In his Commentary on the Parmenides, Proclus criticized Aristotle’s epistemological theory of abstraction. Aristotle had, in On the Soul (De Anima), briefly described how all knowledge must be derived from the abstraction of intelligible forms from sensible objects. He writes:
“Since it seems that there is nothing outside and separate in existence from sensible spatial magnitudes, the objects of thought are in the sensible forms, viz. both the abstract objects and all the states and affections of sensible things. Hence no one can learn or understand anything in the absence of sense, and when the mind is actively aware of anything it is necessarily aware of it along with an image; for images are like sensuous contents except in that they contain no matter.” (De Anima 432a3)
Abstraction is thus rendered as a mental process whereby the active intellect ‘abstracts’ or separates off a representative form from some sensible object by subtracting the individuating matter from the more common intelligible form. The critical function of subtracting individuating matter into a more universal form was previously described as a dialectical ascent towards knowledge (noesis) the Ideas in Plato’s Phaedo (78b-79d). But where Plato’s dialectical ascent, from material individuals to immaterial Ideas, had involved a discursive process of hypotheses and refutations, Aristotle’s abstraction seems to have naturalized this discursive dialectic into an innate and non-discursive intellective faculty: it is no longer a process of hypothetical thought but an innate power of the agent intellect. Once abstraction has been naturalized, then it is possible to subordinate the old Platonic dialectic of Ideas to the new knowledge of perception, induction, and understanding. Aristotle thus makes abstraction the foundation of his theory of induction in the Prior Analytics:
[I]t is impossible to consider universals except through induction (since even in the case of what are called abstractions one will be able to make familiar through induction that some things belong to each genus even if they are not separable, in so far as each thing is such and such), and it is impossible to get an induction without perception – for of particulars there is perception; for it is not possible to get understanding of them; for it is neither from universals without induction nor through induction without perception. (Prior Analytics 18, 81b1-10)
How, then, are the representative images meant to be abstracted from sensible objects and transmitted to the active intellect? Aristotle left to posterity the task of elaborating how the representative form is meant to be abstracted from sensible objects and transmitted to the active intellect. His most authoritative commentator, Alexander of Aphrodisias, described how universal forms (i.e. genera) are “constructed [syntithenai] by a separation in thought [te-iepinoiai cho-rismos] of the other things which exist along with them” (Quaestio 79, 17–18, cf. Riin Sirkel 2011) Hence, the intelligible forms are meant to be transmitted from substances and intellect, by first subtracting the matter from the form; then transmitting the form from the substance to the intellect; and finally by duplicating the form in the intellect. It seems that, in the absence of discursive dialectic, both the mechanics of subtraction and transmission remain opaque, even in Alexander’s more developed theory of abstraction.
In response to the Forms as Thoughts argument of Plato’s Parmenides (132b-c), Proclus launches into a fiery criticism of the entire Peripatetic tradition of abstraction epistemology. In order to reassert the primacy of the One over the many, souls over perception, and Forms over matter, Proclus seeks to reduce to absurdity the possibility that the intelligible forms, or Ideas, can be abstracted, constructed, and – in any sense – derived from sensible substances alone. He first distinguishes the originary and paradigmatic Platonic Forms, or Ideas, from the ‘later-born’ forms that Alexander had purported to construct through abstraction:
“This ‘later-born’ entity, then, which is called a “thought” is obviously different from the reason-principle in the real sense. For the “later-born” is a dimmer entity that the many, inasmuch as it arises from them and is not prior to them, whereas the real reason-principle is more perfect than they. Whence the former is less substantial than the many particulars, whereas the latter is more substantial, and inexpressibly more perfect than the objects of sense.” (253/892, All page citations are taken from the Murrow and Dillon trans.)
