ALL men are mortal. Socrates is a man. Therefore Socrates is mortal. By inventing logic, Aristotle wound up Western thought and sent it clattering down a 2000-year path to science.
Little of what we know about the world comes from direct observation (see “How to think about… Scientific truth”). It is based mostly on drawing inferences from other things we know. Aristotle never had to ID a body to infer that Socrates was mortal. Crick, Franklin and Watson never saw a DNA helix, just its X-shaped X-ray diffraction pattern. Molecules that produce X-shaped diffraction patterns are helical. DNA has an X-shaped diffraction pattern. Therefore DNA is helical.
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Logic, from Aristotle’s syllogism onwards, gives us scaffolds for trustworthy reasoning that help us structure our thoughts. But logic doesn’t by itself guarantee truth. All yellow things are made of cheese. The moon is yellow. Therefore the moon is made of cheese. If your premises are false, your conclusions are likely to be, too.
Pushing the boundaries of logic further into truth is the job of logicians such as at King’s College London. “When the Almighty created us, he had a big lump of logic and he sprinkled bits of it into our heads,” he says. “I regard my job as reconstructing that big lump.”
To capture messy human thought more precisely, in the 19th century logicians began to abandon natural language with all its potential ambiguities. George Boole, a self-taught English mathematician, developed a kind of algebra in which variables had truth values – true or false – rather than numerical ones.
That set the course for the next 100 years. Today, Boole’s logic is the on-off, 1 or 0 beat at the heart of every digital computer. “Mathematical logic led directly to computing,” says Gabbay. “Logic serves computer science in the way that maths serves physics.”
That’s what you might call applied logic, though. In many a university philosophy department, the pure logicians are still beavering away, burrowing further down into what logic actually can say about truth.
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.
This article appeared in print under the headline “How to think about… Logic”
