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Unknowability
In philosophy, unknowability is the possibility of inherently unaccessible knowledge. It addresses the epistemology of that which cannot be known. Some related concepts include the limits of knowledge, ignorabimus, unknown unknowns, the halting problem, and chaos theory.
Nicholas Rescher provides the most recent focused scholarship for this area in Unknowability: An Inquiry into the Limits of Knowledge, where he offered three high level categories, logical unknowability, conceptual unknowability, and in-principle unknowability.
Speculation about what is knowable and unknowable has been part of the philosophical tradition since the inception of philosophy. In particular, Baruch Spinoza's Theory of Attributes argues that a human's finite mind cannot understand infinite substance; accordingly, infinite substance, as it is in itself, is in-principle unknowable to the finite mind.
Immanuel Kant brought focus to unknowability theory in his use of the noumenon concept. He postulated that, while we can know the noumenal exists, it is not itself sensible and must therefore remain unknowable.
Modern inquiry encompasses undecidable problems and questions such as the halting problem, which in their very nature cannot be possibly answered. This area of study has a long and somewhat diffuse history as the challenge arises in many areas of scholarly and practical investigations.
Rescher organizes unknowability in three major categories:
In-principle unknowability may also be due to a need for more energy and matter than is available in the universe to answer a question, or due to fundamental reasons associated with the quantum nature of matter. In the physics of special and general relativity, the light cone marks the boundary of physically knowable events.
The halting problem – namely, the problem of determining if arbitrary computer programs will ever finish running – is a prominent example of an unknowability associated with the established mathematical field of computability theory. In 1936, Alan Turing proved that the halting problem is undecidable. This means that there is no algorithm that can take as input a program and determine whether it will halt. In 1970, Yuri Matiyasevich proved that the Diophantine problem (closely related to Hilbert's tenth problem) is also undecidable by reducing it to the halting problem. This means that there is no algorithm that can take as input a Diophantine equation and always determine whether it has a solution in integers.
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Unknowability
In philosophy, unknowability is the possibility of inherently unaccessible knowledge. It addresses the epistemology of that which cannot be known. Some related concepts include the limits of knowledge, ignorabimus, unknown unknowns, the halting problem, and chaos theory.
Nicholas Rescher provides the most recent focused scholarship for this area in Unknowability: An Inquiry into the Limits of Knowledge, where he offered three high level categories, logical unknowability, conceptual unknowability, and in-principle unknowability.
Speculation about what is knowable and unknowable has been part of the philosophical tradition since the inception of philosophy. In particular, Baruch Spinoza's Theory of Attributes argues that a human's finite mind cannot understand infinite substance; accordingly, infinite substance, as it is in itself, is in-principle unknowable to the finite mind.
Immanuel Kant brought focus to unknowability theory in his use of the noumenon concept. He postulated that, while we can know the noumenal exists, it is not itself sensible and must therefore remain unknowable.
Modern inquiry encompasses undecidable problems and questions such as the halting problem, which in their very nature cannot be possibly answered. This area of study has a long and somewhat diffuse history as the challenge arises in many areas of scholarly and practical investigations.
Rescher organizes unknowability in three major categories:
In-principle unknowability may also be due to a need for more energy and matter than is available in the universe to answer a question, or due to fundamental reasons associated with the quantum nature of matter. In the physics of special and general relativity, the light cone marks the boundary of physically knowable events.
The halting problem – namely, the problem of determining if arbitrary computer programs will ever finish running – is a prominent example of an unknowability associated with the established mathematical field of computability theory. In 1936, Alan Turing proved that the halting problem is undecidable. This means that there is no algorithm that can take as input a program and determine whether it will halt. In 1970, Yuri Matiyasevich proved that the Diophantine problem (closely related to Hilbert's tenth problem) is also undecidable by reducing it to the halting problem. This means that there is no algorithm that can take as input a Diophantine equation and always determine whether it has a solution in integers.