Answer by Lereau for Excluded middle, double negation, contraposition and...
Using the results form the paper mentioned in the update, there is another way we can argue why $\mathsf{Peirce} \rightarrow \mathsf{Explosion}$ can not be possible.Assume it holds, then it means we...
View ArticleAnswer by Potato44 for Excluded middle, double negation, contraposition and...
$\mathsf{Peirce}$ is stronger than $\mathsf{LEM}$, but it happens to be interderivable with generalised excluded middle $(\mathsf{GEM})$$$\mathsf{GEM} := \forall A~B. ~\vdash_m A ~\lor~ (A \rightarrow...
View ArticleExcluded middle, double negation, contraposition and Peirce's law in minimal...
Minimal logic does not assume any falsity $\bot$ or negation $\neg$, so the above mentioned laws can (apart from Peirce's) not be stated as usual. However, if we fix some propositional variable $F$, we...
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