Integrating Perspectives on the Certainty-Uncertainty Paradox

L.E. Maroski

“The more uncertain I have felt about myself, the more there has grown up in me a feeling of kinship with all things.” –Carl Jung, Memories, Dreams, Reflections

Although our present era seems particularly fraught with uncertainty, every time in history has had its uncertainties, sometimes regarding whether the harvest will be sufficient for the winter, sometimes regarding worldwide political instability. Our time is no different, and our time is unique. Not only is there uncertainty at the scale of society, but each person has likely felt greater uncertainty about something in their life recently. Although uncertainty is a ubiquitous experience, why does it seem so overwhelming now, and how can we manage our response to it?

In the quote from Jung, above, an initial interpretation seems to be that feeling certain of one’s identity separates one from others, but when such an ego boundary is more porous, it is possible to feel interconnected and perhaps even question where one’s boundaries end and those of others begin. Uncertainty, not about external circumstances but about one’s self, could have profound effects. Such questioning could lead one to a deeper interpenetration of uncertainty and certainty and self and other, as well as other seemingly separate concepts that co-arise interdependently.

L.E. (Lisa) Maroski blends philosophy, psychology, and science with the spiritual to describe her vision for a new type of language and to provide stepping stones for possible ways to express the paradoxical wholeness of Life. In Embracing Paradox, Evolving Language, her words ring out as a clarion call to visionaries who seek to bring into existence a world of many worlds that works for everybody.

The term “paradox” comes from the Greek para meaning “contrary to” and doxa, opinion (from dokein, “to appear, seem, think”). It came to refer to self-contradictory statements in the 1560s. Some philosophers believe that paradoxes emerged from early Greek riddles (Quine, 1976). Although English has only one word, uncertainty, German has three words that convey its different valences: ungenauigkeit, inexactness; unsicherheit, unsureness; and unbestimmtheit, unascertainable, indeterminable. We will mostly take up “unsureness,” but the other meanings make cameo appearances. By referring to a “certainty-uncertainty paradox,” I am not synthesizing them into a new unity (as with “bittersweet”) but rather bringing terms that seem to be opposites together in a way that highlights their independence as well as their interdependence, even their mutual co-arising. By recognizing that at the core of certainty is uncertainty, and at the core of uncertainty is certainty, it might be possible to reframe one’s experiences.

It was probably no coincidence that after I accepted the request to write this article—when my life was quite stable and I silently wondered how I could say anything about uncertainty—the new administration in the U.S. arrived and threw my life into significant uncertainty. In light of the promised cuts of government staff I feared that I would lose my job. Because I was a contractor, I assumed that contractors would be let go first, given the protections in place for federal employees. My fear was augmented when, one Monday morning, I logged on and got an “Access Denied” message. None of the Information Technology people I contacted could help me restore access. The next day I learned, not from my supervisor but from friends, that government employees were given a buyout package. As a contractor, I got no such thing. What did that mean? Would I now have to pick up the slack left by federal employees who took the bait? I didn’t know whether I would have any work or too much work.

By recognizing that at the core of certainty is uncertainty, and at the core of uncertainty is certainty, it might be possible to reframe one’s experiences.

Despite such experience of high uncertainty, fortunately, it was not radical uncertainty. I do not need to doubt the basis of my existence. I do not doubt that my computer will continue to run, water will flow from the tap, and I will be able to get this article written. Certainties in those domains helped to balance out the uncertainty in my employment domain. My sense of self—who I am and what I stand for—has, ironically, been clarified and solidified.

Because feelings of uncertainty are highly subjective and can involve internal, visceral clenching (which is how my body reacts to uncertainty), let us first look at how others have approached the concept of un/certainty, in order to establish some common ground and thereby also understand un/certainty. Doing so will reveal tools, perspectives, and approaches that take us beyond the visceral level.

We will briefly explore philosophical, psychological, sociological, and linguistic approaches to certainty and uncertainty. Each approach is like a different type of map that enables us to see different aspects of the territory. Philosophy gives us the broad contours, both topological and conceptual. Psychology provides details about the surface and deep terrain, including how we experience the tension between certainty and uncertainty, either in the concepts themselves or as they affect other aspects of lived experience. A sociological lens enables us to look at how we navigate together through collective uncertainties regarding our continued existence on Earth. And finally, after traversing and examining those lenses through which we experience the terrain of un/certainty, we will look at how our language itself filters and shapes our perceptions so that we can begin to envision new ways to get beyond the exclusion of certainty from uncertainty, and vice versa, to be able to express and embody their paradoxical nature.

