One of the ways in which I believe the education system fails our kids is through inadequate instruction on what constitutes evidence and how to make a persuasive argument. Pascal-Emmanuel Gobry wrote an article in National Review entitled The Errors of the Militant Atheist in which he addresses the question of evidence, among many other things. I recommend that you read the whole thing. I liked the passages about evidence so much that I’m posting them here. I add the bold font for emphasis:
“Evidence for a type of claim must be of the same kind as that for the claim being made.”
Science, at least in the sense defined by the scientific revolution, is a process for formulating non-obvious, reliable predictive rules through controlled experiment. This means that not all claims are scientific claims and only a specific type of claim is scientific. Scientific claims are claims that can be validated or falsified through a scientific process — namely, controlled experiment. When the physicist Wolfgang Pauli famously dismissed a paper as “not even wrong,” that was what he meant: Because the claim made could not be adjudicated by scientific means, it did not even qualify as a scientific claim, and therefore could not even be proven wrong.
Some people claim that only scientific claims are meaningful, but this is clearly nonsense. Scientific claims are one specific type of empirical claim, but, for starters, there are plenty of other meaningful empirical claims one can make.
The claim “I had John over for dinner at my house last night” is clearly an empirical claim, clearly meaningful, and yet clearly not scientific. One cannot design a scientific experiment to prove the claim, but one can still produce evidence for (“Here’s a selfie we took over dessert”) or against (“But Sally said she saw you down at the pub last night”). But for the evidence to be meaningful, it has to be of the same kind as the claim being made.
Another type of empirical claim is “Julius Caesar invaded Gaul.” What type of empirical claim is this? It’s a historical claim. It’s not a scientific claim — even if you could reproduce the invasion of Gaul in a lab, it wouldn’t tell you anything about what actually went on over 2,000 years ago. But it’s clearly a meaningful claim, and one that can be empirically investigated — using evidence of the same kind as the claim itself, that is to say, historical evidence. Similarly, then, of the claim “Jesus of Nazareth was publicly executed, and found three days later alive, possessed of a body, with open wounds and yet uninconvenienced by them.” Christians do, in fact, provide voluminous evidence to support the claim. Maybe the evidence is not enough to prove the claim, but it is clearly admissible evidence — historical evidence.
Now, are there meaningful non-empirical claims?
Well, yes. There are claims of logic, for starters.
The claim (a + b)^2 = a^2 + b^2 + 2ab is not an empirical claim in any meaningful sense of the word. It is a logical claim, and a specific type of logical claim — a mathematical claim. The evidence for or against it must be of the same type: mathematical. You can’t design an experiment to prove it, and it wouldn’t make sense to say that it’s true because Caesar invaded Gaul. It wouldn’t make sense either to say that all the great mathematicians have believed it — you have to actually respond to the claim on its merits.
Are there non-mathematical claims of logic? Well, yes. There are the laws of logic, such as the law of non-contradiction. And then there are metaphysical claims. Metaphysical claims are claims based on a certain type of logic — metaphysical logic. For example, the claim that a universe of finite causes cannot explain its own existence and so must find its source in some infinite ground of existence, an uncaused cause, is a logical claim, which can be debated using a specific set of logical tools, just like mathematical claims. Maybe it’s wrong. But it’s a logical claim, not a scientific claim.