What should philosophers teach in quantitative reasoning courses?

Most philosophy departments offer some logic course that satisfies a mathematical, quantitative, or formal reasoning general education requirement. My university describes their quantitative and formal reasoning requirement as follows:

To help you develop important analytical skills, these courses focus on the presentation and evaluation of evidence and argument, the understanding of the use and misuse of data, and the organization of information in quantitative or other formal symbolic systems.

Given that these are quantitative and general education requirements, what should we, as philosophers, teach in these courses?

Almost all of these courses choose topics from the following categories:

  • categorical logic (square of opposition, categorical inferences)
  • categorical logic (diagrams)
  • informal fallacies and reasoning
  • propositional logic (proofs)
  • propositional logic (truth-tables)
  • propositional logic (tableaux)
  • inductive and causal reasoning, including causation vs correlation vs explanation
  • probabilistic reasoning, including the probability calculus

Most of them, in my experience, do not proceed to quantification theory. Perhaps the thought is that this much content is too difficult for this level (but categorical logic is an easier, albeit more cumbersome, way to teach universal and existential reasoning).

So: given the quantitative reasoning aims of “organization of information in quantitative or other formal symbolic systems”,  which of these should we select?

I think that categorical logic should be struck from this list. Categorical reasoning is too unwieldy to be justifiable, even if the diagrams are fun. Formulas need not have the categorical form, and they should not be forced into it, even for pedagogical purposes.

Propositional logic, on the other hand, is woefully inexpressive. But it is a useful tool for teaching transferable analytical skills using syntactic and semantic methods. I cannot sing the virtues of proofs, tables, and tableaux too highly for imparting the analytical habit of mind.

What about informal fallacies? I say that they should be struck. They do not, first, teach any analytical skills. They do help one identify mistakes in reasoning, which may then be leveraged to evaluate arguments and assess the use (or misuse) of data. But they do not in themselves demand much development of analytical skills. They are just labels that bring out faulty reasoning more clearly.

Also, they can be introduced and taught in a week. Familiarity with them is the only real virtue of teaching them. Informal fallacies do not seem to be worth assessing using multiple choice tests or projects outside of class. That seems to be more about testing our ability to remember the names of fallacies—which is not a useful thing to teach—as opposed to sharpening our wits so that we can catch mistakes in reasoning.

If we are concerned to teach one to reason well—to cultivate the analytical habit of mind—then it seems to me that we are better off teaching inductive and causal reasoning, plus the probability calculus. These do cultivate active analytical thinking in a way that passively identifying fallacies does not.

So I will be minimizing or leaving out informal fallacies altogether in my critical thinking class! I am quite excited about what the results will be.

6 thoughts on “What should philosophers teach in quantitative reasoning courses?

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