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Additional resources for Analytic Properties of Feynman Diagrams in Quantum Field Theory
I use the Guyer and Wood (1997) translation of the Critique of Pure Reason, where (A) refers as usual to the pagination of the first edition (1781) of the Critique and (B) to the second edition (1787). e. 30 Hence, the transcendental principles of pure understanding (Kant’s Analogies of Experience) – linked as they are to the metaphysical principles of pure natural science – can be regarded as constitutive with respect to experience because they make possible an empirical causal law (the law of universal gravitation), which qua empirical is based on inductively generalized phenomena, while qua law must have an a priori grounding, namely the one warranted by the transcendental principles.
Hans Reichenbach’s conclusion was that the notion of a priori needed to be reconsidered in such a way that a Kantian kernel could be retained without the allure of non-revisability. 18 According to Reichenbach, the recent scientific developments had revoked the first meaning, but not the second. This was particularly evident in the case of what Reichenbach called axioms of coordination. They are nonempirical (and then non-synthetic) principles that coordinate the mathematical part of a scientific theory with the physical part of the theory.
Retrospective rationality can be argued for by looking at the way the new framework embeds the old one as an approximate limiting case. So Euclidean geometry can be regarded as a limiting case of Riemannian manifolds, and Newtonian space-time can be retrieved from special relativity if the velocity of light goes to infinity. Prospective 20 Friedman (2001), p. 88. , p. 92. 3 From Reichenbach to Friedman 17 rationality is more difficult to grasp. How can it be rational for practitioners of an earlier framework to move to a new one with a possibly different mathematical formalism and brand new constitutive principles that may well appear unintelligible and meaningless to them?