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is a theory of dynamics that argues that, for sufficiently complex systems, even if we know initial conditions fairly well, measurement errors and computational limitations render fully correct long-term prediction impossible, hence guaranteeing ultimate unknowability of physical system behaviors.
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The undecidability of the halting problem and the
Diophantine problem has a number of implications for mathematics and computer science. For example, it means that there is no general algorithm for proving that a given mathematical statement is true or false. It also means that there is no general
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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.
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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
382:",. The halting problem and the Diophantine Problem eventually were answered demonstrating in-principle unknowability of answers to some foundational mathematical questions, meaning Bois-Reymond's assertion was in fact correct.
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itself is an initiate to capture and record knowledge using contemporary technological tools. Earlier attempts to capture and record knowledge include writing deep tracts on specific topics as well as the use of
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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
253:) 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.
408:
at a news briefing on
February 12, 2002. In addition to unknown unknowns there are known unknowns and unknown knowns. These category labels appeared in discussion of identification of chemical substances.
175:'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.
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John M. Myers, F. Hadi Madjid, "Logical synchronization: how evidence and hypotheses steer atomic clocks," Proc. SPIE 9123, Quantum
Information and Computation XII, 91230T (22 May 2014);
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unknowability to humans due to limits of matter and energy in the universe that might be required to conduct the appropriate experiments or conduct the calculations required;
245:
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,
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Cherniak, Christopher. "Limits for knowledge." Philosophical
Studies: An International Journal for Philosophy in the Analytic Tradition 49.1 (1986): 1–18.
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Speculation about what is knowable and unknowable has been part of the philosophical tradition since the inception of philosophy. In particular,
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McEachran, Andrew D.; Sobus, Jon R.; Williams, Antony J. (2016). "Identifying known unknowns using the US EPA's CompTox
Chemistry Dashboard".
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demonstrate the implicit in-principle unknowability of methods to prove consistency and completeness of foundation mathematical systems.
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Horgan, John. The End of
Science : Facing the Limits of Knowledge in the Twilight of the Scientific Age. Addison-Wesley Pub 1996.
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concept. He postulated that, while we can know the noumenal exists, it is not itself sensible and must therefore remain unknowable.
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163:, where he offered three high level categories, logical unknowability, conceptual unknowability, and in-principle unknowability.
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Hilary Putnam, Time and
Physical Geometry, The Journal of Philosophy, Vol. 64, No. 8 (Apr. 27, 1967), pp. 240–247
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that answers to problems of mathematics are possible with human effort. He declared, "in mathematics there is no
545:"Mathematical Problems: Lecture Delivered before the International Congress of Mathematicians at Paris in 1900"
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DeNicola, Daniel R. Understanding ignorance: The surprising impact of what we don't know. MIT Press, 2017
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There are various graduations of unknowability associated with frameworks of discussion. For example:
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conceptual unknowability — analytically demonstrable of unknowability based on concepts and involved.
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Rescher, Nicholas. Unknowability: an inquiry into the limits of knowledge. Lexington Books, 2009.
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Tavel, Morton. Contemporary
Physics and the Limits of Knowledge. Rutgers University Press 2002.
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End of science: facing the limits of knowledge in the twilight of the scientific age
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to organize and summarize entire fields or event the entirety of human knowledge.
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Chaitin, Gregory J. The unknowable. Springer
Science & Business Media, 1999.
586:"Identification of "known unknowns" utilizing accurate mass data and ChemSpider"
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unknowability to humans at a particular time (due to lack of appropriate tools);
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logical unknowability — arising from abstract considerations of epistemic logic.
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unknowability to particular individual humans (due to individual limitations);
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An associated topic that comes up frequently is that of Limits of
Knowledge.
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In principle, many problems can be reduced to the halting problem. See the
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Popular discussion of unknowability grew with the use of the phrase
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https://www.worldcat.org/search?q=ti%3A%22limits+of+knowledge%22
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Matii︠a︡sevich I︠U︡. V. Hilbert's Tenth Problem. MIT Press 1993.
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provides the most recent focused scholarship for this area in
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in-principle unknowability — based on fundamental principles.
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as unsatisfactory, and motivated Hilbert to declare in 1900
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algorithm for finding solutions to Diophantine equations.
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Rescher organizes unknowability in three major categories:
676:"Open Science for Identifying "Known Unknown" Chemicals"
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proved that the Diophantine problem (closely related to
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brought focus to unknowability theory in his use of the
457:. Metaphysics Research Lab, Stanford University. 2018.
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unknowability to any processes, organism, or artifact.
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Unknowability: An Inquiry into the Limits of Knowledge
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Journal of the American Society for Mass Spectrometry
49:. Unsourced material may be challenged and removed.
228:marks the boundary of physically knowable events.
338:Contemporary physics and the limits of knowledge
16:Philosophical idea of things impossible to know
389:discusses unknowability in many of his works.
129:is the possibility of inherently unaccessible
549:Bulletin of the American Mathematical Society
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319:Examples of scholarly discussions involving
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109:Learn how and when to remove this message
439:https://www.worldcat.org/title/298538038
374:International Congress of Mathematicians
141:know. Some related concepts include the
736:https://www.worldcat.org/title/41273107
520:https://www.worldcat.org/title/47838409
508:https://www.worldcat.org/title/34076685
496:https://www.worldcat.org/title/28424180
455:The Stanford Encyclopedia of Philosophy
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630:Analytical and Bioanalytical Chemistry
197:Rescher's categories of unknowability
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680:Environmental Science and Technology
532:https://www.jstor.org/stable/4319805
469:https://www.jstor.org/stable/2024493
47:adding citations to reliable sources
484:https://doi.org/10.1117/12.2054945
403:United States Secretary of Defense
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451:"Spinoza's Theory of Attributes"
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562:10.1090/S0002-9904-1902-00923-3
472:https://doi.org/10.2307/2024493
268:Gödel's incompleteness theorems
145:, the limits of knowledge, the
34:needs additional citations for
674:; Williams, Antony J. (2017).
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262:list of undecidable problems
368:proclamation was viewed by
299:has been wide and diverse.
188:Modern inquiry encompasses
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399:There are unknown unknowns
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606:10.1007/s13361-011-0265-y
584:Little, James L. (2011).
759:Concepts in epistemology
358:Ignoramus et ignorabimus
700:10.1021/acs.est.7b01908
543:Hilbert, David (1902).
251:Hilbert's tenth problem
393:Categories of unknowns
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362:Emil du Bois-Reymond
350:Limits for knowledge
346:Christopher Cherniak
239:computability theory
190:undecidable problems
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672:Schymanski, Emma L.
321:limits of knowledge
312:Limits of knowledge
232:The halting problem
133:. It addresses the
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41:Please help
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379:ignorabimus
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243:Alan Turing
241:. In 1936,
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555:: 437–79.
425:References
226:light cone
167:Background
123:philosophy
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