The Banality of Logic

by F.

It’s pretty natural to think of mathematics as “modeling” the world. For instance, Jane has a lemonade stand and keeps track of how many glasses of lemonade she sells at different prices. She notices a pattern in the data: after a certain price, she sells fewer glasses. She draws a graph. If she puts the price too high, she infers from the model (the graph, or its quadratic equation), she’ll sell zero glasses. Simple and natural.

I think arguments can be considered models, too. Most arguments we care about are about the world. For instance, here’s an argument: If the government raises taxes, then people will consume more leisure time; more leisure time is good; therefore the government should raise taxes. Yes, every once in a while you come across a purely “analytical” argument (a square has four sides; therefore a square has at least one side). But it’s rare and generally uninteresting.

If you read many arguments, though, one thing strikes you again and again: how little the logic of the argument matters. This is because most arguments we care about are empirical. If someone was to make the argument above about taxes, we wouldn’t spend much if any effort worrying about the (apparently first order) logic of the argument. Rather, we would look at the premises. Is it really true that tax increases raise consumption of leisure time? Who says? Under what conditions?

And, more tellingly, even if someone made the argument with faulty logic, this hardly refutes the conclusion in any realistic sense. Yes, maybe in a debate class. But not in the real world when it comes to empirical arguments. Take a look at the argument I made above. The conclusion does not follow from the premises; it’s a sort of mish-mash that resembles the fallacy of affirming the consequent. Yet that’s not particularly exciting. The issue is the phenomenon in the world that is being argued about.

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