 Now trouble for Hume’s Principle begins to arise when we recognize that it is a contextual definition that has the same logical form as this definition for directions. It is central to Frege’s view that the numbers are objects, and so he believes that it is incumbent upon him to say which objects they are. But the ‘Julius Caesar problem’ is that Hume’s Principle, if considered as the sole principle offering identity conditions for numbers, doesn’t describe the conditions under which an arbitrary object, say Julius Caesar, is or is not to be identified with the number of planets. That is, Hume’s Principle doesn’t define the condition ‘\(\#F = x\)’, for arbitrary \(x\). It only offers identity conditions when \(x\) is an object known to be a cardinal number (for then \(x = \#G\), for some \(G\), and Hume’s Principle tells us when \(\#F = \#G\)).