I take Wittgenstein to be saying at 5.63 that the seeing eye is not in the visual field. I can of course see my eyes via a mirror. But these are seen eyes, not seeing eyes. The eyes I see in the mirror are objects of visual consciousness; they are not what do the seeing.
That is not to say that the eyes I see in my visual field, whether the eyes of another person or my own eyes seen in a mirror, are dead eyes or non-functioning eyes. They are living eyes functioning as they should, supplied with blood, properly connected via the neural pathways to the visual cortex, etc. The point is that they are not seeing eyes, subjects of visual consciousness.
If you insist that seeing eyes are indeed objects of outer perception and empirical study, then I will challenge you to show me where the seeing occurs in the eye or where in the entire visual apparatus, which includes eyeglasses, contact lenses, the neural pathways leading from the optic nerve to the visual cortex -- the whole system which serves as the causal basis of vision. Where is the seeing? In the pupil? In the retina? In the optic nerve? Somewhere between the optic nerve and the brain? In the visual cortex?Where exactly? Will you say that it is in no particular place but in the whole system? But this is a very big system including as it does such instruments of vision as sunglasses and night goggles. And let's not leave out the external physical things that are causing certain wavelengths of light to impinge on the eye. And the light itself, and its source whether natural or artificial. Will you tell me that the SEEING is spread out in space over and through all of these items? But then how do you explain the unity of visual consciousness over time or at a time? And how do you explain the intentionality of visual consciousness? Does it make any sense to say that a state of the eyeball is of or about anything? If you say that the SEEING is in the eye or in the brain, then I will demand to know its electro-chemical properties.
I could go on, but perhaps you get the point: the seeing, the visual consciousness-of, is not itself seen or see-able. It is not an object of actual or possible experience. It is not in the world. It is not a part of the eye, or a state of the eye, or a property of the eye or a relation in which the eye stands or an activity of the eye. The same goes for the whole visual system. And yet there is seeing. There is visual consciousness, consciousness of visual objects.
Who or what does the seeing? What is the subject of visual consciousness? Should we posit a self or I or ego that uses the eye as an instrument of vision, so that it is the I that sees and not the eye? No one will say that his eyeglasses do the seeing when he sees something. No one says, "My eyeglasses saw a beautiful sunset last night." We no more say that than we say, "My optic nerve registered a beautiful sunset last night," or "My visual cortex saw a beautiful sunset last night."* We say, "I saw a beautiful sunset last night."
But then who or what is this I? It is no more in the world than the seeing eye is in the visual field. Wittgenstein's little balloon above depicts the visual field. Imagine a Big Balloon that depicts the 'consciousness field,' the totality of objects of consciousness. It does not matter if we think of it as a totality of facts or a totality of things. The I is not in it any more than the eye qua seeing is in the visual field.
So far I am agreeing with Wittgenstein. There is a subject, but it is not in the world. So it is somewhat appropriate to call it a metaphysical subject, although 'transcendental subject' would be a better choice of terms, especially since Wittgenstein says that it is the limit of the world. 'Transcendental' is here being used in roughly the Kantian way. 'Transcendental' does not mean transcendent in the phenomenological sense deriving from Husserl, nor does it mean transcendent in the absolute sense of classical metaphysics as when we say that God is a transcendent being. (That is why you should never say that God is a transcendental being.)
But Wittgenstein also maintains that the transcendental subject is the limit of the world. This implies, first, that it is not nothing, and second, that it is no thing or fact in the world. "The world is all that is the case." (1) "The world is the totality of facts, not of things." (1.1) It follows that the subject is not a thing or fact outside the world. So all the self can be is the limit of the world.
We have to distinguish the world from worldly things/facts. The world is a totality of things or facts, and a totality is distinct from its members both distributively and collectively. So we shouldn't conflate the world-as-totality with its membership (the world taken in extension). So if the metaphysical or rather transcendental subject is the limit of the world as per 5.632, then what this means is that the subject is the limit of worldly things/facts, and as such is the world-as-totality.
This is why Wittgenstein says "I am my world." (5.63)
I take it that Tractatus 5.63 is the central inspiration behind Butchvarov's solution to the Paradox of Antirealism which, in an earlier entry, I formulated as follows:
PA: On the one hand, we cannot know the world as it is in itself, but only the world as it is for us, as it is “shaped by our cognitive faculties, our senses and our concepts.” (189) This Kantian insight implies a certain “humanization of metaphysics.” (7) On the other hand, knowable physical reality cannot depend for its existence or intelligibility on beings that are miniscule parts of this reality. The whole world of space-time-matter cannot depend on certain of its fauna. (7)
The world cannot depend on me if I am a (proper) part of the world. But if "I am my world," then the problem would seem to dissolve. That, very roughly, is Butchvarov's solution.
The solution implies that the philosophical as opposed to the ordinary indexical uses of the first-person singular pronoun, those uses that figure into the Augustinian Si fallor sum, the Cartesian Cogito ergo sum, the Kantian Das 'ich denke' muss alle meine Vortsellungen begleiten koennen, the Cartesian Meditations of Husserl, and the debate about realism and antirealism are really impersonal, despite what Augustine, Descartes, Kant, and Husserl think. For then the philosophical uses of 'I' refer to the world-as-totality and not to a person or to something at the metaphysical core of a person such as a noumenal self.
This notion that the philosophical uses of the personal pronoun 'I' are really impersonal is highly problematic, a point I will come back to.
*People do say things like: "My brain said, 'Stay away from her,' but my little head said, 'Go for it, man!'" Such talk is of course nonsense if taken literally.