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I have previously wrote of the abstract as that which is the common in the multitude. It is a product of the intellect, an intelligible object that derives from whatever can be traced in the world and as a logical extension of it. This view of mine is not actually my own. I first came across it, or at least a version of it, in Plato’s Meno. In that opus a discussion takes place between Meno and Socrates concerning the definition of a certain concept: virtue. As the dialogue unfolds Meno provides several examples of what virtue could be, to which Socrates replies that he is only describing instances of virtue not virtue as such. With clarity and succinctness, Socrates states thus:
Socrates: Would you say “virtue,” Meno, or “a virtue”?
Meno: What do you mean?
Socrates: I mean as I might say about anything; that a round, for example, is “a figure” and not simply “figure,” and I should adopt this mode of speaking, because there are other figures.
Socrates then proceeds to explain that the qualification he makes is one that distinguishes between instances and the common among them, the simile in multis. The abstract can be partially found in [each of] the particularities, while [each of] the particularities are not wholly encompassed by the abstract. To employ the example I often use,
fruit is the common in the multitude of an array of objects that have properties peculiar to it while exhibiting their own characteristics which render them discernible from other classes and elements of
The concepts of
orange etc. are subsets of
fruit or, if we change the direction,
fruit is the higher order abstraction that derives from the study of the patterns present in
orange are themselves abstract, only the scope of their “simile in multis” is narrower than
fruit. This apple is different from that apple, this variety from that and so on. The properties germane to
apple, those essential factors of its discernibility, are not found in
orange and, by that token, cannot be elevated to the status of properties of
Furthermore and to be clear, none has ever tasted
apple but only an apple. No one eats
fruit as such, but only objects that can, with a certain level of abstraction, be understood as belonging to that very set. This, by the way, is a position that is positively influenced by Heraclitus’ theory of universal flux. Yet it digresses from that view in perceiving of intelligible objects as capable of enjoying constancy. The very fact that we can rationally refer to ever-changing objects or to change as such in a manner that can be constant in itself may be suggestive of the need to draw delineations between perceptible and intelligible objects and, moreover, to concede the possibility of each magnitude of our reality having features exclusive to it.
Like Plato, I am of the opinion that objects of abstraction, thoughts in general, do “exist”. Unlike him though, I qualify such existence as simply noetic, neither ontic nor transcendent (also see, among others, Reflections on ontic and noetic presences, Descriptive and synthetic arrays as well as Implicit properties in objects). Where Plato’s position on the metaphysics of abstraction is alluded to, the issue of the status of mathematics will inevitably be brought up. Though we bear no delusions of hereby putting an end to a dispute that has divided thinkers through the millennia, we may express a modest opinion. As I agree with the words of Thomas Colignatus, I quote him below:
When we regard mathematics as abstracting from the world, then the root lies in the world, and then it should not be surprising that the result may apply to some phenomena in that world. There is neither need for some Platonic view in which concepts “exist” as “ideas” in some magical realm outside of physics, for we are merely speaking about abstraction. Just to be sure: abstraction is defined as leaving out other aspects. Abstraction is nothing special but the mere ability of the brain to select some aspects of some mental model and drop (most) other aspects of it. That mental model will relate to empirical phenomena or sensations that the brain experiences.
Thus the “common in the multitude” appears as a reasonable view on abstraction. The “multitude” is at first found in the perceptible realm and, second, in the patterns that are traced in it. There can be abstractions of abstractions such in the aforementioned case of
fruit. The starting point remains the world.
Thank you for reading!