Continuing discussion of the conditional form, as expressed in Peirce’s logical graphs under the existential interpretation, incited me to cite one of my own essays on the subject.
The concept of logical implication or material conditional — its names are legion — is ever a source of logical bedevilment. It has proved no different in the discussion of Peirce’s logical graphs however much potential they bear for resolving the confusion if given the chance.
Here’s a link to an article on Logical Implication I originally wrote for Wikipedia where I attempted to synthesize the more coherent perspectives on the subject I had learned from various communities of usage over the years.
The last time I looked at the Wikipedia relic it had devolved into the usual run-of-the-mill obscurities of nominalism so let’s not go there. The Wikiversity edition still looks okay.
I’ve been meaning for years now to add the graphical representations — maybe these recent discussions will nudge me to do that …