While Bachelard’s Rationalisme appliqué can readily be translated as Applied Rationalism, neither the French nor the English are very revealing of the position being advocated. In particular one would be led very far astray if one were to think of rationalism as a philosophical position which suggests that knowledge can be logically deduced from first principles that are either immediate and self-evident, or reached by analysis, and then to think that Bachelard is talking about how to apply such rationally grounded theoretical knowledge. This is not at all the perspective from which he approaches scientific knowledge.
First, as the beginning of the translated passage indicates, Bachelard is concerned with the processes by which scientific knowledge is acquired. His position is a form of rationalism in the sense that reason has a dominant role here; scientific knowledge is both rationally organized and rationally grounded in experience, and both of these features emerge from the way in which it is acquired. It is not first proposed as theory and then tested empirically (as a Popperian would suggest); the role Bachelard assigns to reason is one of empirical engagement. Applied rationalism is thus an account of empirically (materially) engaged reasoning, not of theoretical reasoning subsequently applied. His position can be hard to grasp because it represents a quite radical departure from philosophical norms, particularly those that analytic philosophy inherited from the logical positivists. He transgresses divisions that others have taken as absolute givens, such as that between abstract and concrete when he talks of the concrete universal.
He is already talking about what Latour would later call the world of hybrids, the material world informed by modern science and technology. This is both the world of industrial mass production and its products and the world of the scientific laboratory where the study of phenomena is heavily mediated by instruments. As Bachelard says, modern science has passed from the phenomenology of nature studies to the phenomeno-technique of the laboratory.1
Second, Bachelard equates reason, reasoning or deduction not with logic but with the development and deployment of mathematics in organizing both thought and experimental practices. It goes without saying that he rejects logicist and formalist views of mathematics. So in a sense he is talking about science as applied mathematics.
1. For more on this theme, see Mary Tiles, ‘Technology, Science and Inexact Knowledge: Bachelard’s Non-Cartesian Epistemology’, in Gary Gutting, ed.,Continental Philosophy of Science, Blackwell, Oxford, 2005, pp.157–75; Mary Tiles, ‘Is Historical Epistemology Part of the Modernist Settlement?’,Erkenntnis, vol. 75, no. 3,2011, pp. 525–43.