Metaphysics is an interesting area of study for a few reasons, mainly because you can’t necessarily prove anything in it. You can’t prove that reality is real and you can’t prove that the truth is true. Obviously, humans are limited in their view of the world, so we obviously can’t answer questions outside of that view. That doesn’t stop some people from trying, like Plato and his Theory of Forms (which I’ve talked about far too many times). However, can we really prove deductive reasoning?
Obviously, we can. Math is a thing. Proofs exist entirely based on deductive reasoning. There’s no way math is false, right?
Well first, let’s think about deductive reasoning. Deductive reasoning is based on conditionals. They’re just if-then statements, or if and only if statements. The problem is, how do you prove those statements? Let’s go back to geometry. Geometry is based on theorems and postulates. Theorems are conditionals that can be proved, but what are postulates? Well, postulates are conditionals that cannot be proved. They are simply assumed to be true because of basic observations. However, that’s actually inductive reasoning. Can we prove that 2+2=4? No. That is a human construct based on observations. In our reality, someplace outside of the observable universe, 2+2 may not equal 4. It seems stupid to think about, and I agree. There is no way we can conceive that 2+2 might not equal 4. But my point is that this is actually inductive reasoning. We can never prove postulates but instead assume them based on patterns. And that is what inductive reasoning is. Inductive reasoning is reasoning where the conclusion is likely to happen, not absolutely certain. In our reality, we have so many instances of situations were 2+2=4. Therefore, we assume that it is always true, no matter what conditions. However, we do not have all instances of 2+2 in reality, which means one of those instances could defy that expectation. That means that the likelihood 2+2=4 is not 100%, because we don’t have all possible outcomes, we only have all observable outcomes.
You might argue that this conclusion is pointless, because it’s another one of those “we can’t prove anything” arguments that lead to an existential crisis. But these “we can’t prove anything” arguments may have some use. If we know that deductive reasoning is based on inductive reasoning, then what really is deductive reasoning? If it’s just inductive reasoning, then the outcome is not 100% probable, making deductive reasoning a false idea. However, we know there’s some difference between inductive and deductive reasoning, because we can sense it. There is a difference between saying 2+2=4 and predicting whether stock market prices will go up or down. And this shows the usefulness of these abstract “we don’t know everything” arguments. Knowing this, we could possibly redefine deductive reasoning unless a counterargument is presented. This shows that these arguments actually do have some real-life application. And that’s why it’s always important to keep them in the back of your head.