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Single Idea 9138
[filed under theme 5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
]
Full Idea
Banning self-reference is too narrow to avoid the liar paradox. With 1) all the subsequent sentences are false, 2) all the subsequent sentences are false, 3) all the subsequent... the paradox still arises. Self-reference is a special case of this.
Gist of Idea
An infinite series of sentences asserting falsehood produces the paradox without self-reference
Source
report of Stephen Yablo (Paradox without Self-Reference [1993]) by Roy Sorensen - Vagueness and Contradiction 11.1
Book Ref
Sorensen,Roy: 'Vagueness and Contradiction' [OUP 2004], p.168
A Reaction
[Idea 9137 pointed out that the ban was too narrow. Sorensen p.168 explains why this one is paradoxical] This is a nice example of progress in philosophy, since the Greeks would have been thrilled with this idea (unless they knew it, but it was lost).
Related Idea
Idea 9137
Banning self-reference would outlaw 'This very sentence is in English' [Sorensen]
The
19 ideas
with the same theme
[problem when liars refer to themselves]:
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6006
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If you say truly that you are lying, you are lying
[Eubulides, by Dancy,R]
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9464
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One of their own prophets said that Cretans are always liars
[Anon (Titus)]
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21564
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Vicious Circle: what involves ALL must not be one of those ALL
[Russell]
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21567
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'All judgements made by Epimenedes are true' needs the judgements to be of the same type
[Russell]
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19187
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The Liar makes us assert a false sentence, so it must be taken seriously
[Tarski]
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8940
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Tarski avoids the Liar Paradox, because truth cannot be asserted within the object language
[Tarski, by Fisher]
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6569
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'This sentence is false' sends us in a looping search for its proposition
[Wittgenstein, by Fogelin]
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21692
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If we write it as '"this sentence is false" is false', there is no paradox
[Quine]
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14964
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The Liar reappears, even if one insists on propositions instead of sentences
[Gupta]
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14969
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Strengthened Liar: either this sentence is neither-true-nor-false, or it is not true
[Gupta]
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13507
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The machinery used to solve the Liar can be rejigged to produce a new Liar
[Hart,WD]
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9138
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An infinite series of sentences asserting falsehood produces the paradox without self-reference
[Yablo, by Sorensen]
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15428
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The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut'
[Burgess]
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13371
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If you know that a sentence is not one of the known sentences, you know its truth
[Priest,G]
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13372
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There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar
[Priest,G]
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11014
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Self-reference paradoxes seem to arise only when falsity is involved
[Read]
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9137
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Banning self-reference would outlaw 'This very sentence is in English'
[Sorensen]
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15355
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Strengthened Liar: 'this sentence is not true in any context' - in no context can this be evaluated
[Horsten]
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16336
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The liar paradox applies truth to a negated truth (but the conditional will serve equally)
[Halbach]
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