The classical distinction in philosophy between intensional and extensional statements is slightly misleading in the above context. Extensional refers to statements P about the world, or to propositions asserting the truth of such statements: 'P is true'. Intensional refers to statements of the form 'I propose that P is true'. Obviously, the latter is the subjectified version of the former, in which the subject is implicit. To the pre-subjective mind all propositions are extensional. To the subjective consciousness, on the contrary, all propositions are recognized as "intensional"-- as intentions of some mind that asserts them. All facts, in other words, are recognized as beliefs.
The extensional statement P is the formal equivalent of the awareness, experience or belief that P is the case. Furthermore, the notion that a proposition is either true or false (the Law of Excluded Middle) formalizes a fundamental fact of experience in the world. That P is either true or false is a formal abstraction of the apparent fact that an object either exists or doesn't. It is either present in awareness or not, and if it is not, it is still held to continue to exist unseen. The Law of Excluded Middle also reflects the basic cognitive decision mandate: the organism must evaluate stimuli in terms of their significance for its well-being. Specifically, it must decide to act or not in a given situation.
In the same sense that 'P is true' is a redundant version of P, the idea that 'Z is real' is a redundant version of the experience Z. In the same way that one cannot add to the truth of a statement merely by repeating it or insisting that it is true, to assert the reality of an experience is normally just to have the experience. This corresponds to the pre-subjective belief in the world-as-experienced. But just as we are suspicious of boasts of modesty, so we are doubtful of explicit claims of truthfulness. (The exception is the legal oath, since breach of the sworn oath constitutes a separately punishable offence.) Mind cannot add to its certainty by having the further experience that its experience is real. Rather, introducing such "meta" concepts raises an eyebrow, casts doubt on the experience when it is so bracketed. This doubt is the hallmark of subjective consciousness, reflected in formal statements as well as in normal speech. Adding "...is true" to a proposition simply acknowledges the possibility of falsehood. The "is true", like the "I propose that...", is taken for granted in our subjective culture since it is understood that any statement can be false. The possibility of falsehood places all statements, so to speak, in quotes. The formal expression of this skepticism is the notion of proof-in-a-formal-system, and is reflected in concepts of legal and scientific proof.
The occurrence of experience in subjective consciousness amounts to the proposition 'this object is not an object', where 'this object' refers to some element of experience as it is (pre-subjectively) apprehended to be part of the world. In other words, it is realized that this element of experience belongs not to the world but to the self. While we subjective moderns find no contradiction in this, we can imagine that pre-subjective man would have. It must, in fact, have been exactly this paradox-- of parts-of-the-world that are not parts of the world-- that led to the expansion of the human cognitive domain to include the subjective.
But when 'this object' refers to something in the subjective domain, the proposition becomes paradoxical even for us. For it then becomes equivalent to 'this experience is not a (true object of) experience' or 'this thought is not (actually) a thought'. The apparent absurdity of such statements led Descartes to found his philosophy on the seemingly irreducible primacy of experience. Must we not admit, however, that the numinous givenness of experience for the subjective mind could be as illusory as we hold that of the world to be for pre-subjective thought?
'This object is not an object' and 'this experience is not an experience' share with 'this statement is false' the fact of lacking a domain, meta to them, in which they can be judged as non-self-negating propositions of the form 'this statement is not provable in system X'. We accept the existence of objects-which-are-not-real precisely because we have the meta-domain of subjective experience in which to judge the reality of objects, just as we accept self-negating statements as non-paradoxical when they can be reformulated in terms of provability. Of the configurations of sensory experience, not all constitute external objects. The fact that there is a remainder is the basis of subjective consciousness. But is there a meta-meta-domain within which to decide the status of an experience-- not whether it is true or real, but whether it is a bona fide experience at all? The role and significance of conscious experience can be fully appreciated only when the domain from which it arises is brought into clear definition.
We have legitimized experience as a category yielding the very basis of a sense of self. One has experience, therefore one exists. This is the meaning of Descartes' cogito ergo sum. Then what else could it mean, to call into question the legitimacy of experience on this second level, than to judge and search experience-- not as evidence for something in the world-- but as evidence for a self? To be sure, the self remains unaffirmed by non-experience. But is it affirmed by experience? Philosophically we have been led, by the invalidity of some objects, to question the domain of objects in general-- that is, the reality of the world. In a similar manner, we might be led to question the validity of the subjective domain as the repository of a self.
The point of Descartes' argument is that, even if a given experience does not prove the existence of a real object, it does prove the existence of a subject. But is this actually so? The indisputable part of his assertion is this: while the content of experience may prove nothing about the world, the occurrence of the experience is unquestionable. But it is merely a tautology to say that if an experience exists, then it definitely exists. However, Descartes takes the further step of concluding that which he actually assumes in the first place: if experience occurs, then there must be a subject for that experience. Indeed, if we have defined experience as the artifact of a subject, then we are simply caught in circular reasoning.
Descartes' syllogism is popularly translated "I think therefore I am"-- which presupposes a subject for "thinking". It ought to read: "There are experiences, therefore I am". In an even purer form it could read: "The phenomenal world is inconsistent (giving rise to the concept of experience), therefore I exists". Either way, it is difficult to see how the conclusion follows from the premise. Rather, to conclude the existence of a subject from some facts of experience seems the same sort of mental act as to posit the existence of external objects on the basis of some facts of experience. In other words, the existence of the self parallels that of the world in that both are logical constructions. If objects are fictional, then so are subjects.
Descartes' reasoning may be illogical, but as a psychological process it may well describe how I concludes its own existence. And if I believes it is a subject for all experiences (in this field of consciousness), and an agent for all actions (of this body), then any such experience or action will be further proof to I of its own existence. This is on the same logical footing as the claim that every morning I make the sun rise, and every sunrise proves my omnipotence. According to Descartes, I exists even when the content of experience is illusory. But if I experience a dream, am I a real subject witnessing an illusion, or an illusory subject believing it is witnessing?
The ego normally arises as a kind of personal theory about the coherence of experience, an explanation for the consistent association of certain contents of consciousness. For example, the proprioceptive and tactile sensations of this hand in picking up the cup of coffee, the sensations of taste in the mouth, and of swallowing hot liquid in the throat, as well as the somatic effects of caffeine to follow, all constellate with visual sensations corresponding to hand, cup, etc., in an emerging sense of self or agency. I, as the passive witness and motor force behind this body, is how the brain makes sense of the association of these diverse inputs. The sense of I-ness may be a wonderfully pragmatic theory that normally works well in the evolutionary scheme. But is it true? Does the self really exist? There are wide variations of the "theory". There are people who believe they make the sun rise or control the weather. Some schizophrenics appropriate a fantastic range of sensory input to the self, believing themselves the focus and the orchestrator of great cosmic events. Other mental patients, and some mystics, completely lose the sense of self, facing a bewildering confusion of sensation with no unifying scheme to make sense of it. Most people's experience, of course, lies between these extremes. But normality does not establish truth. The fact that most people have a normal self, the subject of consistent and limited experience, does not make the self real. From the perspective of every spiritual tradition, entered deeply enough, the existence of ego is considered an illusion, the normal psychosis.