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I'm sorry if this question has been asked before.

My question regards the apparent double nature of the term 'a priori' in Kant's Critique of pure reason. Namely, as a presupposition for experience and also as independent of experience.

On one hand, in the Transcendental aesthetics, Kant consideres space and time as pure - a priori - intuitions, i.e. they're presupposed for the possibility of experience in general. In other words, experience as a whole would not be possible without them (space and time).

On the other hand, Kant uses the expression to describe a certain type of judgments, particularly, Synthetic a priori judgments. These judgments are characterised as independent of experience. The best examples of this kind of judgments are the ones we found in Euclidean geometry, which are not modifiable by experience, and hence not up to empirical verification, but they're not derivative of concepts either.

Is the difference between this two considerations of the same term a legitimate interpretation? I ask because with the advent of non Euclidean geometries and the Theory of relativity, we know that the Synthetic a priori judgments present in classical (Newtonian) mechanics and Euclidean geometries work only in those frames of references. The status of space and time as a priori intuitions however would still remain valid in any geometry or physical model. Would that be a correct assessment in your view? I can't seem to find any contradiction between those two statements. What do you think?

Many thanks!

  • If something is a presupposition of experience then it is independent of it, so you distinction is not very clear. But it sounds like Kant's distinction between constitutive (presupposition) and regulative (imposition) use of a priori, see SEP. However, to Kant space and time are themselves synthetic a priori, and his framework can not accomodate non-Euclidean geometries, it was relativized by subsequent neo-Kantians for this purpose. E.g. Minkowsky geometry is constitutive of special relativity, but is revised in general – Conifold Mar 9 at 4:50
  • Thank you very much for your answer. I guess i could reformulate my question as follows: can we satisfactorily maintain the status of space and time as pure intuitions, even for non Euclidean geometries or for nonclassical physics? – kt3217 Mar 9 at 5:13
  • No, our intuitive apparatus is very restricted. We do not have non-Euclidean 3D intuitions (at least not Minkowskian ones), or even Euclidean 4D ones, relativity of time is also highly unintuitive. We can only keep them as constitutive, as is done in SR, QM and QFT. In GR and quantum gravity projects they are discarded even as such. To keep geometric intuition in play we have to map some projections of theoretical manifolds analytically onto 2D or 3D models that we can intuit, but that is far from "pure". – Conifold Mar 9 at 5:27
  • A priority is defined as "necessary and universal", which fits both characterisations. Mind, a priori means 'from the start', which means that you can presuppose it as a given independently from arbitrary events and experience exactly because it is as necessary and universal a given in any case. Space and time are justified as forms of human sensory experience, nothing more, nothing less. And humans have to experience from within a non-relative perspective (i.e. for a person, relativity cannot be immediately experienced, only "from without" via instruments and deductions). – Philip Klöcking Mar 9 at 6:05
  • So, one could say that space and time are sort of the indispensable building blocks of all possible experience, while the a priori judgements present in Euclidean geometry maintain their status as long as we consider them 'from within'? – kt3217 Mar 10 at 3:49

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