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Because the truth of axioms and the validity of basic rules of inference cannot themselves be established by inference since inference presupposes them or by observation which can never establish necessary truths they may be held to be objects of intuition.
The objects of intuition for Spinoza are particular essences, not particular people.
Why does Spinoza insist that the objects of intuition are essences and not particular, singular things?
With Bolzano, the status of axioms changes: instead of being evident, objects of intuition, they become the starting points of proofs in a deductive theory.
In the Transcendental Analytic, Kant deduces the table of twelve categories, or pure concepts of the understanding, the first six of which he describes as "mathematical" (as opposed to "dynamical") categories because of their concern with objects of intuition (B110).
Schopenhauer's fundamental departure from Kant is already suggested in this passage: "We have immediate cognition of the thing in itself when it appears to us as our own body; but our cognition is only indirect when the thing in itself is objectified in other objects of intuition" (WWR, §6, pp. 40 1).
Similar(53)
To the extent that physics is linked to the transcendent world of objective reality, it cannot arise as the direct object of intuition, but must, like the transcendent world itself, be presented in symbolic form; more exactly, as the result of a process of symbolic construction.
Although this Western spirit is prerequisite to daily conduct, it fails to grasp the ultimate reality, which, in Suzuki's philosophy, is an object of intuition or experience rather than of logical inquiry and must therefore be approached by religious experience of nonduality, especially as it is expressed in the tradition of Zen Buddhism.
When Croce sees essence as the object of intuition and identifies this with expression he is just imposing his prior philosophical speculations on aesthetic experience.
Phenomenologists identified the object of intuition as the essences of things, and in so doing sought to overcome the Kantian noumenon/phenomenon dichotomy as well as the errors of positivism and nominalism.
So suppose that space is not a property of objects independent of intuition in any sense—hence it does not even supervene on properties of objects that are independent of intuition (recall that for Leibniz, space supervenes on the monadic order because objects and relations supervene on that order).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com