A
@BlameDutchie @FediTips @gotofritz
Oh ffs, even the OED recognizes fedi's use of the word "algorithm". Bad enough to criticize someone's word choices when you obviously know what they mean, but to do it when they're actually using the word in a widely recognized sense is just 
Excellent post! It reminds me of this (slightly paraphrased) line of Keats: "axioms are not axioms until they are proved upon our pulses."
On the practical impossibility of reasoning from first principles, here's a lesser-known but much more modern than Aristotle example of this phenomenon, which shows that this is very much still a problem in science.
In 1995 David Auckley and John Cleveland axiomatized origami and proceeded to prove that the set of points in the plane constructible via origami is a proper subset of the points constructible via straightedge and compass.
However, they weren't origami experts and their axioms missed a number of real-life possible folds. More realistic axioms were proposed by various other mathematicians, now known as the Huzita-Hatori axioms. Using these, which reflect actual real-life folding practice, it turns out that the set of points constructible via origami is actually strictly larger than the straightedge-compass constructible points. In particular, a whole new family of polygons becomes constructible.
References:
[1] Auckley and Cleveland: https://arxiv.org/abs/math/0407174
[2] Huzita-Hatori axioms: https://en.wikipedia.org/wiki/Huzita%E2%80%93Hatori_axioms
It's the Gell-Mann amnesia effect all over again.
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The Gell-Mann amnesia effect is a claimed cognitive bias describing the tendency of individuals to critically assess media reports in a domain they are knowledgeable about, yet continue to trust reporting in other areas despite recognizing similar potential inaccuracies.
