AbstractWhat can be inferred from the fact that something is, or is not, conceivable? In this paper I argue, contrary to some deflationary remarks in recent literature, that arguments which use such facts as their starting point may have significant philosophical import. I use Strawson's results from the first chapter ofIndividualsin order to show that Galileo's arguments in favour of the distinction between primary and secondary qualities, which are based on premises concerning conceivability, should not be dismissed: they are the first step towards recognising an important conceptual truth.