In his “A Preface to Metaphysics,” (Fourth Lecture, section 10) Jacques Maritain writes:
“I have already spoken of the most important distinction which the ancient drew between abstractio totalis, which I will call extensive visualisation, and abstractio formalis, which I will call intensive or characterising and typifying visualisation. At first intellectual visualisation is as yet only extensive. That is to say its object is not explicitly the type or essence abstracted by and for itself, in Platonic terminology the supertemporal form in which objects partake. No doubt the essence is there, but contained in the notion after a fashion wholly implicit or blind as it were hinted, not such that thought can employ or handle it. What the intellect expresses to itself and explicitly visualises is simply an object of thought which, as the logician will say when he reflects upon it, is more or less general. Contact has been made with the intelligible order, the order of the universal in general but nothing more. The first step has been taken by which we leave the world of sensible experience and enter the intellectual world.
“This should be followed by a further step, by which we make contact with the order of the universal type and essential intelligibility and the typical form is explicitly abstracted and laid bare. This step is the abstractio formalis, intensive or typifying visualisation by which the mind separates from the contingent and material data the essence of an object of knowledge that which formally constitutes it. this intensive or typifying visualisation is the beginning of scientific knowledge, knowledge in the strict sense.” (Source: Jacques Maritain, “A Preface to Metaphysics – Seven lectures on being” – Sheed & Ward, London, 1945, first published in 1939, page 75)
This should also support the argument in favour of a duality in the human abstraction capacity, which leads –similarly—to extensive and intensive abstraction. In common discussions, “abstraction” is erroneously taken as equivalent to the extensive kind. This skews the discussion in favour of the “concrete” but isolated fact, i.e. “intensive abstraction.” Further reading of Maritain’s treatise is recommended to show how this approach is rooted in classic philosophical thinking.
In a different work, Maritain develops the same idea as follows:
“Now it is by means of an abstraction that we are able to reflect on the nature of philosophy in itself. This abstraction is not a mere fiction. Nor is it what the ancients termed abstractio totalis, that abstraction of the genus from the species, of the logical whole from its parts, which as they very well knew, is prescientific. It is what they called abstractio formalis, that is the drawing out of what is intelligible in reality, or of the complex of formal notes from the things which are, as it were, their bearers. This abstractio formalis is, to my mind, at the base of all scientific work. Thanks to it the mathematician is able to speak of ensembles, the metaphysician, of consciousness and mind; and thanks to it we are here able to speak of philosophy. Turning our gaze from existential conditions it lifts it to the order of essences; it posits a possible before our thought; in sum, it disregards the state to ponder the nature.” (“An Essay on Christian Philosophy,” Section II.4 “Nature and State”)
A precision is important here-despite the clarity of Maritain’s text: while scientific reasoning requires intensive abstraction, it nevertheless presupposes extensive abstractions and cannot operate outside of these. So we should not imagine scientific or philosophical thought that does not articulate and in fact oscillate between one and the other modality of abstraction.