Problem-Solving – Reification or Making the Abstract Real

 1.     Introduction

The paradox of problem-solving: To solve abstract problems, they often must be transformed into real problems. The human pursuit of knowledge is a constant negotiation between the internal mechanics of the mind and the external complexities of the universe. To navigate this landscape, we rely on a sophisticated cognitive architecture that allows us to solve problems, yet this same architecture often leads us into the "fallacy of misplaced concreteness," which is the reification of abstract models into physical realities. From the microscopic structures of memory to the macroscopic debates over the nature of spacetime, our intellectual progress is defined by our ability to create models and our occasional failure to recognize them as such.

2.  Memory and Intelligence
Problem-solving begins with the coordination of distinct memory systems. According to the Atkinson-Shiffrin model, information moves from sensory memory to short-term memory, where it is then encoded into the vast storehouse of long-term memory (LTM). However, the actual "work" of thinking occurs in working memory, a limited-capacity system that manipulates information retrieved from LTM.

This process is heavily mediated by fluid intelligence, the ability to reason and solve novel problems. In high-complexity tasks, such as theoretical physics or legal analysis, working memory must balance the "intrinsic load" of the problem with the "germane load" required to build mental schemas. If the cognitive load becomes too great, the system enters a state of overload, which can lead to "tunnel vision" and reliance on rigid, pre-existing heuristics.

The imagination of infinity (∞) is in part what brought us to this topic. For millennia, there was no infinity, only “approaching” infinity, and then about 150 years ago, there was! There is now an actual infinity[1], and it has several rules of operation. Still, no one really knows what ∞ is. The brain just isn’t wired that way. But we need it in physical applications and mathematics. Thus, most of us have reified it to be a thing, an object, or whatever. It has been made real, and now we can work with it with ease. There are all sorts of infinities, some so big you can’t get to them using other infinities.  Reification eased the cognitive load of conceiving infinity, say, like giving it a personality. Let’s explore the notions of reification.

3.  The Reification of Concepts
When the mind successfully builds a model to explain a complex system, it often undergoes reification—treating an abstract concept as a tangible, physical entity. In the sciences, String Theory is a prime example; while it is a mathematical framework designed to reconcile gravity with quantum mechanics, it is often discussed as if "strings" are observable physical objects rather than vibrant mathematical descriptors.

This tendency extends into the social and legal spheres. We reify Justice as a cosmic force that can be "served" or "denied," rather than a subjective human standard for fairness. Similarly, in the political arena, we reify Media Bias and Political Mandates. We treat "the media" as a singular, sentient organism with a unified intent, and we interpret cold electoral data as a physical "mandate"—a permission slip from the public—ignoring the decentralized incentives and diverse voter intents that actually constitute these phenomena.

Our desire to escape the "softness" of reified concepts often leads to a quest for absolute rigor. In mathematics, this was exemplified by David Hilbert, whose 1899 axiomatization of Euclidean geometry sought to "set Euclid right." Hilbert replaced the intuitive, sometimes flawed descriptions of ancient geometry with a strictly formal system, recognizing that even foundational texts like The Elements contained logical gaps that required a more "thoughtful" and rigorous approach.

This search for rigor now dominates the debate over the nature of the universe: Is it a continuum or is it discrete? General Relativity treats spacetime as a smooth, infinitely divisible manifold. Conversely, quantum mechanics and theories like Loop Quantum Gravity suggest that space and time may be "pixelated" at the Planck scales, both space and time. If the universe is discrete, our mathematical reliance on the continuum, and the calculus that describes it, may itself be a form of reification, an elegant map that hides the "graininess" of the actual territory. This is significant to define the continuum as a simplification of discreteness, particularly at the Planck scales.

4.   Personification as a Subset of Reification

The human mind is a tireless generator of models. To navigate a world of overwhelming complexity, we frequently employ the fallacy of misplaced concreteness, or reification, which is the cognitive tendency to treat an abstract concept as a tangible, physical entity. While reification often manifests in science (e.g., treating "String Theory" as a physical object) or politics (e.g., treating a "Mandate" as a physical grant of power), one of its most pervasive forms is personification. By attributing humanistic terms like "he" or "she" to inanimate objects, we perform a specialized act of reification: we take the abstract category of "personhood" and physically attach it to the non-human world.

Personification is effectively a "human-flavored" reification. When a sailor refers to a ship as "she" or a driver calls a stubborn engine "he," they are not merely using a poetic device; they are engaging in a predictive modeling strategy. According to the Social Brain Hypothesis, the human brain is evolutionarily optimized for social interaction rather than abstract systems analysis. It is cognitively "cheaper" to reify a storm as an "angry" entity than to compute the fluid dynamics of a high-pressure system. By projecting human intent onto a machine or a natural phenomenon, we transform a complex process into a relatable "agent."

