Theories of Abstraction

Anthony Mansueto has done original and very valuable work on the philosophy of religion, and he has done this while linking his reflection to social and historical questions normally avoided by academics.

In the essay “Once Again on the Religious Question” ( ) Mansueto restates and explains the essence of his theses also published in a book titled “Religion and Dialectics” ( )

Anthony Mansueto’s website ( ) is also an excellent source to understand this author’s contributions.

What I find particularly appealing is Mansueto’s re-take of the classical (Aristotelian and Thomistic) theories of knowledge and abstraction, and the reframing of the concept of abstraction in the context of a critique of commodity exchange societies. The author correctly underlines the fact that a “teleological” –i.e. purposive—natural order is already implicit in human labour. Following from that, he shows how an atheistic worldview could become an obstacle to human development because it robs societies from meaning.

I think that Mansueto is still attached to a “modern” understanding of social “evolution,” focusing exclusively on the notions of “progress” and “development” as if these were ahistorical forces (which he derives from universal laws of physics). Nevertheless, despite this attachment to a key aspect of Liberalism, he is right in discarding the unilateral and technocratic notion of abstraction arising from empirical commodity exchange. He rightly sees this metaphysics of abstraction as a mainstay of the modern lack of meaning in society and as the root of nihilism. Thanks to Mansueto we can explore a variety of theories of abstraction.

Mansueto is not correct when he  criticises Marx for the limitations of his analysis of the act of production. He writes: “What is missing here is a recognition that the act of production is itself already an intellectual act. It involves both an understanding of the latent potential,  of the raw material, whether this is physical, biological, or social in nature, and some aim or purpose. Already in the productive act itself we are compelled to think teleologically –to reflect on the possibilities and purposes.” The problem is that this is already Marx’s  stance in Das Kapital (see: Chapter XV, “Machinery and Modern Industry”); hence, any critique of Marx must proceed in a different direction: pointing not that Marx neglected the purposive nature of production, but that the German philosopher considered human labour to be “autotelic” i.e. self-purposive and not contained or predetermined by an ideal human nature. This would  be a better Ansatz to understand the limitations and errors of the Marxian theories, especially regarding the relationship between a relative (immediate) teleology of human activity and an absolute teleology of “nature” or the “universe.”

Because Marx rejects an Absolute teleology (a stance which Mansueto identifies as Atheism) and because he retains only the relative value of human nature as constituted by contingent social relations, his original project of a chain of ever-ascending “modes of production” becomes incoherent. As his work progressed, Marx clearly became less and less focused on any predictions about the future of human societies and began to admit that there was no unidirectional movement of history (see for example his letters on the rural communities in Russia).

Mansueto’s desire to reinstate an absolute direction of history is valuable because of its motivation ( the recovery of social meaning) but it should not lead to another error: forgetting the necessary relativeness and particularity of any human actions, the discontinuity between individuals and the separation between these and their instruments and products.

Instead of this, any useful sociology should admit both relative and absolute purposes (at various levels of aggregation from the individual “upwards” to the local, regional, national and international levels). It is precisely then –when considering this chain of indirect causation, of interlocking purposive actions—when we come to see the importance of Mansueto’s renewal of the concept of abstraction. This renewal is based on a re-introduction of Aristotelian philosophy, in a manner especially useful for a theory of abstraction:

“What we are proposing is, in fact, a revision of the classical Aristotelian-Thomistic theory of knowledge (Aristotle, “De Anima,” Aquinas, “Summa Theologiae”). According to this view, knowledge begins with the external senses, which gather data from the environment. The internal senses then form these data into images which are illuminated by something called the “Agent Intellect,” which abstracts something at least of the intelligible nature of the object which is then received by the potential intellect. Thomas and the Dominican commentators speak of various degrees of abstraction: the abstractio totalis, which abstracts the logical whole from the parts and the abstractio formalis which abstracts the form of a thing from its matter. The abstractio formalis is further distinguished into the abstractio totius, which abstracts from individualizing matter to the essence of a thing, the abstractio formae which grasps the underlying structure of the object arriving at, for example, a mathematical formalisms, and the separatio, which separates the being of a thing from its essence and this makes it possible to rise to knowledge of Being itself, to the transcendental principles of value, and thus God.”

Mansueto explains:

Totalization is fundamentally a matter of classification. Thus we are able to abstract from a visual image of Fido the increasingly higher order taxa dog, carnivore, mammal, vertebrate, animal, living thing, etc. This is something which depends only on participation in social taxa, i.e. in definite social groups which are distinct from other groups and which are grouped together in nested hierarchies—something which sociologists since Durkheim have attested even among the simplest hunter-gatherer societies. Formalization on the other hand, which begins by attempting to rationalize taxonomies and which ends by developing complex mathematical or structuralist formalisms appears only in societies which have a significant market sector and becomes the epistemological ideal only in societies characterized by generalized commodity production.”

With this approach, Mansueto allows us to see that these two fundamental types of abstraction are counter-posed movements or directions of human understanding and rationality: one arising from the natural person and going towards the physical interaction with the world, and another ultimately rooted in the fragmented social world and “forgetful” of the original and final cause of action (the personal context). Formalization, then, comes second in human history, but ultimately rearranges our world by “displacing” or “covering” the original totalizing abstraction. Mansueto proposes the useful idea of “super-abstraction” as the unity of both processes. This is not far from the notion of a complete articulation of the “modalities” of Person, Subject, Agent and Object.

In this structure, totalizing abstraction can be seen as movement from the Person to the the Subject, and from the Object to the Agent, while formalising abstraction appears as a retrograde movement from the Subject towards the Person and from the Agent to the Object, as shown in the diagram below.