Some Thoughts on the Ideal of Exactness in Science and Philosophy

Abstract

The ideal of exactness occupies a peculiar place amid other requirements that one may lay down for intellectual work. Any attempt at assessing this place will have to struggle with the diversity of ways in which the label ‘exact’ has been used. Moreover, this distinctive label is mostly felt to endow whatever it is stuck upon with a special lofty appeal. In what to my knowledge is the only systematic study of the spectrum of its meanings, the adjective is called a “‘psychological’ monster”, which evokes at once a feeling of rigor and purity, and thus appears to legitimize any claim that is made in the name of exactness [König 1966]. Even opponents of one type of exactness might usurp the label for their own purposes, as when Goethe contrasted his idea of an “exakte sinnliche Phantasie” with the so-called exact sciences. The power of this word comes close to that of certain other terms in our modern vocabulary, such as ‘freedom’ and ‘rationality’, which are equally iridescent in their meaning, and which express ideals that also relate in peculiar ways to other values. As concerns rationality, especially scientific rationality, one may note here that exactness is often regarded as one of its ingredients.¹ In our intellectual history, each one of the three terms has frequently been employed to mark a new beginning, a purging of the mind or life from traditions considered obscurantist or stifling.