OK, time for some armchair philosophy of science!
You often hear about how logic and deductive reasoning are at the heart of science, or expressions that science is a formal, logical system for uncovering truth. Many scientists have heard definitions of science that include statements like “science never proves anything, it only disproves things” or “only testable hypotheses are scientific.” But these are not actually reflective of how science is done. They are not even ideals we aspire to!
You might think that logic is the foundation of scientific reasoning, and indeed it plays an essential role. But logic often leads to conclusions at odds with the scientific method. Take, for instance, the “Raven Paradox”, expertly explained here by Sabine Hossenfelder:
Sabine offers the “Bayesian” solution to the paradox, but also nods to the fact that philosophers of science have managed to punch a bunch of holes into it. Even if you accept that solution, the paradox is still there, insisting that in principle the scientific method allows you to study the color of ravens by examining the color of everything in the universe except ravens.
I think part of the problem is that the statement “All ravens are black” sounds like a scientific statement or hypothesis, but when we actually make a scientific statement like “all ravens are black” we mean it in something closer to the vernacular sense than the logical one. For instance:
- “Ravens” is not really well defined. Which subspecies? Where is the boundary between past (and future!) species in its evolutionary descent?
- “Black” is not well defined. How black? Does very dark blue count?
- “Are” is not well defined. Ravens’ eyes are not black. Their blood is not black.
Also, logically, “all ravens are black” is strictly true even if no ravens exist! (Because “all non-black things are not ravens” is an equivalent statement and trivially true in that case). Weirdly, “all ravens are red” is strictly true in that case, as well! This is not really consistent with what scientists mean when we say something like “all ravens are black”, which presumes the existence of ravens. We would argue that a statement like that in a universe that contains no ravens is basically meaningless (having no truth value) and actually misleading, not trivially true, as logic insists.
So the logical statement “all ravens are black” is supposed to be very precise, but that is very different from our mental conception of its implications when we hear the sentence, which are squishier. We understand we’re not to take it strictly literally, but that is exactly what logic demands we do! And if we don’t take it in exactly the strict logical sense, then we cannot apply the rules of formal logic to it. This means that the logical conclusion that observing a blue sock is support for “all ravens is black” does not reflect the actual scientific method.
You might argue that “black” and “raven” are just examples, and that in science we can be more precise about what we mean and recover a logical statement, but really almost everything we do in science is ultimately subject to the same squishiness at some level.
Also, and more damningly:
If we were to see a non-white raven—one that has been painted white, an albino, or one with a fungal infection of its wings— we would not necessarily consider it evidence against “all ravens are black”! We understand that “all ravens are black” is a general rule with all kinds of technical exceptions. Indeed, a cardinal rule in science is that all laws admit exceptions! Logically, this is very close to the “no true Scotsman fallacy,” but it is actually great strength of science, that we do not reach for universal laws from evidence limited in scope, only trends and general understandings. After all, even GR must fail at the Planck length.
So even the word “all” does not have the same meaning in science as it does in logic!
More generally, in science we follow inductive reasoning. This means that seeing a black raven supports our hypothesis that all ravens are black. But in logic there is no “support” or “probability,” there is only truth and falsity. On the other hand, in science there are broad, essential classes of statements for which we never have truth, only hypotheses, credence, guesses, and suppositions. Philosophers have struggled for years to put inductive reasoning on firm logical footing, but the Raven Paradox shows how hard it is, and how it leads to counter-intuitive results.
I would go further and argue that strictly logical conclusions like those of the Raven Paradox are inconsistent with the scientific method. I would simply give up and admit: the scientific method is not actually logical!
After all, science is a human endeavor, and humans are not Vulcans. Logic is a tool we use, a model of how we reason about things, and that’s OK: “All models are wrong, but some are useful.” Modeling the Earth as a sphere (or an oblate spheroid, or higher levels of approximation) is how we do any science that requires knowledge of its shape but it’s not true. Newton’s laws are an incredibly useful model for how all things move in the universe, but they are not true (if nothing else, they fail in the relativistic limit).
Similarly, logic is a very useful and essential model for scientific reasoning, and the philosophy of science is a good way to interrogate how useful it is. But we should not pretend that scientists follow strict adherence to logic or that the scientific method is well defined as a logical enterprise—I’m not even sure that’s possible in principle!