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The earlier post, Models of Integration of Science and Faith – Science and Christianity: Part 5/6, analyses different models for the relationship between of science and Christianity: conflict, independence, complementation, dialogue, integration and transformation. However, the absence of discussion on the epistemological foundations underlying the typology of models gives the impression that it is based on pragmatic and arbitrary criteria. What is missing is a philosophy of nature and metaphysics of knowledge to ensure that the process of integration is empirically well founded and logically coherent . The purpose of the present post on Jacques Maritain’s Three Degrees of Abstraction is to fill a lacuna found in the earlier discussion.
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Many scientists today assert that modern empirical science and the “scientific method” is the best, if not the final arbiter of any truth claim about the world and reality. The premise of this assertion is that physical reality is the only reality and all truth claims must be empirically verifiable.
However, metaphysics from Aristotle to Aquinas have always regarded physical reality to be only a sub-domain of a hierarchy of reality which comprises both the material and immaterial world. Corresponding to this hierarchy of reality is a hierarchy of degrees of knowledge which humans may explore by applying different degrees of intellectual abstraction, that is the process by which the intellect separates a universal concept of “form” from particular existing objects so that it grasps the essence of things.
Jacques Maritain, in his book Philosophy of Nature, defends the idea of the three degrees of abstraction as a foundational principle in epistemology and philosophy of science. This framework serves to distinguish different levels of intellectual cognition and refutes the claim that modern empirical-mathematical science possesses a superior epistemological status over traditional Aristotelian-Thomism metaphysics. Maritain’s project seeks to retrieve resources from Aristotelian-Thomistic philosophy, which maintains that different sciences function within distinct domains of reality, each with its own proper mode of knowledge or degrees of intellectual abstraction.
The Three Degrees of Abstraction
Jacques Maritain follows Aristotle and Aquinas by grounding human knowledge on three levels of abstraction, each corresponding to a particular domain of reality:
1) The First Degree of Abstraction: Physical Abstraction (Abstraction of the Thing)
The first degree, is that of physics which for Aristotle includes the philosophy of nature as well as the sciences of nature. In this first degree of abstraction, “the mind abstracts from singular or individual matter only, and the object which the mind presents to itself can neither exist without sensible matter nor be conceived without it; its notion includes material-sensible constituents. This object is being as subject to change: wherefore Aristotle said: “not to know motion is not to know nature.” (PN13)
This degree focuses on the physical, changing, and contingent aspects of reality. It abstracts individual particularities from material substances and their properties, such as motion, quantity, and quality by relying on both empirical observation and experimentation. In abstraction, the intellect processes the sensible species (representations or forms of objects perceived by the senses) and abstracts the intelligible species (the representations or forms understood by the intellect) which is the essence of the object using categories of substances (intrinsic essence and potentiality) and causality. Maritain writes, “But as long as we stay in this universe of the first order of abstraction, knowledge, however illumined it may be by the very intelligibility of being, however decanted it may be, remains held within the limits of sensible existence, of sensible mutability and its causes… Here the object of knowledge is being as mobile, being under the typical determination of mutability, being as imbued with mutability.” (PN27).
2) The Second Degree of Abstraction: Mathematical Abstraction (Abstraction of Quantity)
Here the mind abstracts from sensible matter, that is from matter as possessing active qualities perceivable by the senses. The object which the mind presents to itself at this degree is abstract quantity which cannot exist without matter but can be conceived without sensible matter; its notion does not include sensible matter.(PN13)
The second degree of abstraction does not rely on sensory input gained from empirical observation and experimentation. “At this degree of intelligibility no longer implies an intrinsic reference to the sensible, but to the imaginable…In this case we are dealing with an intelligible sphere which is not that of the sensible real.” (PN28) It enters a wholly other universe of intelligibility and abstracts from sensible, changeable matter abstract properties like quantity, shapes and geometric forms. Abstraction involves the application of mathematics and deductive reasoning in order to study the relationship between abstract entities.
Analysis of mathematical equations and modelling have been fruitful when applied to study physical reality, but for Maritain, such analysis does not, in itself, constitutes knowledge of being as such. For example, mathematical models of quantum mechanics and relativistic mechanics may be useful in describing and predicting physical interactions from atomic to cosmic structure. However, it does not address the deeper metaphysical questions about existence, essence and being. As such, it would be a mistake to elevate mathematical physics as the supreme form of knowledge because they still do not provide a fundamental or foundational account of reality.
Given the dominance of empirical-mathematical physics in the scientific enterprise today, it is worthwhile to take heed of Maritain’s observation about the danger of reducing reality to mathematical fundamentals.
