Derrida did not have access to the signifier Creal (Créel in French) therefore he could not do better than distinguish two types of Real. Here his real as non-negative inpossible is a formulation of the Creal, while the objective and dicretizable real is what should be called the Real. This Derrida quote is taken from the excellent chapter by Pheng Cheah in the collective book New Materialisms.
Philosophy stands to gain in finding some absolute in the moving world of phenomena. But we shall gain also in our feeling of greater joy and strength. Greater joy because the reality invented before our eyes will give each one of us, unceasingly, certain of the satisfactions which art at rare intervals procures for the privileged; it will reveal to us, beyond the fixity and monotony which our senses, hypnotized by our constant needs, at first perceived in it, ever-recurring novelty, the moving originality of things. But above all we shall have greater strength, for we shall feel we are participating, creators of ourselves, in the great work of creation which is the origin of all things and which goes on before our eyes. By getting hold of itself, our faculty for acting will be intensified. Humbled heretofore in an attitude of obedience, slaves of certain vaguely-felt natural necessities, we shall once more stand erect, masters associated with a greater Master. […]. In this speculation on the relation between the possible and the real, let us guard against seeing a simple game. It can be a preparation for the art of living (2007, p. 86).
Bergson, Henri (2007). The Creative Mind. Translated by Andison, Mabelle. New York, NY: Dover.
Analytic intelligence, while useful for purposes of manipulation and operationality, often ends up mistaking the abstract object for the concrete in a “fallacy of misplaced concreteness” (Whitehead). Out of habit or cognitive bias, we tend to believe that the parts, units, or functions that we distinguish and name are truly there in the real world, like cogs in a machine rather than metaphors. If we take the example of mental health diagnoses, such as bipolarity, depression, or attention deficit hyperactivity disorder, the fallacy of misplaced concreteness pushes individuals to consider these diagnoses as describing their essential identity or inner nature. Seeing their soul as a psychiatric object rather than a site of self-possibility, these individuals are led to believe that other objects such as pills, via the mechanical law of causality, can regulate their being in the world.