I'm having trouble seeing your point in the context of the rest of the discussion. Tyrrell claimed that the pre-theoretic notion of an infinite set - more charitably, perhaps, the notion of an infinite cardinality - is captured by Dedekind's formal definition. Here, "capture" presumably means something like "behaves sufficiently similarly so as to preserve the most basic intuitive properties of." Your response appears to be that there is a good metaphorical analysis of infinitude that accounts for this pre-theoretic usage as well as some others simultaneously. And by "accounts for X," I take it you mean something like "acts as a cognitive equivalent, i.e., is the actual subject of mental computation when we think about X." What is this supposed to show? Does anyone really maintain that human brains are actually processing terms like "bijection" when they think intuitively about infinity?