Logic and Minimum Wage

This is not an economical study that tries to confirm or disconfirm claims about the relationship between minimum wage and the price of goods. This is a mere refutation of a particular low-quality (invalid) argument that’s been used by people who are more interested in bolstering an ideology than they are in attempting to discard bad reasoning habits and falsehoods. If you believe to be in possession of a counterexample to the claim that raising minimum wage tends to influence the price of goods in an upward direction, then you’d benefit greatly from deploying one that is not internally flawed.

The following graphic, posted by The Daily Kos some time in 2016, received a lot of support and defense by people on the left. This is hilarious, especially because the argument is utterly invalid:

Invalid Argument

“If raising the minimum wage increases prices, how come prices have continued to go up even though the minimum wage hasn’t been raised in years?”

The Leftist who hasn’t grasped basic logic thinks she’s found a counterexample to the view that raising the minimum wage increases prices. Her alleged counterexample is that prices have continued to go up even though the minimum wage hasn’t been raised in years. This is a misunderstanding, on her part; it is no counterexample at all. I will illustrate why this is so.

To be clear, she is not mistaken about the content conveyed in her attempted refutation; prices do often go up independently of any increase in minimum wage. Her mistake is a logical one—it is an error related to the structure, rather than the content, of what she says.

A person who views the above graphic as convincing is likely also a person who senses the following to be a valid inference:

This amounts to: “If raising minimum wage increases prices, then not raising minimum wage implies that prices won’t be increased” (which is, presumably, what she takes the original conditional statement to entail, since her snarky rhetorical question addresses not the true meaning of the statement, but a mistaken interpretation of it). Unfortunately, however, this thinking is invalid. Here is the truth table to prove it:

We cannot infer the latter from the former, because the structure of the argument prevents true premises from guaranteeing a true conclusion. That’s the textbook definition of invalidity! A more concrete way of putting all of this is: a person might assert that raising minimum wage increases prices, but in so doing, he is not implying that a hike in minimum wage is the only thing that might influence the price of goods (an accountant’s decision to increase prices, the scarcity of goods, etc).

Of course, the person who has never encountered formal logic will probably not argue about or even have opinions about the nature of the material conditional or the truth conditions thereof. This misunderstanding is essentially a misunderstanding of the conditional (“if…then” statement); she assumes that the person who thinks that raising minimum wage increases prices is saying something much stronger than he is intending: that minimum wage and the price of goods are inextricably entwined, for example.

But why would she think that? Is it because she hasn’t grasped the distinction between a necessary condition, a sufficient condition, and one that’s both necessary and sufficient? This would certainly lead to confusion regarding the material conditional used in the graphic. Perhaps instead the issue is not really a misunderstanding but simple ignorance; if she can’t even begin to conceive of what the study of logic aims to do, then she won’t be able to distinguish shit from Shinola®. But maybe the real issue is that she’s clutching onto a dogma and perhaps that she’s never learned to evaluate or justify any of her beliefs. If that’s the case, then the praise she shovels onto the argument is really veiled worship of a cherished ideology.

So, if the Leftist really wishes to refute the claim in question, she will need to come up with something better than what’s offered in the graphic. I mean, how can we expect her to dismantle the patriarchy if she can’t even think straight?