Philosophical Approach

The concepts of certainty and uncertainty are related to each other in various ways—most commonly, as linear opposites separated by degrees of gradation. As distinct concepts, certainty is not uncertainty; indeed, one seems to be the negation of the other. Of course, it is not as simple as that.

The fundamental question at the core of both certainty and uncertainty is “what do I know that I know?”

The fundamental question at the core of both certainty and uncertainty is “what do I know that I know?” What I know I know (think I know, believe I know) is called epistemic certainty. I know basic mathematics, such that I am certain that 2 + 5 = 7, not only from rote memorization but also from experiences of adding objects or money. Epistemic certainty also includes what I know that I don’t know, such as how to distinguish edible from poisonous wild mushrooms. In this manner, the un/sureness valence of un/certainty functions as an overtone to our knowledge or beliefs that reflects a self-evaluation that is layered onto the content of the knowledge or belief. Another metaphor: this type of un/certainty is like the readout of a reliability meter applied to knowledge. But what gives that readout credence?

The fundamental question at the core of both certainty and uncertainty is “what do I know that I know?”

Epistemic certainty does not encompass the actuality of whether your knowledge is true or accurate. If you have ever tried to put something together without reading the instructions, then gotten stuck, you had high epistemic certainty without it necessarily corresponding to accurate knowledge. Epistemic certainty can always be questioned and thereby refined by a healthy dose of skepticism—is this the whole picture? How do I know this? Might there be more to learn about this?

The limitations of our knowledge are a function of the limitations of our perspective. For a simple example, consider that you are shown an object, like this.

If this were all you saw and you had no other previous experience with such objects, you might insist it does not have a handle. The converse would be true for the object below: you would say that it most certainly does have a handle.

These examples using a coffee mug are metaphoric for how we can or cannot know another’s experience. In other words, we cannot be certain that our experience of something corresponds to others’ experiences. Therefore, it is prudent to seek out perspectives other than those most familiar to us.

In contrast to epistemic certainty, epistemic uncertainty is more difficult to characterize because it is related not just to lack of knowledge but also to doubt and to one’s inability to predict or possibly even imagine the future. As the government firings began, for example, it was difficult to predict where the

DOGE (Department of Government Efficiency) team would strike next. Eventually a pattern emerged (they first dismantled agencies that Elon Musk had a beef with), but then the pattern changed, and even agencies essential for national security were hit. Americans had to face the uncertainty of what life would be like without a government that could perform important governmental functions, including ensuring safety and security.

One could metaphorically characterize epistemic uncertainty as a field from which certainties arise temporarily, like waves forming on the surface of the ocean but then subsiding back into it [John Dotson, personal communication]. However, as Werner Heisenberg’s famous uncertainty principle reveals, there is a limit to what we can know precisely—the more precisely we know the location of a particle the less we can simultaneously know about its momentum. That which we cannot know, called aleatory uncertainty, locks us out of omniscience.

One factor that keeps uncertainty from being overridden by the fantasy of certainty is the seeming randomness or stochasticity of events—from living within an open system to the unintended consequences of our actions, to the reactions of others, to our limited perspectivity. Terry Gilliam’s dystopian movie Brazil, for example, illustrates a completely unforeseen unfolding of events from the random occurrence of a fly falling into a typewriter. We each have less dramatic examples of such uncertainty happening every day of our lives.

The philosopher Ludwig Wittgenstein challenged the notion of certainty and uncertainty as linear opposites, offering instead a more complex, nonlinear relationship between them. In On Certainty, he wrote about what can be doubted (Wittgenstein, 1972). Can the ability to doubt be doubted? In asking that question, he realized that doubting relies on certain things that cannot themselves be doubted, such as the meanings of the very words used to express the doubt. Thus, he recognized that the intentional uncertainty of doubting presupposes and depends on the very certainty it attempts to undermine. Otherwise, you find yourself in an infinite regression of doubt. That infinite regress does not result in any knowledge or certainty. Rather, it shows that the relationship between certainty and uncertainty is not a linear opposition but more like a yin-yang relationship in which certainty is at the core of uncertainty and uncertainty at the core of certainty. By doubting un/certainty, you learn something about your relationship to the fact or proposition that you are doubting, not something new about the fact or proposition itself; for example, you realize what you value or what you assume to be true.

