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But even if the idea of a second A series within which the first falls makes sense (and McTaggart doubts it does, p. 469), it will face the same contradiction. And so, we must construct a third A series within which the second falls. And this will require the construction of a fourth A series and so on ad infinitum. At any given stage the ...
Examples include: "The sequence 1, 2, 3, ... continues ad infinitum." "The perimeter of a fractal may be iteratively drawn ad infinitum." The 17th-century writer Jonathan Swift incorporated the idea of self-similarity in the following lines from his satirical poem On Poetry: a Rhapsody (1733):
The following is a sample of books for further reading, selected for a combination of content, ease of access via the internet, and to provide an indication of published sources that interested readers may review. The titles of some books are self-explanatory.
A man walks a mile from a point α. But there is an infinity of gods each of whom, unknown to the others, intends to obstruct him. One of them will raise a barrier to stop his further advance if he reaches the half-mile point, a second if he reaches the quarter-mile point, a third if he goes one-eighth of a mile, and so on ad infinitum.
Gettier's examples hinged on instances of epistemic luck: cases where a person appears to have sound evidence for a proposition, and that proposition is in fact true, but the apparent evidence is not causally related to the proposition's truth. In response to Gettier's article, numerous philosophers [3] have offered modified criteria for ...
For example, the epistemic regress is a series of beliefs in which the justification of each belief depends on the justification of the belief that comes before it. An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress.
A Sign is anything which is related to a Second thing, its Object, in respect to a Quality, in such a way as to bring a Third thing, its Interpretant, into relation to the same Object, and that in such a way as to bring a Fourth into relation to that Object in the same form, ad infinitum. (CP 2.92; quoted in Fisch 1986: 274)
An argument which does not seem to have such a beginning becomes difficult to imagine. If it can be established, separately, that the chain must have a start, then a reductio ad infinitum is a valid refutation technique. reformatio in peius: change to worse: A decision from a court of appeal is amended to a worse one.