For instance, here's a case for the minimum wage presented by an (otherwise very knowledgeable, I'll grant) Post-Keynesian economist: http://socialdemocracy21stcentury.blogspot.com/2013/02/the-e...
It's pretty weak. The first two are very flimsy normative/moral arguments that, even if true, do not at all imply minimum wage is the solution over say, basic income, unionization, community-based mutual credit or a variety of other initiatives.
The third one is a can opener assumption. "Oh, minimum wage might work, but only in the case of Post-Keynesian full employment with buffer stocks of labor." You might as well speak of spherical cows in a vacuum. Followed by an unsourced claim about post-WWII prosperity being strictly due to Keynesian policies, when there's no consensus what factors exactly caused it.