The issue with that comment was that you were introducing off topic points that weren't previously discussed or defined. You mentioned assistance while mentioning "in isolation" as the basis for my analysis which is the only point in which my analysis could possibly be valid. If you start introducing variables outside the discussion it makes it hard if not impossible to seriously discuss the impact of a policy change or some market force change. For instance we can see that in general as supply increases the price will drop absent other factors. There are tons of factors that could be introduced to make my minimum wage argument invalid. For instance if the market wage is never practically below $5 then a minimum wage of $3.60 is unlikely to have an outcome (unless something changes).
The argument against the minimum wage is in the realm of deductive reason and not something you look around for proof of or proof against. It's basically the economics equivalent of 1+2=3. If there are problems with that equation we need to analyze it in its' space and not look around for cases when we think 1+2 != 3. The problem with verifying laws of economics is that we don't know what we're seeing the effects of in reality. Cultural, weather, moods, government policies, etc. could impact what we're seeing in data without it being clear why or how. Empiricism can inform our analysis or can give us new routes to inquiry on but it can't be used to argue for or against the laws of economics as we understand them. I'd avoid reading economic studies of anything for this very reason.
My point in pulling in other assistance was that we are not implementing a minimum wage in an environment without other assistance so your analysis of what happens when we implement a minimum wage in an environment without other assistance doesn't represent the real world.
Regarding the second half of your comment, it's certainly true that there can be confounding variables, but I think avoiding empiricism does far more harm to reasoning than relying upon it. There is an infinity of internally consistent models. Most of these will have nothing to do with reality. In order to tell which actually represent the world we're living in, we need to look at the world. Intuition alone has proven a poor guide in most other sciences.
The argument against the minimum wage is in the realm of deductive reason and not something you look around for proof of or proof against. It's basically the economics equivalent of 1+2=3. If there are problems with that equation we need to analyze it in its' space and not look around for cases when we think 1+2 != 3. The problem with verifying laws of economics is that we don't know what we're seeing the effects of in reality. Cultural, weather, moods, government policies, etc. could impact what we're seeing in data without it being clear why or how. Empiricism can inform our analysis or can give us new routes to inquiry on but it can't be used to argue for or against the laws of economics as we understand them. I'd avoid reading economic studies of anything for this very reason.