How to think about… Logic | Tech News
Is the sentence ‘this sentence is false’ true or false? The difficulty our messy brains have answering that goes to the heart of what logic is – and isn’t
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.
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 Dov Gabbay 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 …