Version: v2, Published online: 2022

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## 3. Transcendental method and critical idealism

Cohen introduced the expression ‘transcendental method’ to characterize the approach required by the Kantian theory of experience (Cohen 1885: 66). In Cohen’s interpretation, Kant had discovered a new concept of experience that is given in Newtonian science rather than in some experienced things. The transcendental method investigates the conditions that make a priori possible and objectively valid what Cohen, borrowing Trendelenburg’s expression, called ‘the fact of science’. This corresponds to the way of proceeding adopted by Kant in the *Prolegomena* and called by him ‘analytic’: starting from the fact that synthetic a priori judgements are given in mathematics and in the mathematical science of nature, one should be able to derive the grounds for their possibility in pure reason by regressive analysis. Kant’s procedure, however, was meant to provide an introduction to the critique of reason. Cohen relied on the transcendental method to set aside what he considered to be a remainder of a naturalistic approach in Kant’s theory of the faculties of the mind. As a counterpart of this move, Cohen emphasized the historical standpoint of the inquiry. Science is presented in printed books, and the transcendental task is to investigate the grounds for the universality and necessity that is being attributed to it.

Cohen made original use of the transcendental method in *Das Princip der Infinitesimal-Methode und seine Geschichte* [The Principle of the Infinitesimal Method and its History], from 1883. Cohen emphasized the role of infinitesimally small quantities as a necessary presupposition for the determination of movement, and identified the concept of differential as the ultimate constituent of reality. In this connection, Cohen called critical idealism the view according to which the fundamental concepts of the mathematical science of nature produce the objects of experience. Over the next two decades, Cohen worked at a further development of this view into a comprehensive system investigating the origins of reality in pure thought, that of ethical ideals in pure will, and that of the object of aesthetic judgement in pure feeling (Cohen 1902; 1904; 1912).

Not all Marburg neo-Kantians shared Cohen’s later views. Nevertheless, they subscribed to the transcendental method and to the basic tenets of critical idealism. Natorp’s work, after joining Cohen at Marburg in 1885, was mainly devoted to the reconstruction of the prehistory of critical idealism from Plato to the early modern period. Beginning in the 1890s, Natorp developed an account of knowledge inspired in part by Cohen’s interpretation of Kant, but also motivated by the need to account for the fact of modern mathematics, including the mathematical concept of limit and that of the non-Archimedean continuum made up by infinitesimal segments. Natorp’s studies resulted in the publication of his major epistemological work, *Die logischen Grundlagen der exakten Wissenschaften* [The Logical Foundations of the Exact Sciences], in 1910. The book outlines a system of syntheses of knowledge modelled on the relational systems of modern mathematical theories. Natorp emphasized that the determination of the object of knowledge is an infinite task, whereby the object itself is nothing but an unknown X. Natorp’s metaphor of the equation of knowledge marked a departure from Cohen’s view that reality originates in pure thought. Natorp took a different stance also on the question whether there can be a critical investigation of psychical processes in *Allgemeine Psychologie* [General Psychology], from 1912. Natorp’s view was that once the process of knowledge has been investigated in its objective direction, it should be possible to take the opposite direction in order to reconstruct the way in which the mind becomes conscious of sense qualities.

Cassirer’s early works (1902; 1906; 1907a; 1907b) made other important contributions to the study of key figures for the development of critical idealism, in particular Leibniz. Cassirer, on the other hand, went much deeper than both of his Marburg teachers in engaging with mathematical developments of central importance in the history of philosophy of science, including the arithmetization of analysis, the discovery of non-Euclidean geometries, the axiomatization of the theory of numbers, the rise of symbolic logic. Cassirer’s first major epistemological work, *Substance and Function* (1910), introduced a new powerful expression for the relational system of knowledge, by modelling the constitutive concepts of the sciences on the mathematical concept of function. Whereas Aristotelian logic derived universal concepts by abstracting away from all individualities, the mathematical concept of function offered a new account of concepts as universal laws determining all the individual cases that fall under them. The logic underlying this model of concept formation offers an account of mathematical objects as uniquely determined by their mutual relations, but also applies to the lawfulness of the phenomena in the natural sciences. Cassirer’s account was in contradiction with Cohen’s theory of the origin of reality in the concept of differential, but allowed him to defend a version of critical idealism that is in line with the structural turn of mathematics in the late nineteenth and early twentieth centuries.

Cassirer articulated his view further in the attempt to take into account the major conceptual changes of twentieth-century physics (Cassirer 1921; 1936). In this connection, he was one of the first to argue for a relativization of the Kantian a priori to preconditions of scientific research that are subject to change. Beginning in the 1920s, Cassirer also worked on the new philosophical project of a comprehensive study of the various symbolic forms expressing the relations of the Self to the world, including the natural sciences and the humanities, but also myth, art and religion. Cassirer’s philosophy of symbolic forms is clearly distinguished from the epistemology of Marburg neo-Kantianism. Nevertheless, Cassirer continued to rely on the transcendental method in his later epistemological works, and to defend critical idealism, presenting his pluralist perspective on objectivity as a further development of Natorp’s idea of a double direction of the transcendental inquiry (Cassirer 1929: 62). Cassirer sought to extend this approach in a number of directions corresponding to the different symbolic forms.

Biagioli, Francesca. Transcendental method and critical idealism. Neo-Kantianism, 2022, doi:10.4324/9780415249126-DC055-2. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/thematic/neo-kantianism/v-2/sections/transcendental-method-and-critical-idealism.

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