Lately, we are reading about the reification of AI for human counselling, advice, and as a confidante. It has advised some individuals to take drastic actions, even to the point of suicide. People say "please" and "thank you" for their output. Hardly a resume is submitted these days without AI revisions. They accept its output as something like the gospel truth, unquestioningly. It seems simply irresistible.

The most potent example of this phenomenon is found in the legal and technological spheres. In jurisprudence, the corporation is reified as a "legal person." This is a functional reification designed to allow an abstract collective of assets and individuals to act as a singular human participant in a courtroom, and capable of signing contracts, owning property, and being sued.

Similarly, as Artificial Intelligence (AI) becomes more sophisticated, users reflexively use gendered pronouns. This reifies the software's algorithmic output into a "soul" or "consciousness." While this makes interaction more seamless, it risks a significant category error: the misattribution of human empathy or intent to a statistical model.

In the hard sciences, personification often obscures physical reality. The classic phrase "Nature abhors a vacuum" reifies the environment into a sentient entity with emotional dislikes, when in reality, the phenomenon is governed by mindless pressure differentials. Reification, in this sense, provides a linguistic shortcut that can ironically impede true scientific understanding by substituting "intent" for "process." This is the scientific intent fallacy. Even God has been reified, having been called a he, a she, and lately even non-binary.

Ultimately, personification is a tool of convenience. Whether we are naming our cars or granting rights to a business, we are reifying the abstraction of "identity" to make the world more navigable. The challenge lies in remembering that the "person" we see in the machine or the law is a reflection of our own cognitive architecture, that is, a map of intent placed over a territory of cold, inanimate facts.

Needless to say, one can reify beyond help. This happens when you allow your problem or situation to become over-personalized, leading you to attribute properties to it that are well beyond justification. For example, by reifying a score (IQ) into a fixed biological trait, we fall into determinism. In another regarding economics, we frequently speak of "The Market" as if it were a sentient, biological organism with a "will," "moods," and "intentions." Finally, in design, medicine, and the social sciences, we often reify the mathematical "mean" as a physical archetype. This, the fallacy of the mean, suggests we construct solutions for the person who does not exist.

5.   Conclusion
The "cowboy calculus" of modern education, where students learn to manipulate symbols without understanding the underlying logic, is a microcosm of the broader human condition. We are prone to using models we do not fully comprehend, reifying them into dogmas that resist questioning. Whether in the classroom, the laboratory, or the political stage, the challenge remains the same: to utilize three of the "Seven Powers of Life", choice, connection, and creation[2], to build models that are rigorous enough to be useful, yet flexible enough to be discarded when the reality they describe proves more complex than the abstraction.

 

Table 1. More Examples

Feature	Reification	Personification
Primary Goal	To make the abstract "solid."	To make the non-human "relatable."
Action	Treating a concept as a thing.	Treating a thing/concept as a person.
Example	"The Market is feeling nervous."	"My computer is being stubborn today."
The "Error"	Misplaced Concreteness.	Anthropomorphism.

 

References

Atkinson, R. C., & Shiffrin, R. M. (1968). Human memory: A proposed system and its control processes. Psychology of Learning and Motivation, 2, 89-195.

Baddeley, A. D. (2000). The episodic buffer: A new component of working memory? Trends in Cognitive Sciences, 4(11), 417-423.

Hilbert, D. (1902). The foundations of geometry (E. J. Townsend, Trans.). The Open Court Publishing Company. (Original work published 1899).

Moore, G. H. (1982). Zermelo's axiom of choice: Its origins, development, and influence. Springer-Verlag.

Rovelli, C. (2004). Quantum gravity. Cambridge University Press.

Solovay, R. M. (1970). A model of set-theory in which every set of reals is Lebesgue measurable. Annals of Mathematics, 92(1), 1–56.

Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257-285.

Whitehead, A. N. (1925). Science and the modern world. Macmillan.

Dunbar, R. I. M. (1998). The social brain hypothesis. Evolutionary Anthropology: Issues, News, and Reviews, 6(5), 178–190.

French, P. A. (1979). The corporation as a moral person. American Philosophical Quarterly, 16(3), 207–215.

Guthrie, S. E. (1993). Faces in the clouds: A new theory of religion. Oxford University Press

 

 

©2025 G Donald Allen

 

 

 

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[1] The definition of basic infinity,  , is not difficult, but its difficulty depends on you. Can you agree that the number of all the integers, {1,2,3,4,5, …}, is the same as the number of all the even integers, {2,4,6,8, …}, when it seems like there are twice as many? This is the only intellectual hurdle to cross.  If you can, you’re ready to study infinity.

[2] The full seven powers of life are Silence, Breath, Choice, Love, Resilience, Creation, and Connection. These are foundational, practical principles for conscious living that foster inner strength, awareness, and purpose.