Mathematical Logic is a queer field. Its ways are abstract yet rigorous, its results incredibly simple yet often surprising. It is also a much under-appreciated field – its concepts and results, besides being so fundamental to the mathematical formalism we are familiar today, is the only reason why we have computers.
Logic also is an ironic field, in fact, quite profoundly so.
Look around, look at the real world, in all it’s complexity and ambiguity; and try to frame a statement about it that is purely binary – a statement that is either True or False entirely, but never in between.
The world is not black and white. It’s really, really gray. — Joshua Topolsky
You’ll probably be surprised that you are unable to do so. The real world is never black-and-white, there is little about the world that fits an absolute “yes” or “no”.
The real world doesn’t afford the luxury of being so flawlessly deterministic. Things are often indeterminate. Physical quantities settle down at intermediate values. Things come in whole or part. It’s a whole mess of “almost”, “somewhat”, “quite” and “fairly”. Mapping this gray, gray world to an abstract, black-and-white model is seemingly a crude abstraction to make – almost shockingly so. In this regard, the entire field of Logic feels so badly grounded.
Yet here we are, with a profoundly developed field of study that frames a large bodies of our scientific studies and technological endeavors; yet is nearly diametrically opposite to what we experience in the real world. If this isn’t irony, what is!