“The mathematical sciences, being deductive and explanatory sciences draw the sensible real into their proper sphere in order to explain it and consequently to construct a system of explanatory reasons and causes which takes in all the sensible real and explains it, not by ontological causes and principles which are entia realia [real beings] of the intelligible order, but by mathematical beings of reason (entia rationis [entities of reason]) constructed for this purpose, due respect being given both to experimental and numerical data gathered in the world of nature and to rules of mathematical computation and systematization. So there is a constant coming and going from observed and measured real beings to mathematical beings of reason and vice versa. And the more the mathematical ensemble thus wrought becomes full, rigorous and able to explain a great number of phenomena with a small number of principles, the more perfect the explanation will be. It will be perfect but, to explain the sensible real, it will use mathematically constructed entities and the danger will be great, – not inescapable but great, – of mistaking these mathematically constructed entities, entia rationis with their foundation in reality, for ontological causes, for entia realia explaining the essence of the physical real…So what we have in this instance is a material and quantitative analysis of sensible nature which seeks to reconstruct phenomena in a closed world which is a substitute for first philosophy (the world of mathematicism, but of a merely methodological mathematicism which can but be taken erroneously for a properly ontological and philosophical mathematicism). Epiriometrical analysis tends toward this world of mathematicism as toward its asymptote and the danger is that, before arriving at ontology properly so-called, (philosophical ontology) the mind may stop at this pseudo-ontology built of beings of reason and constituting a closed universe.” (PN105-107)
3) The Third Degree of Abstraction: Metaphysical Abstraction (Abstraction of Being)
Finally at the third degree, we come to metaphysical knowledge. Here the mind abstracts from all matter, from what the ancients called sensible matter (proper to the first order of visualization) as well as from intelligible matter, that is extension, quantity itself which is proper to the second order of abstractive visualization. The object of this metaphysical knowledge is being as being, which can not only be conceived but can exist without matter. (PN13-14)
For Maritain, the highest form of abstraction is metaphysics. “What we are dealing with here is real being (just the opposite of what happens in mathematical abstraction), real being disengaged from sensible existence; no longer vested in it as in the first order of abstraction but disengaged from sensible existence, grasped for its own sake in an original intuition.” (PN31). It transcends the material and quantitative aspects of reality and relies on intellectual intuition and rational analysis using categories like substance, essence, existence, act, potency, and causality to uncover the fundamental principles which underlies all reality. These metaphysical categories or principles are not bound by the limitations of material existence, but they provide the rational principles of scientific inquiry and are foundational for understanding reality in its fullest sense.
Maritain contrasts ontological analysis of metaphysics which corresponds to the third degree of abstraction with empirical analysis, “empiriological analysis deals with sensible being but first and foremost as observable or measurable…in ontological analysis carried on at first degree of abstractive visualization, being is considered in reference to sensible and observable data, but the mind consults this data in order to seek in it intelligible reasons that transcend the sense.” (PN79, 80) Indeed, it is fundamental as it addresses the ultimate causes of reality, including God, the nature of the soul, and the first principles of being.
Modern scientism and hierarchical epistemology
Maritain employs this hierarchy of reality and degrees of abstraction in epistemology to challenge scientism, that is, the modern scientific outlook which regards mathematical-physical science as the highest, if not the only legitimate form of knowledge. Mathematical models are powerful tools of empirical science deployed to study material existence, but it would be reductionistic to elevate such knowledge as the supreme form of knowledge. It is acknowledged that empirical-mathematical science yields valuable knowledge, but they are incomplete without metaphysics. After all, its operation is restricted to the second degree of abstraction and is inadequate for analysis, much less yield insights into higher order questions of metaphysics such as nature of existence, the purpose of life, or the existence of God. However, it would be a mistake to pit metaphysics directly with natural empirical-mathematical sciences which was the mistake committed by 17th and 18th century philosophers in their critique of modern empirical science at that time. In the process, the philosophy of nature was either absorbed by natural-empirical sciences or metaphysics. However, based on his understanding on the three distinctive degrees of abstraction, Maritain argues that “: “there is an essential distinction between the philosophy of nature (or “physics”) and metaphysics.” (PN32)
What then is the relationship between the philosophy of nature with natural sciences? Contrary to metaphysics, natural science studies nature based on empirical observation, measurement, and experimentation in order in order to formulate theories based on the empirical data. It does no engage with the deeper philosophical questions about the fundamental principles of material existence, processes which are beyond quantification and mathematical analysis. On the other hand, Maritain argues that while the philosophy of nature investigates the ontological foundation of nature, the subject of investigation, “being as mobile or as changing”, requires a grounding in nature as it investigates the principles, causes, and general structure of the natural world, albeit at higher level than empirical science. It is clear that these two different forms of analysis results in two different types of knowledge. However, insofar as the philosophy of nature shares the same grounding in nature, and also shares in higher order ontological analysis of metaphysics,1“Its intelligibility appeal (ratio formalis quae [formal reason which]) is the moving, or mutability; its objective light (ratio formalis sub qua [formal reason under which]) is an ontological mode of analysis and conceptualization, a way of abstracting and defining which, the while it refers intrinsically to sensory perception, aims at the intelligible essence.” (PN139-140). Explanation – “Intelligibility appeal refers to “the aspect under which the thing presents itself to the knowing mind” and “the objective light is “the formal perspective of conceptualization” (PN126, 128) which refers to the way in which the being in question is abstracted in order to arrive at knowledge of it. the philosophy of nature serves as an intermediary science which serves as a bridge for comparing metaphysics and empirical-mathematical sciences.
