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In philosophy, a supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time. [1] Supertasks are called hypertasks when the number of operations becomes uncountably infinite. A hypertask that includes one task for each ordinal number is called an ultratask. [2]
The thought experiment concerns a lamp that is toggled on and off with increasing frequency. Thomson's lamp is a philosophical puzzle based on infinites. It was devised in 1954 by British philosopher James F. Thomson, who used it to analyze the possibility of a supertask, which is the completion of an infinite number of tasks.
Thomson's conditions for the experiment are insufficiently complete, since only instants of time before t≡1 are considered. Benacerraf's essay led to a renewed interest in infinity-related problems, set theory and the foundation of supertask theory.
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NC = P problem The P vs NP problem is a major unsolved question in computer science that asks whether every problem whose solution can be quickly verified by a computer (NP) can also be quickly solved by a computer (P). This question has profound implications for fields such as cryptography, algorithm design, and computational theory. [1]
The philosophy of science includes the question: What criteria are satisfied by a 'good' theory. This question has a long history, and many scientists, as well as philosophers, have considered it. The objective is to be able to choose one theory as preferable to another without introducing cognitive bias. [4]
For example, by Gödel's incompleteness theorem, we know that any consistent theory whose axioms are true for the natural numbers cannot prove all first-order statements true for the natural numbers, even if the list of axioms is allowed to be infinite enumerable. It follows that an automated theorem prover will fail to terminate while ...
Scientific theories are distinguished from philosophical theories in that each of their theorems are statements about observable data, whereas a philosophical theory includes theorems which are ideas or principles.