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Am Fri, 11 Jul 2025 10:30:35 -0500 schrieb olcott:It is flat out nuts to assume that "A and ~A are both true".On 7/11/2025 3:43 AM, Mikko wrote:How so? If A and ~A are both true, B also is.On 2025-07-10 14:09:55 +0000, olcott said:*This Wikipedia quote*On 7/10/2025 4:05 AM, Mikko wrote:>On 2025-07-09 14:16:44 +0000, olcott said:Then contradiction proves falsehood.On 7/9/2025 9:04 AM, joes wrote:>Am Wed, 09 Jul 2025 07:31:59 -0500 schrieb olcott:>On 7/9/2025 3:29 AM, Mikko wrote:>On 2025-07-08 14:18:32 +0000, olcott said:On 7/8/2025 2:41 AM, Mikko wrote:Should only false conclusions be derivable from false premises?True conclusion from false premeises is fairly common. But thatIt proves that logic is fundamentally incorrect on this point.
is not relevant.
Logic must be a sequence of truth preserving operations or it is
wrong.
False premises must be immediately rejected.
Often one must work with sentences that are not known to be true but
not known to be false, either.
>
That's right: if a contradiction is inferred then at least one of the
preimises is false. But that does not tell which premise is false.
>
>
> the principle of explosion is the law according to which *any
> statement can be proven from a contradiction*
>
Here is the exact meaning of:
*any statement can be proven from a contradiction*
∀x (⊥ ⊢ x).
>
Is proven to be incorrect in that it diverges from truth preserving
operations.
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