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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.
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 .
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.
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]
The question of whether natural or real numbers form definite sets is therefore independent of the question of whether infinite things exist physically in nature. Proponents of intuitionism, from Kronecker onwards, reject the claim that there are actually infinite mathematical objects or sets. Consequently, they reconstruct the foundations of ...
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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.
A rediscovery of the 'system' must begin with the realization that it is the questions which are important, the logic of their sequence and the consequent logic of the answers. A ritualistic repetition of the exercises contained in the published books, a solemn analysis of a text into bits and tasks will not ensure artistic success, let alone ...