Indeterminacy, in philosophy, refers to uncertainty found in science and math, as well as uncertainty that comes from how words or ideas are defined. This concept is connected to deconstructionism and to Friedrich Nietzsche's critique of Immanuel Kant's idea of the noumenon, which is the belief that things exist beyond what humans can directly understand.
Indeterminacy in philosophy
The problem of indeterminacy happens when people notice that definitions often loop back on themselves. In dictionaries, it is common to find circular definitions, especially for important ideas like "existence." A definition uses other words, and in any dictionary, if someone follows the chain of words to understand a term, they will eventually face this issue of unclear meaning.
Philosophers and scientists usually avoid using terms that are unclear because such terms cannot be measured or tested. A hypothesis that depends on something that cannot be measured or defined cannot be proven wrong, which makes it impossible to support with evidence. This idea connects to Karl Popper’s work on the scientific method, which emphasizes that data from experiments must be measurable. Scientists rely on measurable results to draw reliable conclusions and ensure agreement among observers.
Immanuel Kant suggested in his book Critique of Pure Reason that there must be a "thing in itself"—a cause of what we experience but not something we can directly observe. Some models in science, like those involving singularities in physics, resemble this idea. However, these models often try to remove such unclear elements to create more accurate descriptions of the universe. In psychology, definitions of mental disorders, as discussed by philosophers influenced by Michel Foucault, sometimes depend on ideas that cannot be directly observed or described. For example, the concept of a "delusion" in diagnosing schizophrenia is hard to define because it depends on things that cannot be measured. If a belief is considered a delusion because few people share it, this could lead to incorrect conclusions, like calling a scientific idea a delusion if it was once unpopular.
Friedrich Nietzsche criticized Kant’s idea of the "thing in itself" and similar concepts, arguing that they are too vague. In his writings, Nietzsche questioned the usefulness of terms like the "noumenon" (a concept in Kant’s philosophy) and the idea of "exact equality." He pointed out that even simple mathematical statements like "x = x" show differences between the two "x" symbols, as they are separate and not identical in every way. This suggests that the idea of exact equality may not be meaningful.
Jacques Derrida explored the idea of indeterminacy in his work Plato's Pharmacy, analyzing a story from Plato where Socrates argues that writing is less valuable than speech. In the story, the god-king of Egypt rejects writing as a harmful invention, ignoring its potential benefits. The Greek word "pharmakon," which means both a remedy and a poison, highlights the difficulty of defining something clearly. Derrida argued that the term cannot be fully categorized as either good or bad.
Michel Foucault discussed how the concept of "insanity" is also hard to define clearly. A simplified version of his argument can be found in Hunter S. Thompson’s book Kingdom of Fear, which states: "The only difference between the Sane and the Insane is IN, yet within this world, the Sane have the power to have the Insane locked up." This idea is further explained in a summary of Foucault’s work Madness and Civilization, which notes that society has historically used confinement as a way to control and define who is considered "mad."
Indeterminacy in new physical theories
Science often tries to remove unclear definitions, things that do not cause effects, and uncertain characteristics by using more observation, experiments, descriptions, and explanations. Occam's razor helps simplify models by removing things that do not cause effects, but some scientific models, like quantum mechanics, show that certain uncertainties exist. For example, in quantum mechanics, it is impossible to know both the exact position and exact speed of a particle at the same time. This idea is known as Heisenberg's uncertainty principle.
Steven Weinberg, a scientist who believes a complete theory of everything might one day exist, once said that people sometimes think a final theory is impossible because each step toward understanding has led to more complexity. However, he argued that this complexity simply means the final theory has not yet been found. Scientists have never believed they had reached the end of all knowledge.
The idea of a "theory of everything" suggests that all physical laws might one day be explained by a single idea. However, some challenges might prevent this, such as how the universe's starting conditions affect outcomes or how complex solutions in mathematics make predictions exact but unhelpful.
Chaos theory explains that predicting the behavior of complex systems is difficult because it is impossible to collect all the needed information about them.
At this time, it seems possible that a complete theory explaining all natural phenomena may never exist. Instead, new discoveries might lead to more complex and detailed explanations. In this view, the idea of "indeterminacy" or the "thing in itself" represents something that can never be fully understood, much like how numbers in math can get closer to a limit but never actually reach it.
Some scientists believe the universe follows strict rules, and they have criticized the idea of uncertainty in science. For example, Albert Einstein once said, "God does not play dice," arguing against the idea that small particles behave unpredictably. In this statement, Einstein was criticizing quantum mechanics, which suggests that the behavior of tiny particles is based on probabilities rather than fixed rules.
At first, it might seem that uncertainty is not helpful for living things. However, some traits that appear unhelpful now might become important later, even if they disappear over time. Humans are the only known species that use ideas about uncertainty. It is also possible that our brains cannot handle every tiny detail, so we must use general ideas instead of separate ones for every small difference, like the number of hairs on a dog. However, this is not the same as the deeper uncertainty that exists in the natural world.
Synonymous concepts in philosophy
In quantum mechanics, the terms "uncertainty" and "indeterminacy" describe the same idea. Words like "unquantifiability" (meaning something cannot be measured) and "undefinability" (meaning something cannot be clearly defined) are sometimes used to mean the same as "indeterminacy." In science, "indeterminacy" may also be used to describe situations where something cannot be proven or predicted. Additionally, things that are completely unobservable cannot be described precisely, making them indeterminate.