Category Archives: Epistemology

Jean Piaget: Knowledge Evolves

Jean Piaget (1896-1980) was a Swiss biologist, psychologist, and philosopher known most prominently for his studies of the cognitive development of children. He was a voluminous writer in multiple fields whose publishing career began at age ten and continued unabated for about seventy years. He is one of the most important psychologists and cited intellectuals of the twentieth-century.

The desire to find a bridge between biology and knowledge was Piaget’s lifelong goal, and evolution provided that bridge, since both life and mind evolve.[i] What Piaget discovered after decades of empirical study was that interactions between biological organisms and their physical environment were strikingly parallel to those found in the relation between minds and reality—in both domains evolution proceeds similarly.

The key concepts in Piaget’s thought were: organization, adaptation, assimilation, accommodation, and equilibration. An animal is an organization, a complex, physical structure. If a biological organism is in a state of disequilibrium—for example it’s hungry—it is motivated to adapt to its environment—search for food. This process of adaptation comes about by assimilating from the environment—eating—and then accommodating to what’s been assimilation—undergoing the digestive process. The end result of the adaptive process is that the organism returns to a state of biological equilibrium—its hunger satisfied.

In a similar way humans exist as organisms in a cognitive environment. If an organism is in a state of cognitive disequilibrium—say it’s unsure of a truth claim—it is motivated to adapt to its cognitive environment—say by signing up for a class about the topic. This process of adaptation consists of both the process of assimilating new knowledge—attending a lecture—as well as accommodating to what’s been assimilated—by reconciling the new information with previous cognitive structures. The end result of the adaptive process is that the organism achieves a higher level of cognitive equilibrium.

Together organization and adaptation constitute what Piaget calls the process of equilibration—essentially a biological drive to produce optimal states of equilibrium between organisms and their physical and cognitive environments. The result in biological evolution is organisms more adapted to or equilibrated with their physical environments, and in cognitive evolution organisms more adapted to or equilibrated with their cognitive environment.

The empirical evidence to support his view comes from multiple sources. For instance, the cognitive development of a child—the evolution of individual mind—and the development of better scientific theories—the evolution of the group mind—both provide overwhelming evidence for the progressive evolution of knowledge toward better theories about the world, contra Kuhn. The equilibration process drives both individuals and groups to higher levels of equilibrium between mind and reality. In other words thought gradually adapts to reality. While Piaget did not discuss whether the evolution of cognitive structures would construct or discover meaning, we might infer that meaning, if real, will be approached by the increasing power of mind—mind that is the product of the process of equilibration that in turn moves mind closer and closer to truth.

Summary – Knowledge evolves in a progressive direction characterized by a better fit between mind and the real.


[i] For more see John G. Messerly, Piaget’s Conception of Evolution (Lanham Md.: Rowman & Littlefield, 1996).

Do We Live in the Matrix? Discussed in Two Pages

The Brain in a Vat – Your brain could be attached to a supercomputer so that your everyday experiences are perfectly simulated—even though “you” are just a brain attached to a computer. How do you know reality is not like this? You don’t. Four hundred years ago Rene Descartes explored similar themes—that an evil demon might be deceiving us about everything we see and think. Can we offer any evidence against such a scenario? Before considering this question let us consider another unusual possibility.

Subjective Idealism – When you “see” a tree what you experience are sense-data (colors, patterns, sounds, etc.). But why assume there is a tree, external to you, that provides this sense-data? Why not just assume there are only ideas or experiences within your mind, and no physical phenomenon at all. This conclusion was embraced by the philosopher George Berkeley: “reality is constituted entirely of minds and their ideas.” The basic objection to idealism is that our experience suggests there is an external world. Berkeley assumed that his god was always perceiving the universe thereby making it real.

Do We Live in the Matrix? – There could be evidence for this view. For example, we might wake up in a hospital and see a white-tinged background. But even if we had this experience we might conclude we’ve gone crazy.  And we have no evidence that we live in a simulated realities or that subjective idealism is true. (There are good arguments that we live in a simulation.) But are there any reasons to reject the view that we live in a matrix?

