How to think, a primer

This week I have been attending the annual meetings of the American Philosophical Association (Eastern Division) in New York, and the topic of thinking was, well, on everyone’s mind. While browsing through the book displays, I picked up a copy of Lewis Vaughn’s Writing Philosophy, which includes a nice little summary of the fundamental types of reasoning. Readers and commentators of this blog might want to keep it handy.

To begin with, of course, there is the fundamental distinction between deductive and inductive reasoning. Deductive reasoning is the type that is used largely in mathematics and formal logic, though it has a place in both science and everyday discourse. Deduction is the process by which one derives conclusions from a set of premises. If the formal structure of the deductive argument is correct, and the premises are true, the conclusion is guaranteed to be true. Of course, often enough some of the premises are questionable, or are derived from the other kind of logical reasoning (see below), which does not guarantee truth.

There are three fundamental types of deductive reasoning:

* Modus ponens (affirming the antecedent), where one proceeds as follows: (premise) if x then y; since x, (conclusion) therefore y. For example, if Socrates is a man, then he is mortal; Socrates is a man, therefore he is mortal.

* Modus tollens (denying the consequent): (premise) if x then y; not-y, (conclusion) therefore not-x. For example, if Socrates is a cat, then he has four legs; Socrates does not have four legs, therefore he is not a cat.

* Hypothetical syllogism: (first premise) if x then y; (second premise) if y then z; (conclusion) therefore if x then z. For example: Socrates is a man; all men are mortal; therefore Socrates is mortal.

The other fundamental kind of reasoning is induction, which is a way to come up with generalizations based on some initial observations. Inductive conclusions are powerful, and represent the basis of most science and everyday thinking, but – unlike deductive ones – are not guaranteed to yield truth, even if the premises are in fact correct and the reasoning is valid (i.e., formally correct).

Here are the three kinds of inductive reasoning:

* Enumerative, when one examines a sample and draws broader conclusions about the characteristics of the population from which the sample was taken. This is how much statistics, and of course opinion polls, work. The conclusions are strong in direct proportion to the size and representativeness of the sample.

* Analogical: this is reasoning by analogy, or metaphor. It is very common in both science and philosophy, and it can be illuminating. However, it is only as good as the analogy is relevant. Philosophers point out that some analogical reasoning contains what they call dis-analogies, i.e. parallels that actually do not stand up to scrutiny, and therefore undermine the conclusion. A classic example of disanalogy, as pointed out by David Hume, is the argument from design for the existence of a supernatural god (both because the universe is not meaningfully analogous to a machine, and because proponents of the argument typically refuse to draw the additional logical implications of an analogy between god and human designers, such as mortality, imperfection, etc.).

* Consilience: this is often referred to as “inference to the best explanation,” and it is essentially what scientists, as well as forensic investigators, do all the time (Sherlock Holmes, the Arthur Conan Doyle character, actually engaged in consilience, not deduction – contrary to what its author wrote). The idea is to examine as much relevant information as possible, and then draw the most likely (notice: not necessarily the truthful) conclusion compatible with the available data. Darwin’s theory of evolution is a masterful example of inference to the best explanation (despite perennial creationist nonsense), and he famously referred to it as “one long argument.”

Good, so now we don’t have any more excuses for sloppy thinking or writing, do we?