(_b_) The principles which are said to be _necessary_ or _logical_ ‘_presuppositions_’ all turn out to be hypothetical when they are examined. They are needed, no doubt, to solve the problem in hand, _if_ the particular way it is formulated is taken for granted. But if either the order or the formulation of problems is altered, they cease to be either ‘necessary’ or ‘presuppositions’. For example, the ‘axiom of parallels’, _alias_ ‘Euclid’s postulate’, is a necessary presupposition of geometry, if the existence of parallels is assumed. But if we prefer it, we can just as well (with Aristotle) make it our axiomatic ‘presupposition’ that the interior angles of a triangle are equal to two right angles, and can then deduce the existence of parallels. I.e. Euclid might have deduced what he assumed, and assumed what he deduced. If, moreover, we do not desire to construct a Euclidean geometry at all, we can deny _both_ presuppositions, and proceed from _alternative_ postulates, which lead to the various metageometries. The only things, in short, which all scientific principles presuppose are the desire to construct a science, and the desire to construct it in a particular way, which is simplest, or easiest, or most systematic, or most in accordance with the reigning prejudices. But these desires are the very things which the logician’s account of principles always omits to mention. Again, the whole of Kant’s scheme of _a priori_ presuppositions in the theory of knowledge rests upon an arbitrary assumption, viz. that mental data are to be conceived as originally discrete and are therefore in need of ‘synthesis’. But it is just as possible to conceive an analysis of knowledge which starts from the ‘presupposition’ of a continuum or flux, and proceeds to trace out the principles by means of which this continuum is broken up into a world of apparently distinct things and processes. Nor is it possible to say in advance of experience which of such ‘presuppositions’ is going to be more convenient and more conducive to scientific progress.