Induction and deduction

Types of argument In our last session we looked at what makes something an argument – what distinguishes arguments from non-arguments. Now we are going to look at what distinguishes some kinds of arguments from other kinds. In particular we will be looking at the distinction between inductive and deductive arguments.

Induction and deduction Inductive and deductive arguments are both types of argument. So using the definitions we landed on in the last session, we can say that both inductive and deductive arguments present a series of claims, such that one of those claims (the conclusion) is presented as being supported by or following from some of the other claims (the premises).

Induction and deduction But the way in which the premises are supposed to support the conclusion are different in the cases of induction and deduction. In an inductive argument, if the premises are true, the conclusion is probably true, but not necessarily; and the conclusion states new information not contained (not even implicitly) in the premises.

Induction and deduction Whereas in a valid deductive argument, if the premises are true, the conclusion must be true; and the conclusion does not give new information that is not already contained (implicitly) in the premises.

Induction and deduction Sometimes the difference gets put like this: induction moves from specific cases as a premise to formulating a general rule as the conclusion. Whereas deductive arguments start with general rules as premises and derive specific conclusions.

Induction and deduction There’s something in this line of thought for sure (induction does seem to centrally involve formulating general rules on the basis of many specific cases). But I don’t think it will work as a general definition or even as a distinguishing characteristic.

Induction and deduction To see this, consider the following argument: (1) Ted is from the UK. (2) If Ted is from the UK, all swans have long necks. (3) All swans have long necks. The conclusion of this argument is (3). But (3) is clearly a more general claim than (1), which is a premise of the argument. And yet this is surely a deductive argument.

Induction and deduction So let’s stick to these two key distinguishing features: In a deductive argument, if the premises are true, the conclusion must be true. We might say that the premises necessitate or guarantee the truth of the conclusion. Whereas an inductive argument can only ever offer probabilistic support for its conclusion. At the very best, the truth of the premises of an inductive argument renders the conclusion very likely.

Induction and deduction And, in a deductive argument the information contained in the conclusion is in some sense already contained there in the premises. Whereas in an inductive argument, the conclusion goes beyond the information contained in the premises to add something new. It might be useful to look at some examples.

Examples of deductive arguments Some cards are diamonds. All diamonds are red. So, some cards must be red. If you like dark beer, you should take the stout or the porter. You do like the dark beer, and the stout is bad so you shouldn’t take that. So you should take the porter.

Examples of inductive arguments Jen is an American. Most Americans say ‘sidewalk’ instead of ‘pavement’. So Jen probably says ‘sidewalk’ instead of ‘pavement’. Every morning the sun has risen. So tomorrow morning the sun will rise.

Indicator words As we said earlier, deductive arguments tend to deal with necessities. Deductive arguments claim that if the premises are true, then by necessity, the conclusion must be true too. By contrast, inductive arguments deal with probabilities. They claim that if the premises are true, then the conclusion is probably true too. So words like ‘must’ or ‘necessarily’ are often indicators that we are dealing with a deductive argument. Whereas words like ‘probably’ are often indicators that we are dealing with an inductive argument.

Setting aside induction There is much more that can be said about inductive arguments. For example, they seem to rely on some sort of principle along the lines of ‘we can reasonably expect the future to resemble the past’. But specifying exactly what this amounts to, and exactly what makes some inductive arguments strong and others weak turns out to be very tricky. (The ‘problem of induction’ is one of the classic problems of philosophy, and there is an awful lot of literature devoted to it.)

Setting aside induction So in this class we are going to set aside induction. Because by contrast, philosophers have had much more progress in specifying the rules that distinguish good deductive arguments from bad ones. This practice of specifying such rules covers much of the subject matter of logic.

Deduction and logic So from here on out we will be focusing on deductive arguments. And we will be trying to get to the bottom of what separates good deductive arguments from bad deductive arguments.