Sorry for the delay in responding to your query, Dean. I’ve just got home to Ireland having attended the 2013 Austrian Economics Research Conference at Auburn. I had a wonderful time (as usual) not least occasioned by the company and conversation of the proprietor of this Classroom! While I was away normal service was somewhat disrupted but I’m back at work now. However, I’m still a little jet-lagged so let’s hope I don’t make some madly egregious blunder! And I know you addressed your query to all and sundry not just to me so let’s see what others have to say.
I’m not sure there’s a logical fallacy of any kind here though a defender of a minimum wage (MW) might respond that he’s promoting a minimum (underscored) wage, not a large, handsome or quasi-maximum wage (as would be the case with $100 per hour or $1,000 per hour) and so might take exception to your rhetoric.
The economic argument against MW is simple and elegant and takes the form of a trilemma: (1) If MW equals the (discounted) marginal value product (DMVP) of labour, then it’s redundant; (2) if MW is less than the DMVP then it’s again (economically) pointless; (3) if MW is greater than the DMVP then it will reduce employment (actual and/or potential), labour-retention laws to one side. The more MW exceeds DMVP, the greater the unemployment effect – hence the typical argument strategy you started with.