valid is what we call a connecting premise. We have had to add connecting premises in many of the arguments we have so far considered. Usually, when people give arguments, the premises they give explicitly will be only those which pertain to the particular facts or sub-ject-matter they are talking about. For example, someone might say 'My cat won't have kittens; she's been spayed'. The arguer explicitly sets forth the relevant fact about her particular cat, but doesn't bother to state explicitly the generalisation she assumes, that spayed cats can't have kittens. Probably she assumes this to be common knowledge; if she did not, then she would have made the premise explicit. The point then is that arguers very often leave implicit the more general assumptions they make. That is what happened in the inflation case and the politician case discussed earlier.

You can see why we call these premises 'connecting premises'. Typically an arguer informs us of some proposition, as support for another proposition. The connecting premise is what connects them. It enables the arguer to get from one to the other. But the arguer doesn't bother to spell it out, because they assume that their audience will understand what assumption is being made.

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