Kennington writes "But Lemmon used only deduction rules, with no axioms." (1) I'm afraid he didn't undertand what he read. It is perfectly impossible to have a logical system with no axiom. By axiom I mean a $a statement with no $e statement.
It is often said that natural deduction has no axiom. But it is because the rule Gamma, ph |- ph is implicit. (Where Gamma it the stack of hypotheses.) And this rule is an axiom even though the unique axiom of natural deduction. (1) http://www.topology.org/tex/conc/diary.php?item=2019052201 -- FL -- You received this message because you are subscribed to the Google Groups "Metamath" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/metamath/2d18ac38-db8f-4981-b619-0552f5a7bcd8%40googlegroups.com.
