Subject-object problem

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From Wikipedia: In philosophy, the subject-object problem arises out of the metaphysics of Hegel. Hegel's metaphysics distinguishes between subjects, roughly, observers; and objects, what is observed. Hegel attached deep significance to these statuses; subjects were active, internal, socially participant, gifted with cognition and will. Objects were passive, external, acted upon but never really internalized by the subjects. According to Hegel, the original philosopher of dialectics, the subject and object become thesis and antithesis, which according to his views unite in a new synthesis. Full article

The problem also has implications in modern issues in maths and physics.