Epistemic certainty can be imitated albeit falsely when belief is substituted for knowing. To be overly certain of one’s beliefs, however, can be a form of addiction and/or a form of psychopathy. Although there is a natural tension between certainty and uncertainty, when the tension within uncertainty becomes unbearable, that is, when one cannot face truth to resolve the tension, it can be tempting to believe one’s own lies in order to maintain (a false) “certainty.” (One’s reliability meter malfunctions.) The movie Sunset Boulevard shows this: an aging movie star cannot face the fact that she is a “has been.” She needs to be certain that her fans still adore her. Her butler helps to feed that delusion. In this case, she has succumbed to a pathology called pseudologia phantastica, in which one believes one’s own lies, not necessarily to intentionally deceive others but because one can maintain a conscious feeling of certainty only by deceiving oneself. Thus, ontological un/certainty, which philosophers deal with, differs from psychological un/certainty.

Psychological Approach

It is possible to see the importance of a nondual understanding of certainty-uncertainty by applying an analytical psychological lens, in particular, by examining the unconscious and conscious dimensions of certainty and uncertainty and how they manifest in lived experience. Let’s consider the combinations of conscious and unconscious awareness with certainty and uncertainty.

First, consider the conscious dimension. This dimension is readily available to awareness, especially when attention is directed to it. Conscious certainty includes many of the “givens” of life as dictated by one’s culture—e.g., that the sun will rise, the electric bill will come due, and that someday each of us will die. Often, however, conscious certainty does not feel like certainty because the element of choice or of judgment is gone. It occurs as “what’s so” or what “just is.” It is in the “isness” that the certainty resides, unquestioned and sometimes unquestionable. Conscious certainty can also be experienced as a self-perceived ability to predict an outcome or a future occurrence and conscious uncertainty as the inability to predict the future.

Conscious uncertainty can arouse fear and its downstream emotions, such as anger, anxiety, and catastrophizing, specifically when one knows that one currently has such emotions. In the example from my own life, I am very conscious of the uncertainties regarding my employment. In other domains, conscious uncertainty looks like this: he loves me; he loves me not? Is the snowstorm going to delay the flight? Rarely do we consciously confront uncertainties such as, “do I exist?”

For many indigenous cultures that co-create the rising of the sun or do not have a sense of conscious certainty about events such as the sun rising each day (perhaps a volcanic eruption that blocked the sun for months in the past resulted in culturally created conscious uncertainty), rituals were developed to ensure (i.e., transform conscious uncertainty toward conscious certainty—but not completely otherwise the ritual would be pointless) that the sun will rise again tomorrow, that rain will come, and so on. Currently, many of us in the U.S. are facing high levels of conscious uncertainty about whether we will receive Social Security checks in our retirement, whether our democratic system of government will devolve into total authoritarianism, and whether climate chaos will be able to be reversed or at least abated.

The forms of unconscious certainty and uncertainty are harder to recognize, particularly in oneself, although they might be more evident in others. Although Wittgenstein did not use the psychological language of conscious and unconscious, he recognized that foundational certainties operate unconsciously and make conscious uncertainty or doubt possible. Unconscious certainty involves beliefs that are taken for granted at a more fundamental level than conscious certainty. For example, when you walk across your living room floor, as you have done thousands of times already, you have developed an unconscious certainty that the floor won’t dematerialize and that your foot will be supported by it. Such object permanence developed through experiences that confirm and reinforce each other. Similarly, we develop event predictability through calendrical regularities, such as birthdays and holidays, which allow life to feel more stable and knowable, thereby reducing some it its inherent uncertainty.

The forms of unconscious certainty and uncertainty are harder to recognize, particularly in oneself, although they might be more evident in others.

