## Logical Paradoxes | Internet Encyclopedia of Philosophy

If you know that your beliefs are jointly inconsistent, then youshould reject R. M. Sainsbury’s definition of a paradox as“an apparently unacceptable conclusion derived by apparentlyacceptable reasoning from apparently acceptable premises” (1995,1). Take the negation of any of your beliefs as a conclusion and yourremaining beliefs as the premises. You should judge this jumbleargument as valid, and as having premises that you accept, and yet ashaving a conclusion you reject (Sorensen 2003b, 104–110). If theconclusion of this argument counts as a paradox, then the negation ofany of your beliefs counts as a paradox.

## Zeno's Paradoxes (Stanford Encyclopedia of Philosophy)

“… The paradox… reflects a higher level of intellect and, by not forcibly representing the unknowable as known, gives a more faithful picture of the real state of affairs….”

## The Currency Paradox | Thoughts on the Economy of …

Assume there is a true sentence of the form ‘p but p is notknown’. Although this sentence is consistent, modest principlesof epistemic logic imply that sentences of this form areunknowable.

Church’s referee report was composed in 1945. The timing andstructure of his argument for unknowables suggests that Church mayhave been by inspired G. E. Moore’s (1942, 543) sentence:

## Paradox Definition, Meaning & Examples | Literary Terms

Supertasks: A further strand of thought concerns what Black(1950–51) dubbed ‘infinity machines’. Black and hisfollowers wished to show that although Zeno’s paradoxes offeredno problem to mathematics, they showed that after all mathematics wasnot applicable to space, time and motion. Most starkly, our resolutionto the Dichotomy and Achilles assumed that the complete run could bebroken down into an infinite series of half runs, which could besummed. But is it really possible to complete any infinite series ofactions: to complete what is known as a ‘supertask’? Ifnot, and assuming that Atalanta and Achilles can complete their tasks,their complete runs cannot be correctly described as an infiniteseries of half-runs, although modern mathematics would so describethem. What infinity machines are supposed to establish is that aninfinite series of tasks cannot be completed—so any completabletask cannot be broken down into an infinity of smaller tasks, whatevermathematics suggests.

## paradox meaning - definition of paradox by Mnemonic …

An apparent counterexample can be set aside as anomaly if it conflictswith a highly confirmed law of nature. But if the counterexample onlyconflicts with a speculative generalization, the theory should berejected.

## paradox Definition and Meaning - Dictionary Central

Applying the Mathematical Continuum to Physical Space and Time:Following a lead given by Russell (1929, 182–198), a number ofphilosophers—most notably Grünbaum (1967)—took up thetask of showing how modern mathematics could solve all of Zeno’sparadoxes; their work has thoroughly influenced our discussion of thearguments. What they realized was that a purely mathematical solutionwas not sufficient: the paradoxes not only question abstractmathematics, but also the nature of physical reality. So what theysought was an argument not only that Zeno posed no threat to themathematics of infinity but also that that mathematics correctlydescribes objects, time and space. It would not answer Zeno’sparadoxes if the mathematical framework we invoked was not a gooddescription of actual space, time, and motion! The idea that amathematical law—say Newton’s law of universalgravity—may or may not correctly describe things is familiar,but some aspects of the mathematics of infinity—the nature ofthe continuum, definition of infinite sums and so on—seem sobasic that it may be hard to see at first that they too applycontingently. But surely they do: nothing guarantees *apriori* that space has the structure of the continuum, oreven that parts of space add up according to Cauchy’sdefinition. (Salmon offers a nice example to help make the point:since alcohol dissolves in water, if you mix the two you end up withless than the sum of their volumes, showing that even ordinaryaddition is not applicable to every kind of system.) Our belief thatthe mathematical theory of infinity describes space and time isjustified to the extent that the laws of physics assume that it does,and to the extent that those laws are themselves confirmed byexperience. While it is true that almost all physical theories assumethat space and time do indeed have the structure of the continuum, itis also the case that quantum theories of gravity likely imply thatthey do not. While no one really knows where this research willultimately lead, it is quite possible that space and time will turnout, at the most fundamental level, to be quite unlike themathematical continuum that we have assumed here.