Proclus then proceeds to argue that the soul may not “derive these common properties from the objects of sense themselves” because the objects of sense, or impressions are distinct from the objects of opinion that are ‘derived from sense-object’: since impressions are in sensible objects, opinions are in the intellect, and sensible objects are distinct from the intellect, the impressions of sensible objects must remain distinct from the opinions of the intellect. Abstraction theory stipulates, however, that the abstract intelligible forms may be transmitted over and between this distinction between sensible impressions and intellective opinions. What motivates this transmission of intelligible forms? If the sensible objects do not innately possess forms, then Proclus can conclude that the power to motivate the transmission of intelligible forms cannot arise from “any other source than the soul itself”:
“And it does not derive these common properties from the objects of sense themselves; for that which is derived from sense-objects is an impression (phantasma) and not an object of opinion, and must remain the same, when taken within, as when it was originally apprehended, in order that I may not become false or “non-existent”, but it may not become anything more perfect or noble; nor is it produced from any other source than the soul itself.” (253-2540/893)
Proclus then asks how souls may “produce these general notions” without the Forms, or “reason-principle of things”. He denies that the soul may “derive these common properties from the objects of sense themselves” because, as he has previously distinguished, the ‘general notions’ that are meant to be constructed from impressions are not opinions but must “remain the same” as nothing more than abstract perceptions, impressions, or phantasms, of the perceptible:
“Further, if Matter possesses the common element in the many individual entities in its essential state, and is thus essence more truly than individuals (for it is eternal, while each of them is such to destruction, and takes its individuality from it; for it is through the form in it that each thing participates in essence), while the Soul possesses only the ‘later-born’ common properties, how can we avoid making the Soul of lesser account than Matter, if the form residing in Matter is more perfect and more of an essence than that in the Soul? For this latter is what is most properly termed ‘later-born’, while the former is eternal; and the latter arises from the many particulars, while the former is the principle of coherence for the many, and so the latter is an offspring of the former.” (254/893)
Proclus then offers an indirect argument against abstraction: if matter were an element common to all individuals, and the individua could be destroyed while their common element of matter endured, then matter would be construed as the absolute essence of all things while all individual determinations would be construed as perishable accidents. Since matter would then be essentially prior to the all of the individual determinations that are abstracted into the ‘later-born’ properties of by the soul, matter would be rendered superior to souls. But Proclus protests: “how can we avoid making the Soul of lesser account than Matter, if the form residing in Matter is more perfect and more of an essence than that in the Soul?” Proclus considers this to be an absurd conclusion because he believes that matter impotent to generate and transmit intelligible forms to souls. Hence, even if it were - per impossibile – supposed that matter were essentially prior to souls, then matter could not be known by souls through the transmission of any intelligible forms.
“Furthermore, the general concept in the many is narrower in range than each of them; for each of the individual entities is amplified by additions and accidental accretions, and the ‘later-born’ concept comprehends each of the many; for which reason it serves as a predicate for each of these, and the individual is in any one of the general concepts as a whole; for this common quality is predicated not only of the general concept mentioned above, but of every individual subject as a whole. How, then, could it be composed from that source, and out of the common quality in the many?” (254/894)
Proclus’ most decisive argument seems to be that, since the abstract intelligible forms are always ‘narrower in range’ merely one among many particular predicates, and no collection of predicates is sufficient to compose a whole individual, then any collection of abstract intelligible forms of predicates requires some ‘additional accretion’ to constitute an individual. This seems to be an early example of the problem of individuation: how are many predicate-properties united in one individual subject? Aristotle had proposed matter as the individuating ground of all predicate-properties. But once Proclus has, in the previous argument, rejected matter as an ultimately individuating ground, the Aristotelians are compelled to find some further source of individuation (e.g. Scotus’ Haecceity) Each of the general concepts abstracted is a predicate of the individual entities. But since each abstracted predicate is ‘narrower’ and does not contain all of the added accidental accretions of the individual entity, it seems that no individual entity could ever be known by knowing all of its predicates. However, the theory of abstraction purports to uncover the common concepts that are abstracted from the individual entities. But since the subject term of the individual entities cannot be known, it seems that neither can the abstraction of the common concepts from the individual entities ever be known.
“For if on the one hand it arises out of the many themselves, where are we to see that infinite number of men, to all of which we apply the same predicate? Or if it arises out of the common quality in the many, how can this be more comprehensive than its own cause? It must therefore take its origin from somewhere else, and receive from some other source this power of comprehending each form. Of this source, indeed, it is an image, coming into existence in a way contrary to what one would expect, by virtue of reminiscence, on the basis of sense-objects, of the causal principle aroused within us.” (254/894)
Proclus then asks how it is possible for one general concept ‘arise’ from many individuals or many qualities if its cause is no ‘more comprehensive’ than the indeterminacy of matter. Since all of these alternatives involves contradictions of one from many, Proclus concludes that the general concepts of abstraction must originate from “some other source” which is the “power of comprehending each form” through the Intellect.
“I would go so far as to add this, that every proof is made on the basis of concepts prior and more august and more universal than itself… how then can the universal concept be worthy of honour, if it is ‘later-born’? For in ‘later-born’ entities the more universal a concept is, the less substance it has; which leads to the species having more substance than the genus. Our rules about the truest type of proof would then have to be abandoned, if we lay down that only ‘later-born’ universals reside in soul; for these are certainly not more powerful than, nor causative of, nor prior in nature to, more particular concepts.” (255/ 894)
Proclus concludes that “every proof is made on the basis of concepts prior and more august and more universal than itself”, i.e. than the concepts abstracted premises and supposits of the proof. Hence, the subordination of soul to matter must compel us to abandon the ‘truest type of proof’, i.e. dialectic through division, definition, and demonstration. The absurdity of abstraction from matter implies that we must accept that essential reason-principles are prior to ‘later-born’ concepts that are abstracted by the soul from material individuals.
“If these results are absurd, it must then follow that prior to the ‘later-born’ concepts there exist essential reason-principles, which are always present and active in the divine souls and those of the classes of being superior to us, but which in us are sometimes obscured and sometimes operative, and that sometimes on the theoretical level only and sometimes on the providential level, when we, in union with the gods, take a hand in administering the whole world (cf. Phaedr. 246c2).” (255/ 894)
For a further criticism of Aristotle's abstraction of numbers, see my commentary on Metaphysics XIII 6-8: