This last remark leads me to a further consideration.  Science and Philosophy are alike created by the simple determination to be thorough in our thinking about the problems which all things and events present to us, to use no terms whose meaning is ambiguous, to assert no propositions as true until we are satisfied that they are either directly apprehended as true, or strictly deducible from other propositions which are thus apprehended.  But now that the area of facts open to our exploration has become far too vast for a modern Francis Bacon to ‘take all knowledge for his province’, and convenience has led to the distinction between the philosopher and the man of science, a practical distinction between the two makes its appearance.  It is convenient that our knowledge of detail should be steadily extended by considering the consequences which follow from a given set of postulates without waiting for the solution of the more strictly philosophical questions whether our postulates have been reduced to the simplest and most unambiguous expression, whether the list might not be curtailed by showing that some of its members which have been accepted on their own merits can be deduced from the rest, or again enlarged by the express addition of principles which we have all along been using without any actual formulation of them.  The point may be illustrated by considering the set of ‘postulates’ explicitly made in the geometry of Euclid.  We cannot be said to have made geometry thoroughly scientific until we know whether the traditional list of postulates is complete, whether some of the traditional postulates might not be capable of demonstration, and whether geometry as a science would be destroyed by the denial of one or more of the postulates.  But it would be very undesirable to suspend examination of the consequences which follow from the Euclidean postulates until we have answered all these questions.  Even in pure mathematics one has, in the first instance, to proceed tentatively, to venture on the work of drawing inferences from what seem to be plausible postulates before one can pass a verdict on the merits of the postulates themselves.  The consequence of this tentative character of our inquiries is that, so far as there is a difference between Philosophy and Science at all, it is a difference in thoroughness.  The more philosophic a man’s mind is, the less ready will he be to let an assertion pass without examination as obviously true.  Thus Euclid makes a famous assumption—­the ’parallel-postulate’—­which amounts to the assertion that if three of the angles of a rectilinear quadrilateral are right angles, the fourth will be a right angle.  The mathematicians of the eighteenth and early nineteenth centuries, again, generally assumed that if a function is continuous it can always be differentiated.  A comparatively unphilosophical mind may let such plausible assertions pass unexamined, but a more philosophical mind will