Definition: The principle of the uniformity of nature is used to justify both inductive reason generally and scientific research in particular. It can be understood as simply arguing that "the future will look like the past." Thus, however nature has acted in the past is pretty much how we can expect it to act in the future.
Science relies heavily upon this premise of uniformity because, without it, it would not be possible to infer from past events what we can expect to happen in the future. Scientific prediction and scientific theorizing would simply not be possible without uniformity.
More generally, induction itself relies upon uniformity because that is what allows us to take particular cases and infer from them general rules and principles. However, if induction relies upon the uniformity of nature, then the uniformity of nature cannot itself rely upon inductive reasoning.
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What is an Argument?
It helps to know what, exactly, an argument is before you can critique one and tell what is wrong with it. Sometimes, people say they are making arguments when they are not!
How do you critique an argument?
Assuming that we have established that we have an actual argument, the next step is to examine it for validity. There are two points on which an argument might fail: its premises or its inferences.