To answer this question let us return to Descartes who argued:

  • An evil demon might be deceiving me about empirical and mathematical knowledge. But if I am being deceived, I must exist, since I must be to be deceived.
  • If I have experiences I must exist. Hence “I think, therefore I am.”
  • The idea of a god stands out, the idea of a perfect being which must be.
  • Since we exist and god exists and god isn’t a deceiver, then the external world exists.
  • Thus, our senses and reason are reliable.

Problems – Even if there are gods and they gave us senses and reason to understand the world, why do they sometimes deceive us? Descartes says it is our fault when our faculties deceive us, because we often employ them carelessly, or others try to deceive us. But this isn’t very convincing. Furthermore, Descartes’ argument is circular: reasoning is trustworthy because god made it that way, and we know that god exists because its reasonable.  So he hasn’t satisfactorily demonstrated that we can know anything with certainty. For all we know we may still live in a simulated reality.

Direct Realism – We still haven’t explained why a belief in a physical world is more reasonable than belief in the matrix-like scenario. But maybe this isn’t a problem. Consider how sense perception works. We look at something, have an experience, and then make an inference about the external world. But maybe this is all wrong—maybe we don’t infer trees, we see trees! Thus common sense answers the problem of how we know the world—we perceive it, rather than perceiving some data and then making an inference. This view is known as direct realism.

Problems – 1) Direct realism is consistent with idealism, brain in vat, evil demon, etc.; 2) direct realism doesn’t fit with what we know about the complicated ways brains process information and sense-data; 3)modern science confirms that sense experience is not a passive process, but an active one involving the brain; and 4) we assume a physical world primarily because we have inherited the ways of processing information that contributed to the survival of our ancestors. So while our perceptual system is useful, it is also full of gaps, and with different brains we would see things differently.

Natural theory – We could say that we see trees and then have an experience which causes the belief in an independently existing tree. This is sometimes called the natural theory or indirect realism. It says that we don’t directly experience a tree, and it assumes both the existence of an external world and senses that give reliable knowledge about the world. But while we might believe the natural theory, we haven’t shown that any of the other possibilities are mistaken. For all we know we do live in a computer simulation.

The Simulation Argument – In fact we may already be living in a computer simulation. The Oxford philosopher and futurist Nick Bostrom argues that advanced civilizations may have created computer simulations containing individuals with artificial intelligence and we might unknowingly be in such a simulation. Bostrom concludes that one of the following must be the case: civilizations never have the technology to run simulations; they have the technology but decided not to use it; or we almost certainly live in a simulation.

Conclusion – In the end I am agnostic about whether or not we live in a simulation.

Review of Marcelo Gleiser’s, The Limits of Science and the Search for Meaning

(This review was reprinted in Humanity+ Magazine, June 10, 2014)

There is a new book on the intersection between science and the meaning of life: The Island of Knowledge: The Limits of Science and the Search for Meaning  by Marcelo Gleiser, the Appleton Professor of Natural Philosophy and Professor of Physics and Astronomy at Dartmouth College.

Gleiser’s main thesis is that our observations yield only an “island of knowledge.”Thus there are limits to science’s ability to answer fundamental philosophical questions. These limits to our knowledge arise both from the tools we use to explore reality and the nature of physical reality itself. What we can know is limited by the speed of light, the uncertainty principle, the incompleteness theorem, and our own intellectual limitations. Recognizing these limits does not entail abandoning science and embracing religion. We should continue our scientific investigation of the nature of the cosmos, Gleiser argues, for by coming to know the universe we come to know ourselves. 

Obviously Gleiser is right—there are limits to scientific knowledge as the incompleteness theorem and uncertainty principle strongly suggest. As the island of our knowledge grows, so too does the ocean of uncertainty which surrounds it. Still science gives us our best chance to understand the nature of the cosmos, and hence the the most firm foundation upon which to understand the meaning of the cosmos.

Gleiser also argues that science and religion focus on the same question.

