An interesting paradox.
Thus we have a paradox.
It was sincerity veiled as self-parody, insecurity veiled as breeziness – and all the better for that uneasy paradox.
WITH a writer such as Herman Melville, whose exorbitance is matched by a mountainous bibliography, a brief pocket life might seem a paradox.
But there are always more paradoxes.
This hypothesis is plausible for newcomers to the sorites paradox.
We consider this an impossibility, hence the paradox, but maybe we don’t have to?
Bradley and Stefánsson (2016) also develop a new decision theory partly in response to the Allais paradox.
The prelates may not have understood this moral paradox, but its most grotesque consequence showed up quickly.
Therefore, in the following the presentation will be structured not according to type of paradox but according to type of solution.
For this reason, Earman and Norton conclude with Benacerraf that the Thomson lamp is not a matter of paradox but of an incomplete description.
The Borda count, formally defined later, avoids Condorcet's paradox but violates one of Arrow's conditions, the independence of irrelevant alternatives.
What is essentially the same paradox, but in a form somewhat easier to analyze, is the one in which a particle passes through the two arms of Mach-Zehnder interferometer.
Much has been written about what lessons to draw from Carroll’s paradox, but this much seems clear: the Tortoise refuses to accept (Z) because he refuses to apply modus ponens to the premises he accepts.
But as Gregory points out, the fact that the majority of DNA in our genomes is non-coding might make the C-value discrepancies less of a paradox, but it gives rise to a whole range of further puzzles (Where does this extra DNA come from?
Philosophers of law have not been especially concerned with the question of how to solve (or to resolve) the paradox, but they have debated the nature of borderline cases, and its implications for the role of judges in a community, and for the possibility of the rule of law.
Even this intensional explication would still be vulnerable to the problems of irrelevant properties and the modus tollens paradox but for the adoption of a condition to exclude the occurrence of predicates that are not nomically relevant to the explanandum event from the explanans of an adequate scientific explanation.
Given the insight that not only cyclic structures of reference can lead to paradox, but also certain types of non-wellfounded structures, it becomes interesting to study further these structures of reference and their potential in characterising the necessary and sufficient conditions for paradoxicality.
Leibowitz in response concedes to Kasher that there is no paradox, but stresses that no matter how many times one goes around the circle, the ultimate commitment to the life of mitzvoth must come from beyond the circle, from a conative – rather than cognitive – commitment that is beyond reason (see “Responses,” 277–278).
The study of non-standard models did not start with Gödel’s results—Skolem, in particular, was already aware of them earlier in a different context (he had discovered that first-order theories of set theory have unnaturally small, namely, countable models, in Skolem 1922; cf. the entry on Skolem’s paradox)—but the first incompleteness theorem elucidates the existence of non-standard models in the context of arithmetic, while the nonstandard models elucidate the first incompleteness theorem.
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The study of non-standard models did not start with Gödels results—Skolem in particular was already aware of them earlier in a different context he had discovered that first-order theories of set theory have unnaturally small namely countable models in Skolem 1922 cf the entry on Skolems paradox—but the first incompleteness theorem elucidates the existence of non-standard models in the context of arithmetic while the nonstandard models elucidate the first incompleteness theorem