Space,time and extension is the central problem of modern science.The distinction between primary and secondary qualities constitutes the fundamental metaphysical belief of modern scientific founders such as Galileo and Descartes.By solving the problem of Geometrization,Galileo and Descartes intended to an-swer the question how mathematics,in particular geometry,can apply to a mathematized natural world.The solution explains the truthfulness of our knowledge of natural world by attributing such primary quali-ty as spatial extension to natural body,and interprets the similarity of the structure between our represen-tation and natural things based on the representational realism,so as to explain the truthfulness of human external knowledge in terms of correspondence theory.According to Kant,Galileo and Descartes'solving the problem of Geometrization to lay the founda-tion of science is unsuccessful.Kant puts forth the thesis of the non-spatiality of thing-in-itself(called Ts),i.e.,space doesn't represent any determinations of thing-in-itself.Space is only the intuitive form of our outer sense,and thing-in-itself are non-spatiality.Kant needs to rebuild the foundation of modern sci-ence.Because according to Ts,extension is not the property of natural body,but the property of mind,though Kant remains regarding extension as primary qualities,and mathematics as the science of studying extension.However,according to Ts,the conclusions studying extension from mathematics only applica-ble to bodies in our mind,not to natural bodies in the world.Hence,explain the nature of extension is the key task for Kant to build the foundations of modern science.Only in this way can Critique of Pure Reason succeed in its efforts to establish a foundation for science by addressing the question of how synthetic a pri-ori propositions are possible.Kant's accounts of spatiality bases on his doctrine of substance and attribute,and correlate to his doctrine of light(or ether).Kant regards spatiality as the predicable attribute of sub-stance,which is produced by interacting non-locality between substances.According to Kant,extension in not a property abstract from experience,while its occurrence on our outer sense receiving the effect from ether(ether is the medium to propagate the information from thing-in-itself to our outer sense organs)to attain the matter of spatial representation.The ether proofs in Opus postumum indicate that Kant uses lo-cal causality to explain how ether propagate the information from thing-in-itself.Kant's explanation on spatiality is the strange mixture of local causality and non-local causality.This leads to Kant's failure in trying to rebuild foundations for modern science because he can neither solve the problem of Geometriza-tion,nor answer how scientific theory can describe the world.He also falls into dualism and agnosticism.Kantian doctrine of space implies that mechanism basing on local causality must be given up and the foun-dations of science should be rebuilt based on topology and basing on non-local causality.
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