Hume accepted that there are laws of nature, or at least that we must believe in them as a matter of habit. However, he denied that we have any rational basis for demonstrating any law-like behavior in nature. I argue that Hume's assertion is demonstrably false.
Prove A: There are laws of nature.
Assume ~A: There are no laws of nature.
~A --> B: If there are no laws of nature, then all probabilities are inscrutable.
~B: There are probabilities that are scrutable.
Hence, ~~A: by modus tollens.
Therefore, A: There are laws of nature.
In short, if there are no probabilities that can be applied to the workings found in nature, then there are also no probabilities that can be applied to Hume's skepticism about there being laws of nature. Hume's skepticism, therefore, is inscrutable and hence, self-defeating.