There is a complementary and hierarchical relationship between empirical-mathematical science with the philosophy of nature. Both disciplines apply methods of analysis and concept formation based on the first degree of abstraction. However, empirical-mathematical science is restricted to empirical investigation and the philosophy of nature includes metaphysical reflection. That is, while empirical-mathematical science investigates the sensible qualities of sensible beings and provides empirical data and description of the material existence, the philosophy of nature interprets and synthesizes the scientific data and theories within a broader ontological framework. As such, the philosophy of nature provides “regulative principles as directive principles orienting though and research, but not entering into the very structure of these sciences themselves.” (PN111)
Scientism which reduces reality to purely physical or mathematical description (both qualitative and quantitative) overlooks the ontological aspects of nature. In contrast to the fragmented approach of modern science, Maritain argues that (Thomistic) metaphysics offers the most comprehensive epistemology because it integrates all three degrees of abstraction rather than restricting itself to the second. The result is a unified vision of knowledge which preserves the integrity of different domains of science.
Conclusion
Maritain’s doctrine of the three degrees of abstraction serves as a philosophical framework to counter the epistemological imperialism of modern empirical-mathematical science. By demonstrating that physics and mathematics operate within limited degrees of abstraction, he defends that necessity, if not, primacy of metaphysics. His critique of scientism emphasizes that while modern science excels in practical applications, it does not possess the ultimate explanatory power that metaphysics provides. In the spirit of Thomism, Maritain suggests that true wisdom consists in acknowledging the proper place of each knowledge discipline within the hierarchy of knowledge grounded in the metaphysical study of being.
READING- From Jacques Maritain, Philosophy of Nature (Philosophical Library, 1951).
“We can present all this in an illustrative diagram. Let a sphere (I) represent the first order of abstraction. The intellectual eye of the “physicus” [physicist] falls on the sensible surface and penetrates into the sphere where, supposing this sphere to be heterogeneous, it finds different strata of intelligibility. Starting from sensible phenomena it plunges deeper and deeper into the ontological depths within this universe of knowledge. This is the sphere of the sensible real, the sphere of intelligible being more or less vested in the sensible; ‘more or less’ for this sphere is not homogeneous; there are specific differentiations within this universe of knowledge.
Now in the second order of abstraction, the mathematical order, let us say that at the moment in which the mind’s eye falls upon the sphere of the sensible real, it discerns therein intelligibles of another kind into whose concept sensible matter does not enter although they cannot be realized in existence without matter, and so it ricochets so to speak toward an ideal sphere different from the sphere of the sensible real, towards a sphere (II) representing a universe of knowledge whose object is intelligible being more or less vested in logical existence, in the purely ideal existence proper to what philosophers call beings of reason (entia rationis) or ideal entities (which, by the way, bespeaks the particularly close relationship there is between mathematics and logic). This intelligible being more or less vested in logical existence implies imaginable residues in its concept just as intelligible being in the first order of abstraction implies sensible residues in its concept. So the word “ens” [being] has a wholly different bearing in one case and in the other. To come finally to the third degree of abstraction, suppose that the philosopher’s intellectual glance stays in the real in order to fathom it and that, being refracted in the sphere of the sensible real, it passes beyond this sphere and discovers a third, much vaster universe (III) that may be called the sphere of the pure intelligible, or again the realm of the trans-sensible real (sphere of the metaphysical trans-sensible which itself opens on to the analogical knowledge of trans-intelligible objects). It is as if, by dint of diving ever deeper into the ocean, one finally succeeded in finding at the bottom of the sea a magical mirror reflecting the sky. The glance is thus reflected above towards purely intelligible objects and this is the glance proper to the metaphysician, to metaphysical visualization. What we are dealing with here is real being (just the opposite of what happens in mathematical abstraction), real being disengaged from sensible existence; no longer vested in it as in the first order of abstraction but disengaged from sensible existence, grasped for its own sake in an original intuition.” (PN29-31)
Thus, Maritain rejects the scientistic claim that modern physics is the ultimate epistemology, arguing instead for a hierarchical structure of knowledge in which science, philosophy of nature, and metaphysics each have their proper and necessary place.
Postscript
A complete description of Jacques Maritain’s philosophy of nature would include the following elements:
1. Hylomorphism where all physical substances are composed of two fundamental principles: matter (hyle) and form (morphe).
2. The teleological (goal-directed) nature of every natural being.
3. Hierarchy of beings – Nature is a hierarchical reality with distinct ontological levels, ranging from inanimate objects to plants to animals to humans.
4. Each level of reality incorporates lower levels while adding new principles of organization and action, resulting in emerging higher level of complexities. Conversely, higher forms of organization cannot be reduced to their material components. Hence, Maritain rejects reductionism of physical sciences.
4. Natural beings exhibit intrinsic directedness toward specific ends. Every being acts towards the goal of fulfilment its own nature. As such, the mechanistic view of nature is incomplete.
5. True knowledge is holistic. Natural laws reflects how the natural world participates in divine wisdom and order and forms the basis for natural law and ethics.
Reference
PN: Jacques Maritain, Philosophy of Nature (Philosophical Library, 1951).