The case against boolean logic
1 points by dhruvp
1 points by dhruvp
I do not think using the law of excluded middle in proofs is the source of authoritarianism.
Not the source, but a strongly associated urge which can't be decoupled from the effects of authoritarianism. Quoting the opening paragraph from Wikipedia, "authoritarianism is a political system characterized by the rejection of political plurality…" An embrace of LEM doesn't make an authoritarian, but you're not likely to find many authoritarians who reject it. Keep in mind that LEM is false in general; it's a non-theorem in effective topoi and refutable in Johnstone's topos, for example.
I am reminded in particular of the dinosaur-style black-and-white thinking exhibited by foundations-of-maths folks when talking to category theorists. The category theorists know that there are many topoi with many different ways to approach maths, but the foundations-of-maths folks insist that classical logic and (fragments of) century-old set theories are the only working path.
To combat such propaganda techniques always remember the two rules of the contexts:
There are many of them. No-one gets to decide which is more important.
Is this true in all contexts? This seems like awfully Boolean thinking; in my context some contexts are more important than others!