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peak experiences, cultural objectivities, justice, mathematical objects, emptily intending,

When we add 2+3, we can see, as it were, with our mind's eye that it equals 5.  Very elaborate proofs, however, cannot be seen to be valid as a whole.  In other words, no single one glance of the "mind's eye" will confirm that the argument as a whole is valid.  Or rather, it is not presently humanly possible, but anyone who asserts that it is valid is likely to imagine a Herculean mind (to steal from Dworkin) that could see all at once the validity of such arguments.  To put it in the language of phenomenology, we "emptily intend" this sort of fulfillment even though it is presently practically unattainable.

Might this sort of empty intending be relevant to our concept of justice?

Consider the following analogy:  knowing the right way to interact with friends and family is comparable to apprehending the validity of the simple equation (2+3=5) just as knowing how strangers in society are to interact is comparable to knowing that an extremely complex argument is valid.  Just as A is to B, so is C to D (where A=friends and family; B=simple equation; C=strangers; D=complex argument).

This seems a bit convoluted, but I think I'm onto something.  After all, it seems plausible that the concept of justice both presuppose and be ordered toward fulfillment (phenomenological pun intended) in friendship and family.  Beliefs regarding justice seems to involve reference to how the whole fits together (not in a neat, deductive manner, however), and seeing how they do fit together would be like a Herculean mind grasping the truth of an exceedingly complex argument.

Justice is to be conceived of as being just as concrete as how my family functions well.  That is, the justice in question, by the way, is not a Platonic ideal: rather, it's how my society works or functions well.  It's a cultural object that is not quite a thing, but is commonly apprehended by all.

More on this later on...

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