The Sheffer stroke or NAND operation is a single logical connective which is functionally complete, meaning that all the other propositional connectives can be derived from it. It is thus an affirmation which contains negation (a|a being equivalent to not-a), and is a symmetric operation (a|b is indistinguishable from b|a) from which the asymmetric 'entails' operation can be derived, ((a|a)|(a|b) being equivalent to a->b). Doesn't it then, in the small world of propositional logic, do exactly what a concept like intentionality seeks to do for the unbounded world of experience? In the larger case you can't really prove it works, because there's always the you doing or validating the proving, and which somehow lies outside the what that is being demonstrated. But the idea of a single act, or class of acts, which constitutes the all, is an attractive one. You might prefer to call it purpose, or purposiveness, but the example of the happily named stroke is a telling one. Certain characteristics seem essential. For example, that it is binary, or relational, that it can take itself as one of its terms, that it has alternative forms (such as the Pierce arrow) and that for all its autonomy it requires bracketing, or an ordering which witnesses the sequence of the events of its application. So, accepting this in a general way, you can see that the infinite complexity of the world, including your own place in it (which appears as fundamental asymmetry) could be generated out of some simple, but not intuitive relation, one which does not pretend to be self-referential. If you search for the self-reference that you are certain is there then this structure obligingly folds over on itself, growing more complex and displacing your goal yet further. For whatever it is that witnesses all this - that places the brackets, as it were - there is only a play of symmetry and hence no question of self-reference, or of the 'real' existence of the subject.