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All EDI is an API (of a very specific and defined type).

All API are not EDI.

Therefore API !== EDI

All couches are furniture, but couches are not "equivalent" to furniture.

+1 I like your syllogism. API isn't EDI if you apply any logic to determine this. The article's goal was to dispel the typical pitting of EDI vs. API by showing that EDI can be API.

All of Alma Cogan is dead, but only some of the class of dead people are Alma Cogan.

Correct. And Alma Cogan is dead, but being Alma Cogan is not equivalent to being dead. They have other properties that differ. This article claims the two are equivalent.

https://youtu.be/FZqs36C5sgM?t=24s

Dang, I missed the reference. Thanks for the link.

And while obviously my argument is overly simplified to make a short comment, I find the article's arguments ridiculously absurd. I suppose I shouldn't expect more from a page that's just marketing material for their company.

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