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In Max Muller's translation of the Critique of Pure Reason, Kant states, in "Transcendental exposition of the concept of space", that:

Space must originally be an intuition; for from a mere concept it is impossible to obtain propositions which go beyond the concept, such as we do, however, be encountered in us a priori, that is prior to any perception of an object, and must therefore be pure, not empirical, intuition.

I understand the reasoning behind why space is a pure and not an empirical intuition. However, I do not understand why Kant wrote that space must be an intuition and not a concept; is it not possible to obtain synthetic a priori propositions which go beyond the concept as argued in Part V of Introduction B? Or does the process of obtaining a proposition, in this context, differ from what had been mentioned in the introduction?

Disclaimer: I am a high school student attempting to understand Kant's Critique of Pure Reason, supported by my independent research, so I may misconstrue some of Kant's ideas and I apologize for that. If possible, please try to tailor your responses to a reader with a weaker background and poorer grasp of philosophical concepts. If I come across as a dilettante, I am sorry for wasting your time in reading the post.

John123
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  • It's been a long time since I've read Critique of Pure Reason, but didn't Kant argue that concepts can only lead to analytical truths, truths which are already present within the concept? – David Gudeman Oct 22 '22 at 16:12
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    Kant's What Does It Mean to Orient Oneself in Thinking? may be helpful here. https://assets.cambridge.org/97811071/49595/excerpt/9781107149595_excerpt.pdf – DJohnson Oct 22 '22 at 18:35
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    In Kant's time logic was understood in a very narrow way, as Aristotelian syllogistic. Propositions that one could derive from concepts in that fragment of logic were the trivial ones that reshuffle definitions. Since geometric propositions clearly go beyond that (e.g. theorems about triangles say much more beyond their definition as three points connected by three segments) they had to draw on something else, the intuitions, see Friedman, Kant's theory of geometry. In modern geometry the intuitions are replaced by extra axioms and stronger logic. – Conifold Oct 23 '22 at 04:51
  • @DavidGudeman I thought that Kant argued that synthetic a priori knowledge is possible? Was it not Hume who argued that concepts can only lead to analytical truths as he argued that only a posteriori knowledge can be synthetic? My main point of confusion is whether geometry is synthetic a priori knowledge, and how it relates to intuition (which I thought refers to the immediate process in which we immediately obtain knowledge from an object?) – John123 Oct 25 '22 at 00:30
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    Yes, Kant argued that synthetic a priori knowledge is possible. What I vaguely recall is that he said that such knowledge requires intuitions and that concepts alone do not lead to such knowledge. Don't take my word for it though, because I'm not sure I recall that detail correctly. It was just a hint for further research. – David Gudeman Oct 25 '22 at 00:50
  • @Conifold, the axioms do not replace intuitions; they represent intuitions. – David Gudeman Oct 25 '22 at 00:51

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