Basic logic tends to be overlooked even as it underlies the most basic technologies of today’s civilization. But has the last word been uttered on the matter, between modus ponens and syllogisms? Not according to Douglas Heaven in NewScientist (30 June 2018, paywall):
One major work-in-progress is an assumption Aristotle called “the most certain of principles”: that things are either true or not true. Inconveniently, this makes conventional logic blow up on occasion. Take the sentence “this sentence is false”: is that true or false?
Neither true nor false
Many-valued logics get round this by allowing statements to be true, false, possible – and more. Paraconsistent logics provide ways to deal with statements that are both true and false, contradictions that would yield nonsense in more traditional logic.
As logic evolves, it is becoming closer and closer to what’s really in our heads – and, paradoxically, harder to understand. Logic has also suffered as the internet and other media have sped up the spread of emotional arguments, says Gabbay. “Illogical arguments are more effective now than logical ones.”
His own pet project is to bring logic out of our heads and closer to our hearts, by developing a formal system of logic, plus rules for reasoning with it, that can capture emotional aspects of argumentation, including personal attacks, appeals to “common sense”, straw-man arguments and so on. “All of the things that were considered to be logical fallacies up to now urgently need to be modelled,” he says – the next stage in the evolution of logic as our guide to truth.
I wish he’d hurry. Having a formal approach to writing arguments which are not only formally correct but are also convincing to people who don’t care about being formally correct would certainly be nice.
