Talk:Axiomatic system (logic)
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Conjunction introduction and elimination
editAm I reading this right?
A -> B -> A ^ B
I'm not seeing any mention of the branching rule used. This should be explicitly mentioned somehow. I'm assuming left branching and reading it this way: "(A implies B) implies (A and B)"
This would mean that if we accept that A implies B we have to accept B. What? And it means that if we accept that A implies B we have to accept A. What? Something seems to be wrong here.
If we assume some sort of right branching scheme it could be: "A implies (B implies (A and B))"
Which seems fine. But right branching schemes require reading all the way to the end of a potentially very long expression before you can even figure out how to group terms, and then going back to the beginning of the expression and employing the previously discovered grouping while reading the expression. Could this really be how a standard notation for a Hilbert system works? It seems to me there must be something wrong here. Perhaps the expression in question was formulated incorrectly. But either way, to avoid confusion, some convention should be employed to allow a reader to figure out notation conventions. Perhaps a section on notation should be included in each article that covers a logical system. If Wikipedia employs certain agreed upon conventions about logical notations, then one or more articles about those conventions should be crafted and those articles could be linked to in a sufficiently prominent way from articles about logical systems. Readers should not have to guess, and notation systems used should be made explicit somehow. Comiscuous (talk) 19:48, 19 December 2021 (UTC)
Archived old talk page, redid much of the article
editI have archived all talk page topics that were more than five years old. I moved the article because "Hilbert system" is not what axiomatic systems in logic are always called, or even usually called, or even often. I also redid its first section, changing the part that someone made up from scratch into something that is actually supported by WP:RS, but also moving some the long, unsourced consistency and completeness proofs from Propositional calculus to here, because they are too long to go there anyway, and hopefully they can be changed into properly sourced proofs at some point. I removed the old maintenance template and added other ones to reflect the article's new range of issues.Thiagovscoelho (talk) 02:32, 2 July 2024 (UTC)