This is a study of Frege's permutation argument in Part I, Section 10, of Frege's Basic Laws of Arithmetic.

It is a commonplace that Frege thought ordinary language to be seriously defective. Yet his remarks about ordinary language are not always unflattering. Comparing the relation between his formal language and ordinary language to the relation between the microscope and the eye, Frege remarked: ‘[the eye], because of the range of its applicability and because of the ease with which it can adapt itself to the most varied circumstances, has a great superiority over the microscope’. The point, of course, is (...) that, for Frege, the deficiencies of ordinary language arise in connection with the scientific endeavour: ordinary language is not an acceptable medium in which to pursue truth. As he goes on to observe: ‘… viewed as an optical instrument [the eye] reveals many imperfections … as soon as scientific purposes place strong requirements upon sharpness of resolution, the eye proves to be inadequate. On the other hand, the microscope is perfectly suited for just such purposes’. (shrink)

SOME PHILOSOPHERS (NOTABLY RICHARD SWINBURNE AND NINIAN SMART) HAVE ARGUED THAT WHILE THERE IS A LOGICAL POSSIBILITY OF A MIRACLE OCCURRING, THERE COULD NOT BE A REPEATABLE MIRACLE. I DISCUSS VARIOUS INTERPRETATIONS OF THIS CLAIM AND ARGUE THAT THERE IS NO INTERESTING SENSE IN WHICH IT IS TRUE.