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What is an example of a logical paradox?
Why is a statement a paradox?
What is a liar paradox in logic?
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May 26, 2024 · Logical paradox example. “This statement is false.” The liar paradox is a semantic paradox that exposes the limitations of classical binary logic when handling self-referential statements. If true, the statement must be false, and if false, it must be true. Set theory paradox.
- Classical Logical Paradoxes
- Moving to Modern Times
- Some Recent Logical Paradoxes
- Paradoxes of Self-Reference
- A Contemporary Twist
- References and Further Reading
The four main paradoxes attributed to Eubulides, who lived in the fourth century BC, were “The Liar,” “The Hooded Man,” “The Heap,” and “The Horned Man” (compare Kneale and Kneale 1962, p114). The Horned Man is a version of the “When did you stop beating your wife?” puzzle. This is not a simple question, and needs a carefully phrased reply, to avoi...
Between the classical times of Aristotle and the late nineteenth century when Cantor worked, there was a period in the middle ages when paradoxes of a logical kind were considered intensively. That was during the fourteenth century. Notable individuals were Paul of Venice, living towards the end of that century, and John Buridan, born just before i...
It was developments in other parts of mathematics which were integral to the discovery of the next logical paradoxes to be considered. These were developments in the theory of real numbers, as was mentioned before, but also in Set Theory, and Arithmetic. Arithmetic is now taken to be concerned with a “denumerable” number of objects — the natural nu...
The possibility that Cantor’s diagonal procedure is a paradox in its own right is not usually entertained, although a direct application of it does yield an acknowledged paradox: Richard’s Paradox. Consider for a start all finite sequences of the twenty six letters of the English alphabet, the ten digits, a comma, a full stop, a dash and a blank sp...
There have been developments, in the last few years, which have shown that the previous emphasis on paradoxes involving self-reference was to some extent misleading. For a family of paradoxes, with similar levels of intractability, have been discovered, which are not reflexive in this way. It was mentioned before that a form of the Liar paradox cou...
Asher, N. and Kamp, H. 1986, “The Knower’s Paradox and Representational Theories of Attitudes,” in J. Halpern (ed.) Theoretical Aspects of Reasoning about Knowledge, San Mateo CA, Morgan Kaufmann.Asher, N. and Kamp, H. 1989, “Self-Reference, Attitudes and Paradox” in G. Chierchia, B.H. Partee, and R. Turner (eds.) Properties, Types and Meaning 1.Beall, J.C., 2001, “Is Yablo’s Paradox Non-Circular?,” Analysis61.3.Copi, I.M., 1973, Symbolic Logic4th ed. Macmillan, New York.Oct 27, 2020 · In fact, it is a strange type of problem, called a logical paradox, with no solution. It is difficult to pinpoint who came up with the first paradoxes, but two Greek philosophers, Eubulides of ...
A paradox is a statement that contradicts itself, or that must be both true and untrue at the same time. Paradoxes are quirks in logic that demonstrate how our thinking sometimes goes haywire, even when we use perfectly logical reasoning to get there. But a key part of paradoxes is that they at least sound reasonable.
A famous example of a logical paradox is the “liar’s paradox,” which is generally formulated as “this statement is false.” The statement is a paradox because if the statement is false, then that makes the statement true.
Russell illustrated the logical structure of his paradox with an amusing example. Imagine a village whose barber (an adult male villager) shaves all and only the adult male villagers who do not shave themselves.
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. [ 1 ][ 2 ] It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. [ 3 ][ 4 ] A paradox usually involves ...