Unconscious uncertainty truly is unconscious. It might not manifest as our usual feelings and anxieties of conscious uncertainty. In fact, conscious certainties can hide unconscious uncertainties, resulting in cognitive-emotional dissonance. “For example, a mother may be incapable of giving up the belief that her son did not commit a gruesome murder, and yet, compatible with that inextinguishable belief, she may be tortured by doubt” (Reed, 2022). Unconscious uncertainty can also be seen in complexes or pathological responses that erupt when conscious certainty is used unconsciously as a shield to protect oneself from experiencing conscious uncertainty. For example, unconscious uncertainty can manifest as irrational fears that emerge unexpectedly, displacing the original uncertainty onto something that can be faced consciously. One member of a couple, for example, might deflect their unconscious uncertainty about their spouse’s fidelity by projecting onto their adolescent child a conscious “certainty” (not necessarily accurate) that the adolescent is being promiscuous. Such projection enables the unconscious uncertainty about the spouse’s fidelity to remain hidden and unexamined. At the same time, it surfaces the anger associated with infidelity but redirects it toward the wrong person, often someone more vulnerable. Similar projections of unconscious uncertainty happen at the societal level, when uncertainty about one’s social standing is intensified by actions of the owner class (e.g., by outsourcing jobs overseas) but projected onto those of lower social standing, such as immigrants.

Sociological Approach

When humans developed the capacity to destroy the earth with nuclear bombs, the collective unconscious certainty that the infinite game—life on Earth—would continue indefinitely gave way to widespread conscious uncertainty about our fate—“our” including all species on Earth. (James Carse [1986] defined finite games as those meant to be won/lost, such as sporting events and elections, in contrast to infinite games which are played so that the game can continue to be played ad infinitum; life is considered an infinite game, as is democracy. Democracy can continue indefinitely because it has finite games—elections—embedded within it.) The finite, win-lose nuclear war games of humans threatens our own foundation—namely, if Earth is destroyed then both the finite games and the infinite game here cease (Carse, 1986).

In an illustrative case of life imitating art, or as with Werner Heisenberg, life imitating science, Heisenberg introduced the term “uncertainty” into physics with a specific technical meaning relating to the “simultaneous measurement of canonically conjugate variables, such as position and momentum, or energy and time” (Frayn, 2010, p. 98). He also recognized the conjugate nature of certainty and uncertainty: the more precisely you measure one variable, the less precise your measurement of the related variable can be; and this ratio, the uncertainty relationship, is itself precisely formulable” (Frayn, 2010, p. 98). Heisenberg, the head of the German nuclear program during WWII, struggled with his own moral uncertainty as to what to do with the knowledge that gave him the capability to develop nuclear weapons. If he developed them for Hitler, he might help his own country win the war, but he also knew that Hitler might use them in horrific ways. Heisenberg was caught in the tension of different, competing contexts—on the one hand, he worked for the Nazis yet he also wanted to distance himself from them and their ideology, particularly their condemnation of “Jewish physics,” which was essentially the type of physics he was doing. He also did not want to be perceived as a traitor. He did not want his country to think he had lost them the war intentionally nor did he want them to think they lost due to his incompetence. To what extent he was conscious of those conflicting motivations is not known for sure, as biographers have struggled to determine, with certainty, whether Heisenberg intentionally slowed the German nuclear program.

In contrast, the Americans developed nuclear weapons from the conscious certainty that Hitler and his fascist regime had to be stopped. At the same time, they grappled with uncertainties—perhaps conscious, perhaps unconscious—about whether the atom bomb would ignite the atmosphere and destroy life on Earth. I am not condoning the use of nuclear weapons, only showing what we humans do when faced with conscious certainty and uncertainty. Today we face a similar situation regarding artificial intelligence.

Even while the nuclear threat still looms, we have added more types of threats to the continuation of the game of life, including our disrupting of Earth’s homeodynamic processes (often called climate change) as well as the deployment of automated learning systems (artificial general intelligence, AGI) that have already figured out how to lie and manipulate us. The long-term consequences of continuing to develop AGI are not known, but the developers are certain that they must continue the AGI race just so that the opposition (whether another company or another country) doesn’t win this self-defined game. Just as nuclear weapons were developed to win the war—without regard to the consequences of nuclear radiation and fallout—AGI is being developed just to win a finite game that could, ironically, end the role of humans in the infinite game of life.

As a society we also now must deal with a new type of epistemic uncertainty in the form of mass-produced, intentionally spread misinformation (lies spread unconsciously) and disinformation (lies spread consciously, with intent to deceive or manipulate). Many previously authoritative (i.e., trustworthy) sources of information have been undermined, sometimes from within, often from without. There is now public gaslighting as well as blatant mendacity across the media spectrum. Who can we trust when it is becoming increasingly clear that no one sees the whole picture, as the mug example above illustrates?

