isn't Arnold's standard of scientific evidence strangely strict? Few results in economics rest on an "experiment or a naturally-occurring event where the results are extremely unlikely to occur unless X is true."
I thought I was simply stating in layman's terms the definition of statistical significance. That is the most commonly used approach in empirical work in economics. When we say, "I found that X has a significant effect on Y," we are saying that the probability of observing the sample results would be low if X had no effect on Y.
As an aside, these formal statistical tests often are not strict enough, in my opinion, because of specification searches (see Leamer's book of that title).
But take an example that uses no econometric(k)s. Gregory Clark wants to argue that in the 1800's British workers were much more productive than Indian workers. He asks that if British and Indian workers were close substitutes, why would you ship cotton from India to Britain, turn it into cloth, and ship the cloth back to India? Instead, if they were close substitutes, you would observe English companies building cloth factories in India in order to serve the Indian market more cheaply. In other words, shipping cotton to England and cloth back to India is something that is unlikely to occur if workers are close substitutes. Instead, it provides evidence, meeting my "strangely strict" standards, that British workers were more productive.
That is an example of a persuasive scientific argument.
As to global warming, I do not want to bet on global temperature going forward, because that is not the nature of my skepticism. I have no strong priors about the distribution of possible global temperatures going forward.
My skepticism is about the effect of man-made CO2 on global warming. If Bryan or anyone else can devise a bet that focuses on that parameter, then that would allow me to put money on my skepticism.