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Results tagged with paradox
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user 40746
This tag is for arguments that produce an inconsistency with common sense.
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Do all paradoxes of naive set theory have something in common?
If P(x) is the formula "x ∉ x", then ...
the assumption that a set h has P(x) purity ...
(i.e. the assumption that for all t, if t∈h then P(t))
... implies that there exists a set k, where k exhibits …
- 292
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Is there a simple paradox like Russell's paradox that arises if we assume
Clearly, to avoid Russell's paradox, we would refrain from assuming that we can select a constant c and have a set of all x such that {x,c} is an element of the set whose existence is posited above. … It's not immediately obvious how one would obtain a paradox. For example, consider the following property: {x,empty set} not an element of x. …
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Although Russell's paradox has the virtue of simplicity, is it a distraction from other para...
Russell's paradox historically arose as a counter-example to Frege's simple assertion regarding the existence of sets corresponding to properties. … primarily because there doesn't seem to be any way to deduce -- within that system -- the contradiction that arises in Russell's paradox? …
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What is the justification for the claim that observing something that is both a raven and bl...
Suppose that I have access to a machine that allows me to input a positive integer (perhaps up to ten decimal digits) and the machine will -- depending only on the input -- output a statement.
If the …
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