Sentence:  I only know myself as a human entity; the scene, so to speak, of thoughts and affections; and am sensible of a certain <WSD>doubleness</WSD> by which I can stand as remote from myself as from another. However intense my experience, I am conscious of the presence and criticism of a part of me, which, as it were, is not a part of me, but spectator, sharing no experience, but taking note of it; 
Meaning of the word marked with <WSD> tags:  The state of being double or doubled.