315 | Branden Fitelson on the Logic and Use of Probability

Hello, everyone, and welcome to the Mindscape podcast. I'm your host, Sean Carroll. One of the things that I always like to say about science and how it gets done is that science never proves things. This is something that is an important feature of science, especially in the modern world where what science does, how it reaches conclusions, how trustworthy it is, these are all under contestation by different parts of society. So it's important to understand what science is and how it actually reaches its conclusions. And the the claim that science never proves things, which is something that most scientists would go along with me on, comes from a comparison to real proof in mathematics or for that matter in logic. You know, most scientists have taken some math classes at least enough to know what it means to prove something in the old fashioned sense of Euclid and geometry or Aristotle and logic proving a conclusion from some well articulated premises. In the philosophical study of logic, this is known as deductive reasoning. You have some premises and you reach a conclusion. And science just doesn't go that way. Right? Science looks at the world. It looks at all sorts of things in the world, and it tries to figure out what the patterns are that the world follows. Always knowing that tomorrow, you might do a new experiment that will overturn your best guess as to what the pattern was, or maybe someone will do something as simple as just thinking of a better pattern. Right? A theoretical physicist coming up with a better idea for what the laws of physics really are. So if science doesn't prove things, if it just sort of comes closer and closer in some sense to getting it right, then what is what's going on? You know, one very common idea about what's going on is inductive logic rather than deductive logic. In inductive logic, we begin to see a pattern. You know, a, b, c, d, e, f, g. The next one is probably gonna be h. Right? Because we think that probably you're just mentioning the alphabet in alphabetical order. But there's all sorts of paradoxes that come up when you do inductive logic, like, how do you know that it's not a, b, c, d, e, f, z? That's a that's a sequence of letters that you that you could have. My old math teacher in college used to hate those SAT questions or standardized test questions that would give you a series of numbers and ask you to guess the next one. Because he said, I can I can make any number I want? I can come with a formula that would give you any number I want after the ones that you already showed me. So philosophers, unsurprisingly, are very interested in making as rigorous and careful as possible this idea of either induction or whatever should replace induction as the logic of understanding …