Linguistic Approach

Because our understanding and experience of un/certainty occurs via language, I will also examine linguistic expressions of un/certainty, including their webs of associations, as well as the conceptual metaphors that underlie these concepts. I then propose ways to bring together these “opposites” into a yin/yang-like unity.

We express our certainty and uncertainty by using language. Language is more than just words and their etymologies. Words/concepts are related to other concepts through webs of associations conditioned not only by derivation but also by use. Such webs are unique to each individual, but likely there are many overlaps among people who share a culture. Wittgenstein, in Philosophical Investigations, claimed that words/concepts do not have an essence but they do show family resemblances (Wittgenstein & Anscombe, 1958). Further, we know what a word means by how it is used. The figure below shows my web of associations for the pair “certainty-uncertainty.”

As you can see, the terms certainty and uncertainty also call to mind other pairs of concepts, such as believe-doubt, trust-distrust. This example of a web of associations is relatively abstract; it doesn’t include specifics about what I know, believe, whom I trust to have reliable information, and so on. Those particulars would also be part of each person’s web of associations. It is in those very details that our ability to communicate has been breaking down. Some of us would put conspiracy theorists on the “trust/certainty” side of the web while others would put legacy media on the “trust/certainty” side. Some wouldn’t know where to put those sources of information. Given that type of meta-uncertainty, it is understandable that people are uncertain about how to deal with their uncertainty.

In English, we tend not to express un/certainty directly, so such webs also include the less formal expressions we use, such as, “I think that…; I know that…; I have no idea whether…; I might have…; do you suppose that…; and your guess is as good as mine.” Waiting for Godot is an ode to uncertainty.

If certainty is at the core of uncertainty, is it possible not just to become conscious of the certainty at the heart of uncertainty and the uncertainty at the core of certainty, but to be able to access the opposites together and the psychic energy that the tension between them provides?

Underlying our everyday discourse about un/certainty is a largely unconscious system of metaphors that we use not only to express such concepts but also to reason about them. Such conceptual metaphors were identified by George Lakoff and Mark Johnson in a groundbreaking book called Metaphors We Live By (Lakoff & Johnson, 2008). Certainty is often expressed by metaphors of solidity (foundation, rock, ground), is characterized as an object or property that someone or something (e.g., knowledge) can have, and is good (up, high, moral). Conversely, uncertainty is characterized by risk, chance (gambling), and by terms such as “undermine” which convey the removal of firm foundations. These metaphoric associations also fit into the web of associations.

Those types of implicit metaphors that underlie our literal language unconsciously influence how we think about things and reason about solving problems. Similarly, moral certainty often derives from one’s subjective rationality, which then is used to justify behavior. For example, if it is argued that crime is a beast, it would be rational to want to kill such a beast, eliminate the threat it poses, eradicate it, and so on. Conversely, if one believes that crime is a virus, it would be rational to pursue methods to heal those afflicted (Thibodeau & Boroditsky, 2011). Thus, the metaphoric framing that we use to define problems influences how we reason about solving them. Indeed, we see vast differences in cultures, whether criminals are imprisoned or whether methods of reconciliation or restitution are used. Thus, sometimes certainty is only as deep as the metaphors used to characterize a situation.

How can we more consciously utilize language in the dance of certainty and uncertainty? Our dancing with them must involve more than simply shifting from one foot to the other. Trying to stand on both feet simultaneously effectively stops the dancing. Perhaps the dance involves stepping out of such an either/or mindset.

Indeed, Wittgenstein pointed the way when he realized that we necessarily rely on some things to remain certain while engaging in intentional uncertainty (i.e., philosophical doubt) (Wittgenstein, 1972). As yin is at the heart of yang, and vice versa, his ideas suggest that certainty is at the heart of uncertainty.

Even as we express uncertainty in language, it is necessary to assume some certainty that the words one uses can and will be understood by others—that we have sufficient shared agreement about their meanings. We can look not just to the words for certainty but also to the grammar—i.e., aspects of language that tell us what must be expressed. For example, some languages require speakers to indicate grammatically how it is they know something. These syntactic elements are called evidentials. English does not have syntactic evidentials, but when necessary we can (but are not required to) specify how we know, for example, that “there was a cougar nearby.” We could express it using different sentence constructions, depending on whether the knowledge was first-hand (“I saw the cougar”), through signs (“I saw cougar footprints by the river,” or, these days “my neighbor’s doorbell camera showed footage of a cougar on their porch”), or from hearsay (“Uncle Bob told me that he saw a cougar”). Evidentials provide a rough indication on the “reliability meter” of certainty. Consider how different social media would be if we were required grammatically to assert that your re-post is simply hearsay.

