History of PhilosophyLecture 4

Inductive arguments

By David Kelsey

Inductive arguments

• Prediction: – Inductive arguments give us a way of extending our beliefs about things we

know of to things unknown.– Inductive arguments make predictions about things unknown or about the

future.– Inductive arguments assume: – Examples:

A general formula

• A general formula: Here is a general formula which is followed by almost all inductive arguments:

– Some thing or class of things X has properties a, b and c.– Another thing or class or things Y has properties a, b and c.– X has some further property p.– Thus, Y also has property p.

• The Harley example:– Some Harley Davidson motorcycle’s are new, are taken care of and well

maintained & are of a particular make and model…– My Harley is like this also.– The other Harley’s leak oil.– Thus,

More examples

• Banging the gate: – On Monday, Tuesday and

Wednesday I left at 9am, and banged the gate shut loudly.

– On Thursday I will leave at 9am and bang the gate shut loudly.

– On Monday, Tuesday and Wednesday the dog barked loudly at me as I left.

– Thus,

• Peaches:– The peaches I bought at the

marked were all sitting in a particular crate, were all about the same age and were all about the same ripeness.

– The entire batch of peaches at the market are sitting in the same crate, are of the same age and are the same ripeness.

– The peaches I bought were all mushy.

– Thus,

The sample

• The sample: the thing or group of things which we believe something about.– The sample is just the thing or things that we know something about.

– Examples:

The Target

• The target: the thing or things that we extend our belief to.– The target is just the thing or things about which there is something we don’t

know.

– And while we don’t know something about the target,• We reason from other things (the sample,) that the target will have some

property.

– Examples:

The Target #2

• Single and Plural targets:– The target can be a single thing, like– Or it can be an entire class of things, like

• Sometimes the members from the sample are drawn from the target:

• Sometimes the members of the sample aren’t members of the target:

The property in question

• The property in question: some of its features:– We know that the sample instantiates this property.

– We don’t know whether the target instantiates this property.

– We infer that the target instantiates this property because the sample does.

– Examples:

Arguments by analogy

• An argument by analogy:– 1. Ordinarily has one thing or event for a target.

– 2. Never has it’s sample drawn from the target class.

– Examples of arguments by analogy:

Inductive Generalizations

• An Inductive Generalization:

– 1. Always has a class of things or events for a target.

– 2. Always has it’s sample drawn from the target class.

– For example:

4 principles about good inductive reasoning

• Representative-ness principle: – The more alike one another our sample and target are, the stronger our argument,

– the less like one another our sample and target are, the weaker our argument.

• Representative sample: A sample that is similar in relevant respects to the target.

– The more an inductive argument’s sample is similar to its target in all relevant respects the more representative the sample is said to be.

• Question: what’s a relevant respect?

• Biased sample: A sample that is significantly different from the target in one or more relevant respects.

Principles two, three& four

• 2) If, in giving an analogical argument, we don’t know whether our target has some relevant property:

• 3) If we do know that our target has some relevant property P:

• 4) In general, the larger the sample the stronger the argument.

Exercises

• Are the Following Inductive Generalizations or Arguments by analogy?– 1. With 7 out of the last 9 El Nino’s, we saw below-average rainfall across the northern

United States and Southern Canada. So the chances are we’ll see the same with the next El Nino.

– 2. Bill Clinton lied to the American public about his relationship with Monica Lewinsky; therefore, he probably lied to the American public about most things.

– 3. You’re going out with a Georgette? Well, don’t expect much because I’ve known three and they’ve all been stuck up annoying brats. I’ll bet this one will be too.

• What is the sample, target and property in question for each of the following inductive arguments?

– 4. Too much sun will make your face all wrinkly; I suppose it would have that effect on your hands, too.

– 5. Most of my professors wear glasses; it’s a good bet most professors everywhere do the same.

– 6. Yamaha makes great motorcycles, so I’ll bet their pianos are good, too.

Answers to the Exercises

• Answers:– 1. Argument by analogy

– 2. Inductive generalization

– 3. Argument by analogy

– 4. The sample: your face; The target: your hands; Property in Question: Being wrinkly from exposure to the sun

– 5. The Sample: most of my professors; The Target: Most professors everywhere; The property in question: Wearing glasses

– 6. The Sample: Yamaha Motorcycles; The Target: Yamaha Pianos; The Proerty in question: Being good