You often hear debaters talking about proof, and it's pretty clear in most cases they don't know what they're talking about. So as a public service, Noble Readers, I thought I would offer my two pennies worth on the topic.
As anyone who has a taste for hard liquor will tell you, there are different sorts of proof, but we might, on this occasion confine ourselves to two in particular, and to draw the distinctions between them. First let's look at "mathematical proof." Mathematical proof is the sort that the Greek geometer Euclid liked to demonstrate. It consists of stating a set of initial assumptions which are regarded as facts, and using logic to build on those assumptions. The result is a new fact which must be inescapably true if the assumptions you begin with are true.
This is all very well in mathematics, which is a subject that lives in its own little idealized world. But what about the "real" world? Science must live in the real world, because the whole idea of science is to describe the real world. Science uses mathematics help it to do this. A lot of the time it uses a branch of mathematics called "statistics" to work out what is likely to be true or false, at other times it will attempt to describe the real world using equations that express physical laws. One example of the latter are the equations that describe the way an object with a given mass falls in a gravitational field when there is no air present to alter its motion. You can, if you feel it necessary, alter those equations to descibe the way the same object moves when there is air present. Or you can alter the equations another way to describe how the same object would move if it were dropped, not on Earth, but say, on the moon or on Mars.
But to return to the idea of scientific proof: science doesn't prove facts like mathematics proves facts. The way science works is by excluding concepts that can be shown to be wrong. Let me illustrate: science does not say things like "the Earth is round," rather it says things like, "the Earth cannot be flat because ..." and then comes a set of observations that show why it cannot be flat. Questions that are amenable to scientific investigation, therefore, have to be "falsifiable," that is, open to being proved false, a condition famously set forth by the philosopher Karl Popper.
So next time you hear someone say "science has proved that" something or other is so, you know they don't know what they're talking about.