Tag: conjectures

Science’s social framework

Science is a special kind of endeavour. Philosophers have been seeking to specify in what ways it is special for almost four hundred years (at least since Francis Bacon). Karl Popper is known for his attempt to characterise it negatively, as refutable conjectures about the world. But this is not the sum of what he said. What is and is not refutable requires discussion, which is a social process; if conjectures about the world are to be refuted a social framework is needed for their testing. Popper’s negative method requires institutions and traditions. [9]

Science: more or less likely

It is not unscientific to make a guess, although many people who are not in science think it is. Some years ago I had a conversation with a layman about flying saucers—because I am scientific I know all about flying saucers! I said “I don’t think there are flying saucers”. So my antagonist said, “Is it impossible that there are flying saucers? Can you prove that it’s impossible?” “No”, I said, “I can’t prove it’s impossible. It’s just very unlikely”. At that he said, “You are very un­scientific. If you can’t prove it impossible then how can you say that it’s unlikely?” But that is the way that is scientific. It is scientific only to say what is more likely and what less likely, and not to be proving all the time the possible and im­possible. [165-6]

The art of explanation

By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the “truth” but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity—to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs—you deny them mathe­matics itself. So no, I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m com­plaining about the lack of mathematics in our mathematics classes. [29]