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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 .
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.
A graph that shows the number of balls in and out of the vase for the first ten iterations of the problem. The Ross–Littlewood paradox (also known as the balls and vase problem or the ping pong ball problem) is a hypothetical problem in abstract mathematics and logic designed to illustrate the paradoxical, or at least non-intuitive, nature of infinity.
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.
Besides the cardinality, which describes the size of a set, ordered sets also form a subject of set theory. The axiom of choice guarantees that every set can be well-ordered, which means that a total order can be imposed on its elements such that every nonempty subset has a first element with respect to that order.
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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]
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