/sci/ - Science & Math

[Anonymous No.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

[Anonymous No.11882390]

>>11882383
Proof that integers don't exist:
Let [math]n := n+1[/math].
Then [math]n[/math] equals its own succesor, in clear violation of Peano's axioms.

[Anonymous No.11882398]

>>11882390
If all self referential statements are false, then LEM is false because it refers to itself.

[Anonymous No.11882403]

>>11882383
Equivalence is only valid when all variability is accounted for.

[Anonymous No.11882463]

>>11882403
Expand upon this?

[Anonymous No.11882476]

>>11882403
So you're saying S has no truth value. That doesn't make the proof invalid

[Anonymous No.11882478]

>>11882398
>If all self referential statements are false
who ever said that?
its taken as an axiom in epistemological systems that "all axioms are true"

[Anonymous No.11882481]

>>11882478
>muh set of sets

[Anonymous No.11882486]

>>11882478
Yes so self referential statements are ok

[Anonymous No.11882491]

>>11882486
They're okay when they don't lead to contradictions.

[Anonymous No.11882508]

>>11882383
>Let S := ¬S
Okay. What’s the point of the rest of the text you added after?

[Anonymous No.11882560]

>>11882383
Let X be false
Then X is false

Amazing.

[Anonymous No.11882585]

>>11882383
Even though you're just presupposing your conclusion as others point out (S = ~S), you are also using a proof by contradiction to complete your point, which would only be deductively valid if noncontradiction is necessary.

I came here because I wanted people *less* retarded than /v/ and /pol/, not more..

[Anonymous No.11882756]

>>11882383
Retard

[Anonymous No.11882763]

>>11882383
>The axiom of law of noncontradiction results in a contradiction, so the law of noncontradiction is false

[Anonymous No.11882831]

imagine doing proofs in english instead of Hilbert calculus or sequent calculus