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/sci/ - Science & Math

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>> No.11891222 [View]
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11891222

Disproof of LNC:
⊢S := S=false
⊢lnc := ¬(a^¬a)
⊢(S=false)=false
⊢S=true
⊢S=(true=false)
⊢S=false
⊢S^¬S
⊢¬lnc

>> No.11882383 [View]
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11882383

Disproof of law of noncontradiction

Let S := ¬S. By substituting S into ¬S we get ¬¬S, which is S. So S implies S and not S.

Assuming the law of noncontradiction, S and not S is false. Therefore the law of noncontradiction says ¬S. However, substituting S into that, the law of noncontradiction says ¬¬S, so the conclusion is S and ¬S. The axiom of law of noncontradiction results in a contradiction, so the law of noncontradiction is false

>> No.11882378 [DELETED]  [View]
File: 69 KB, 1000x750, B1VfPlcXC2S._CR0,0,3840,2880_._SL1000_[1].jpg [View same] [iqdb] [saucenao] [google]
11882378

Disproof of law of noncontradiction

Let S := ¬S. By substituting S into ¬S we get ¬¬S, which is S. So S implies S and not S.

Assuming the law of noncontradiction, S and not S is false. Therefore the law of noncontradiction says ¬S. However, substituting S into that, the law of noncontradiction says ¬¬S, so the conclusion is S and ¬S. The axiom of law of noncontradiction results in a contradiction, so the law of noncontradiction is false

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