The notion of reflexivity (i.e., to self-referentiality) or, the more closely related notion, self-reflexivity.
We can start off by saying that a reflexive relation is something that certain things can have to themselves. Or, alternatively, literally everything has the reflexive relation of self-identity .(If this is a genuine relation, or, indeed, a genuine property.) Stones are seen, by some, to be self-identical; though they are seen by no one as being self-reflexive. The self-identity reflexive relation (though not the self-reflexive relation) is something everything has to itself.
The self-identity reflexive relation or property, for example, is sometimes called a “strongly reflexive” relation. A “weakly reflective” relation is, on the other hand, sometimes stated as “everything has it to itself that has it to anything”.
We can have beliefs about our beliefs, thoughts about our thoughts, and so on.
A thought about a thought is not self-referential or self-reflexive. It's not the thought itself that refers to or thinks about itself (or even the content of the thought that does so): it's the person who has the thought who thinks about his own thought. The thinker himself is self-reflexive, not the thought itself. The thought is not self-referentially related to itself either. It’s just that the thought itself is thought about. Again, it's the owner of the thought (so to speak) who is self-reflexive (about his thought). The thought (or thoughts) about the thought can therefore be called second-order thoughts. Again, the base thought (as it were) is neither self-referential nor self-reflexive. A thought could, of course, be self-referential; or at least its content could be. However, I don’t think that the thought (or a thought itself) can ever be self-reflexive. The possible self-referentiality of a thought’s content would not also be an example of self-reflexivity.
There is an example of self-reflexivity which is more closely related to examples of self-referentiality.
Once example is what takes place when the self/person analyses the (same) self/person. That is, when the subject and object of self-analysis can be said to be one and the same thing – i.e., the self that analyses is the (same) self that is analysed. Thus, in the light of what we've said about self-referential statements, we can now ask:
Can the self/person both have thoughts (about himself) and also be the object/subject of these thoughts?
This wouldn’t be like the putative property self-identity which was referred to in the last paragraph. (In which it was said that all objects are said, by some, to have the property of being identical to themselves.) There is no such strict identity when it comes to the self/person and the self’s thoughts about itself. On a traditional reading, thoughts about the self come and go; whereas the self’s substance stays put. Thus, on this reading at least, thoughts about the self are not identical to the self itself. And even if we don’t believe in selves as bare particulars, the thoughts about the self would still not be identical to the self the thoughts are about. This would even be the case if part of the self (at a particular point in time) included those thoughts about the self (that has such thoughts). In this instance, particular thoughts about the self can’t be identical to the self taken as a totality at any given time. There may, however, be a partial identity (at least if we accept the bundle theory of the self); though not complete identity (which is the case if we accept the property - or relation – self-identity).
To give a taster of self-reflexivity or possible self-referentiality, here are a few points that put obstacles in the way of such states.
We can ask:
How can a human subject take himself to be the subject of study; as Descartes famously claimed he did when sitting next to his fire?
Perhaps we can never actually get to the essence (or totality or complete truth) of ourselves because it's precisely the same self that's trying to get to the essence, etc. of itself. It is, therefore, attempting to be both subject and object. (In a Cartesian manner, if we can’t discover our own “true essence of mind”, how can we even begin to discover the true nature of external reality?) According to many philosophers, it's a Cartesian myth that we can objectively “perceive” our own minds or states of consciousness. It's not a fact, then, that the mind (or the items within it) are “transparent” to the self-analysing mind itself. Perhaps we can never get to every item or working within our own minds. Perhaps we can't, specifically, recognise that it has been “conditioned” to, say, believe certain things or see particular things in certain ways. To put it bluntly, if it's the self that is analysing the (same) self (or the self that's analysing itself), then the “unseen” conditionings, workings, non-transparent items, etc., of the self (as object) would also be the conditionings, workings, non-transparent items, etc. of the self that's doing the (self) analysis. It could therefore only be a self which is split into two (quite literally) which could be both subject and object at one and the same time. Though then we can simply say that after such a split we will no longer be talking about two selves, encamped within the same mind-brain: not one self that's split in two. And if that were the case, then there would be no authentic self-reflexivity and certainly no self-referentiality.