tell us what sense is. It only imposes a condition on a theory of meaning (and ultimately) belief: that it must account for distinctions in cognitive value or 'mode of presentation' (this is not a trivial thesis —- some philosophers today would deny that an explanation of Frege's Puzzle must occur within semantics or the theory of meaning: see Salmon 1985). In this paper I want to explore one way of meeting this condition for the theory of names in natural language, by examining Kripke's well-known 'Puzzle about Belief' (Kripke 1979)..