This system went in the direction of a dynamic relativisation of these antitheses. Here too of course, modern mathematics provided them with a model. The systems it influenced (in particular that of Leibniz) view the irrationality of the given world as a challenge. And in fact, for mathematics the irrationality of a given content only serves as a stimulus to modify and reinterpret the formal system with whose aid correlations had been established hitherto so that what had at first sight appeared as a given'content, now appeared to have been created. Thus actuality was resolved into necessity. This view of reality does indeed represent a great advance on the dogmatic period(of holy mathematics) But it must not be overlooked that mathematics was working with a concept of the rational specially adapted to its own needs and homogeneous with them(and mediated by this concept it employed a similarly adapted notion of actuality, of existence). Certainly, the local irrationality of the conceptual content is to be found here too: but from the outset it is designed- by the method chosen and the nature of its axioms-to spring from as pure a position as possible and hence to be capable of being relativised. [15 But this implies the discovery of a methodological model and not of the method itself. It is evident that the irrationality of existence(both as a totality and as theultimate material substratum underlying the forms), the irrationality of matter is qualitatively different from the irrationality of what we can call with Maimon, intelligible matter. Naturally this could not prevent philosophers from following the mathematical method(of construction, production and trying to press even this matter into its forms. But it must never be forgotten that the uninterrupted'creation'of content has a quite different meaning in reference to the material base of existence from what it involves in the world of mathematics which is a wholly comprehending the facts, whereas for mathematics creation and the possibility of ehension are identical. Of all the representatives of classical pl it was ficht his middle period who saw this problem most clearly and gave it the most satisfactory formulation. What is at issue, he says, is "the absolute projection of an object of the origin of which no account can be given with the result that the space between projection and thing projected is dark and void, I expressed it somewhat scholastically but, as I believe, very appropriately, as the projectio per hiatum irrationalem"[16 Only with this problematic does it become possible to comprehend the parting of the ways in modern philosophy and with it the chief stages in its evolution. This doctrine of the irrational leaves behind it the era of philosophical'dogmatismor-to put it in terms of social history -the age in which the bourgeois class naively equated its own forms of thought, the forms in which it saw the world in accordance with its own existence in society, with reality and with existen The unconditional recognition of this problem, the renouncing of attempts to solve it leads directly to the various theories centring on the notion of fiction. It leads to the rejection of every'metaphysics'(in the sense of ontology)and also to positing as the aim of philosophy the understanding of the phenomena of isolated, highly specialised areas by means of abstract rational special systems, perfectly adapted to them and without making the attempt to achieve a unified mastery of the whole realm of the knowable. (Indeed any such attempt is dismissed as unscientific) Some schools make this renunciation explicitly(e.g. Mach Avenarius Poincare, Vaihinger, etc )while in many others it is disguised. But it must not be forgotten that-as was demonstrated at the end of Section I -the origin of the special sciences with their complete independence of one another both in method and subject matter entails the recognition that this problem is insoluble. And the fact that these sciences are exact is dueThis system went in the direction of a dynamic relativisation of these antitheses. Here too, of course, modern mathematics provided them with a model. The systems it influenced (in particular that of Leibniz) view the irrationality of the given world as a challenge. And in fact, for mathematics the irrationality of a given content only serves as a stimulus to modify and reinterpret the formal system with whose aid correlations had been established hitherto, so that what had at first sight appeared as a ‘given’ content, now appeared to have been ‘created’. Thus actuality was resolved into necessity. This view of reality does indeed represent a great advance on the dogmatic period (of ‘holy mathematics’). But it must not be overlooked that mathematics was working with a concept of the irrational specially adapted to its own needs and homogeneous with them (and mediated by this concept it employed a similarly adapted notion of actuality, of existence). Certainly, the local irrationality of the conceptual content is to be found here too: but from the outset it is designed – by the method chosen and the nature of its axioms – to spring from as pure a position as possible and hence to be capable of being relativised. [15] But this implies the discovery of a methodological model and not of the method itself. It is evident that the irrationality of existence (both as a totality and as the ‘ultimate’ material substratum underlying the forms), the irrationality of matter is qualitatively different from the irrationality of what we can call with Maimon, intelligible matter. Naturally this could not prevent philosophers from following the mathematical method (of construction, production) and trying to press even this matter into its forms. But it must never be forgotten that the uninterrupted ‘creation’ of content has a quite different meaning in reference to the material base of existence from what it involves in the world of mathematics which is a wholly constructed world. For the philosophers ‘creation’ means only the possibility of rationally comprehending the facts, whereas for mathematics ‘creation’ and the possibility of comprehension are identical. Of all the representatives of classical philosophy it was Fichte in his middle period who saw this problem most clearly and gave it the most satisfactory formulation. What is at issue, he says, is “the absolute projection of an object of the origin of which no account can be given with the result that the space between projection and thing projected is dark and void; I expressed it somewhat scholastically but, as I believe, very appropriately, as the projectio per hiatum irrationalem”. [16] Only with this problematic does it become possible to comprehend the parting of the ways in modern philosophy and with it the chief stages in its evolution. This doctrine of the irrational leaves behind it the era of philosophical ‘dogmatism’ or – to put it in terms of social history – the age in which the bourgeois class naïvely equated its own forms of thought, the forms in which it saw the world in accordance with its own existence in society, with reality and with existence as such. The unconditional recognition of this problem, the renouncing of attempts to solve it leads directly to the various theories centring on the notion of fiction. It leads to the rejection of every ‘metaphysics’ (in the sense of ontology) and also to positing as the aim of philosophy the understanding of the phenomena of isolated, highly specialised areas by means of abstract rational special systems, perfectly adapted to them and without making the attempt to achieve a unified mastery of the whole realm of the knowable. (Indeed any such attempt is dismissed as ‘unscientific’) Some schools make this renunciation explicitly (e.g. Mach Avenarius, Poincare, Vaihinger, etc.) while in many others it is disguised. But it must not be forgotten that – as was demonstrated at the end of Section I – the origin of the special sciences with their complete independence of one another both in method and subject matter entails the recognition that this problem is insoluble. And the fact that these sciences are ‘exact’ is due