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    The Liar paradox arises from unrestricted self-reference,... — Carmelics
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    Challenges→Arithmetical truth cannot be defined in arithmetic

    The Liar paradox arises from unrestricted self-reference, not from defining truth in arithmetic per se.

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    Reasons For

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    Reason for
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    • 1.Self-referential sentences like 'this sentence is false' create paradox regardless of the truth definition used.
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    • 2.Formal systems with restricted self-reference (like Peano arithmetic) remain consistent without truth predicate issues.
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    • 3.The paradox persists across natural language and formal systems, suggesting self-reference is the root cause, not truth definitions.
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    Reasons Against

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    Reason against
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    • 1.Self-reference alone is harmless; 'this sentence has five words' refers to itself without paradox.
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    • 2.The paradox fundamentally depends on what 'true' means—different truth definitions yield different conclusions about the Liar.
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    • 3.Even with unrestricted self-reference, systems avoid paradox if truth is defined via hierarchical levels (Tarski's solution).
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    Related

    Arithmetical truth cannot be defined in arithmeticEven with unrestricted self-reference, systems avoid paradox if truth is defined...Formal systems with restricted self-reference (like Peano arithmetic) remain con...Self-reference alone is harmless; 'this sentence has five words' refers to itsel...
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    Self-referential sentences like 'this sentence is false' create paradox regardle...The paradox fundamentally depends on what 'true' means—different truth definitio...The paradox persists across natural language and formal systems, suggesting self...

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