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Indeterminacy, in philosophy, can refer both to common scientific and mathematical concepts of uncertainty and their implications and to another kind of indeterminacy deriving from the nature of definition or meaning. It is related to deconstructionism and to Nietzsche's criticism of the Kantian noumenon.
The problem of indeterminacy arises when one observes the eventual circularity of virtually every possible definition. It is easy to find loops of definition in any dictionary, because this seems to be the only way that certain concepts, and generally very important ones such as that of existence, can be defined in the English language. A definition is a collection of other words, and in any finite dictionary if one continues to follow the trail of words in search of the precise meaning of any given term, one will inevitably encounter this linguistic indeterminacy.
Philosophers and scientists generally try to eliminate indeterminate terms from their arguments, since any indeterminate thing is unquantifiable and untestable; similarly, any hypothesis which consists of a statement of the properties of something unquantifiable or indefinable cannot be falsified and thus cannot be said to be supported by evidence that does not falsify it. This is related to Popper's discussions of falsifiability in his works on the scientific method. The quantifiability of data collected during an experiment is central to the scientific method, since reliable conclusions can only be drawn from replicable experiments, and since in order to establish observer agreement scientists must be able to quantify experimental evidence.
Immanuel Kant unwittingly proposed one answer to this question in his Critique of Pure Reason by stating that there must "exist" a "thing in itself" – a thing which is the cause of phenomena, but not a phenomenon itself. But, so to speak, "approximations" of "things in themselves" crop up in many models of empirical phenomena: singularities in physics, such as gravitational singularities, certain aspects of which (e.g., their unquantifiability)can seem almost to mirror various "aspects" of the proposed "thing in itself", are generally eliminated (or attempts are made at eliminating them) in newer, more precise models of the universe; and definitions of various psychiatric disorders stem, according to philosophers who draw on the work of Michel Foucault, from a belief that something unobservable and indescribable is fundamentally "wrong" with the mind of whoever suffers from such a disorder: proponents of Foucault's treatment of the concept of insanity would assert that one need only try to quantify various characteristics of such disorders as presented in today's Diagnostic and Statistical Manual – delusion, one of the diagnostic criteria which must be exhibited by a patient if he or she is to be considered schizophrenic, for example – in order to discover that the field of study known as abnormal psychology relies upon indeterminate concepts in defining virtually each "mental disorder" it describes. The quality that makes a belief a delusion is indeterminate to the extent to which it is unquantifiable; arguments that delusion is determined by popular sentiment (i.e., "almost no-one believes that he or she is made of cheese, and thus that belief is a delusion") would lead to the conclusion that, for example, Alfred Wegener's assertion of continental drift was a delusion since it was dismissed for decades after it was made.
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