The urge to know our origins and our place in the cosmos is a defining part of our humanity. Creation myths of all ages ask questions not so different from those scientists ask today, when they ponder the quantum creation of the Universe “out of nothing,” or whether our Universe is but one among countless others, all of them exhalations of a timeless multiverse. The specifics of the questions and of the answers are, of course, entirely different, but not the motivation: to understand where we came from and what our cosmic role is, if any. To the authors of those myths, ultimate questions of origins were solely answerable through invocations of the sacred, as only the timeless could create that which exists within time. To those who do not believe that answers to such questions remain exclusively within the realm of the sacred, the challenge is to scrutinize the reach of our rational explanations of the world and examine how far they can go in making sense of reality and, by extension, of ultimate questions of origins.

Gleiser’s point here is uncontroversial—similar desires motivate creation myths and scientific cosmology. As for popularity, religious myths win hands down, but for those not attracted to religious answers Gleiser’s suggestion is insightful. They must make epistemic judgments and reconcile themselves with whatever comfort limited knowledge provides. This may not be an easy way to live, but it is an authentic way. Surely that counts for something. Gleiser’s book makes for a thoughtful read on a timeless topic, especially when humans are in desperate need of new narratives to replace the old religious ones.

Reflections on Noson Yanofsky’s, “The Outer Limits of Reason”

But as for certain truth, no man has known it, nor will he know it; neither of the gods, nor yet of all the things of which I speak. And even if by chance he were to utter the final truth, he would himself not know it: for all is but a woven web of guesses. ~ Xenophanes


Just finished reading Noson Yanofsky’s, The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us.  He covers paradoxes, conundrums, puzzles, impossibilities, limitations, perplexities and obstructions in philosophy, mathematics, computer science, physics, and logic. Topics include: self-referential paradoxes, the ship of Theseus, Zeno paradoxes, different sizes of infinity, the halting problem, the Monty Hall problem, chaos theory, the travelling salesman problem, quantum mechanics, relativity theory, and more. Much of the book is tough going, although Yanofsky does make difficult topics understandable.

Of particular interest to a philosopher is his conclusion. After an entire book on reason’s limitations, he meditates the definition of reason. While many definitions have been offered, Yanofsky settles on: “Reason is the set of processes or methodologies that do not lead to contradictions and falsehoods.1 Processes that do not lead to contradictions and falsehoods are reasonable ones; whereas if we derive a falsehood or contradiction we overstepped the bounds of reason.

Of course determining whether some idea or process is reasonable or steps over the limits of reason is hard to determine. At one time scientists believed in ether, phlogiston, phrenology and spontaneous generation. Often the problem lies in relying on intuition, which sometimes misleads. The earth may seem stationary and flat, but it is not; motion may seem independent of speed, but it is not. But what of dark energy, dark matter, string theory, supersummetry and the like? For now we don’t know if some theories have overstepped the bounds of reason, but as we learn more we will hopefully find out.


Yanofsky is at his best extolling the virtues of reason. “Jonas Salk did not find a cure for polio using intuition … Imagination was not used to get humans to the moon … World hunger will not be solved by feelings of love and warmth…”2 Moreover to go beyond reason is dangerous, even if the answers to our problem are out there. Yes there is a shortest route for the travelling salesman, but we cannot know it; and we cannot prove that Godel’s sentence—this logical statement is not provable—is true, even though it is. In short, there is knowledge out there that we can’t access.

Why not then just speculate? Because there is nothing intelligent we can say when we go beyond reason, especially if we are trying to avoid contradictions or falsehoods. To go past reason leads inevitably to mistakes, and is characterized by guesses and conjectures. He counsels accepting our limitations lest we fall into error. Yet there is a bright side; we live, we love, we have aesthetic and moral experiences. As for reason, it both powerful and limited, but it is not all we have. In this we should take comfort.


1. Noson Yanofsky’s, The Outer Limits of Reason: What Science, Mathematics, And Logic Cannot Tell Us, 345.

2. Noson Yanofsky’s, The Outer Limits of Reason: What Science, Mathematics, And Logic Cannot Tell Us, 349.