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Peirce's law
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Revision as of 16:45, 27 July 2009
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16:45, 27 July 2009
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A stronger form of Peirce's law also holds, in which the final implication is observed to be reversible:
A stronger form of Peirce's law also holds, in which the final implication is observed to be reversible:
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<math>((p \Rightarrow q) \Rightarrow p) \Leftrightarrow p</math
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<math>((p \Rightarrow q) \Rightarrow p) \Leftrightarrow p</math>
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===Proof 1===
===Proof 1===
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Given what precedes, it remains to show that:
Given what precedes, it remains to show that:
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But this is immediate, since <math>p \Rightarrow (r \Rightarrow p)</math> for any proposition <math>r.\!</math>
But this is immediate, since <math>p \Rightarrow (r \Rightarrow p)</math> for any proposition <math>r.\!</math>
Jon Awbrey
12,080
edits