If certainty is at the core of uncertainty, is it possible not just to become conscious of the certainty at the heart of uncertainty and the uncertainty at the core of certainty, but to be able to access the opposites together and the psychic energy that the tension between them provides?

To return to my situation as an example, my uncertainty lies initially in the fear that I might lose my job and the subsequent cascade of further unknowns that I would have to consider if I did lose my job—for example, will I be able to afford to continue living here if I lose my job; what do I want to do with my life now? In addition to such personal unknowns, we are facing similar uncertainties at a societal level. For example, what if the government collapses because there aren’t enough people left to keep it functioning minimally; do we still have enough trust in our fellow humans to help each other out during these crises?

You probably noticed that I combined certainty and uncertainty into one word by writing “un/certainty” to convey both simultaneously. It is convenient to do that with terms that are spelled similarly. However, it would not work as well for complementarities of different words, such as “self” and “other,” to write them as“un/self” or even “self/other.” Thus, to continue to engage interdependent concepts simultaneously, we will need to develop novel ways to express them—and I do mean novel structures, not just neologisms (Maroski, 2024). A structure such as reminds the reader that self and others are not opposite ends of a continuum but are interdependent aspects of a greater reality, that each one of us, as a seemingly separate self, relies on others not simply for comfort, services, etc, but to give us a sense of self in the first place. If there were no others, there would be no self. And the dance is ongoing, a process, not a static thing or state.

Relationships like that of certainty and uncertainty, in which one concept is at the heart of the other, can be characterized by a new type of relationship category, which I call fu-an-gu, a glyph I invented for a science-philosophy novel to convey paradoxes of the following type: “the deeper you go, the less it looks like itself; andwhen you reach the core, it looks like the opposite of what you started with” (Maroski, 2024). Wittgenstein looked deeply into doubt and found that it required certainty. Physicists looked deeply into matter and found energy.

By looking for the certainties at the heart of the uncertainties we face, not only can we circumvent a vicious downward cycle, but we can find some solidity with which to anchor ourselves to weather the storms of uncertainty then rebuild life, society, and hope.

It is my hope that by becoming aware of the structures of language that maintain our predilection to focus on one part of a complementarity (such as “uncertainty” or “conscious” or “self”), we can begin not only to realize our responsibilities within the dynamics of Earth and all of her inhabitants, including us, but also to develop new forms of language that reflect our inherent interdependencies and minimize the dissociation of “parts” from the whole of existence. In addition, by acknowledging the interdependence of concepts such as certainty and uncertainty, we gain a more insightful and constructive lens for navigating the vagaries of life. By looking for the certainties at the heart of the uncertainties we face, not only can we circumvent a vicious downward cycle, but we can find some solidity with which to anchor ourselves to weather the storms of uncertainty and begin to rebuild life, society, and hope.

And, while writing this article, I did lose my job in the DOGE cuts. I have no idea how I will earn money in the future, but I am certain, and committed, that it will be by bringing forth these ideas about language and paradox into the world.


References

Carse, J. P. (1986). Finite and Infinite Games. New York: Free Press.

Frayn, M. (2010). Copenhagen: Knopf Doubleday Publishing Group.

Lakoff, G., & Johnson, M. (2008). Metaphors We Live By: University of Chicago Press.

Maroski, L. E. (2024). Embracing Paradox,
Evolving Language: Expressing the Unity and Complexity of Integral Consciousness
. Longmont, CO: Untimely Books.

Quine, W. V. (1976). The Ways of Paradox, and Other Essays: Harvard University Press.

Reed, B. (2022). Certainty. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy.

Thibodeau, P. H., & Boroditsky, L. (2011). The Role of Metaphor in Reasoning. PLOS ONE, 6(2), e16782.

Wittgenstein, L. (1972). On Certainty: HarperCollins.

Wittgenstein, L., & Anscombe, G. E. M. (1958). Philosophical Investigations: The English Text of the Third Edition: Prentice Hall.