Source : Rapport de jury de l'agrégation externe de philosophie 2016 , présenté par Paul Mathias, Inspecteur Général de l'Education Nationale , page 15
https://philosophie.ac-versailles.fr/IMG/pdf/rj-2016-agregation-externe-philo_661733.pdf
Note: in case you're interested, in the French Educational System, " Agrégation" is a competitive exam aiming at selecting future high school teachers ( and granting those who succeed with a theoretical right to teach as assistant-professors at University).
I think you will concede that the wording of this philosophy paper is astonishing ( which is far from being by tself a bad point).
In fact, it seems even hard to state clearly what is in question here.
What I'm asking myself, in order to elucidate the philosophical importance and even the meaning of this paper is :
(1) what reason do we have to doubt as to what is the object of reflection? in what measure is this controversial? what difference would it make if we could identify such an object? what is at stake in this paper? is there any " hidden" alternative ( an " either ... or ") behind this subject?
(2) which great philosophical author has attempted to answer this question? in particular, is this question only understandable in the context of German Idealism or of Phenomenology?
(3) has any author ever negated the existence of an " object of reflection" or of an object deserving the title of " the object of reflection"?
(4) has this question been debated in recent philosophical literature? ( I found this by Tylor Burge : https://philosophy.ucla.edu/wp-content/uploads/2016/08/Burge-Reflection.pdf)
My thoughts on this subject :
(1) The object of reflexion is the self; however the self is not an object but a subject. Hence an "aporia"!
(2) Phenomenological approach : the object of reflexion is neither the thinking subject nor things as things , but things as intented by consciousness, the " noema" or " intentional object", or the relation between the mind and its objects.
(3) Sartrian approach : the object of reflection is not the Self but the Ego, a genuine object that is posited by second order consciousness; the reflexivity of consciousness should not be confused with reflection and does not turn the Self into an object ( https://plato.stanford.edu/entries/self-consciousness-phenomenological/)
(4) The object of reflection is .... reflection itself!
(5) Leibnizian approach : there is a threat of infinite regress here ! there is always a thought that is not yet captured by reflection, namely, the act of reflection!
(5) Hegelian approach : the object of reflection is the Subject- Object, the Absolute
(6) Medieval approach : the object of reflection is not real being ( ens reale) , but being of reason (ens rationis) , for example when I say that " man is a species" ( cf. Chauvin Lexicon philosophicum, " reflexio mentis" , second case : https://www.iliesi.cnr.it/Lessici/page.php) , or " this tree is the object of my perception" ( this relation of " being perceived" being nothing for the tree itself).