Critical Thinking Lecture 11 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 Peaches: 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 1) If, in giving an analogical argument, we don’t know whether our target has some relevant property: 2) If we do know that our target has some relevant property P: 3) In general, the larger the sample the stronger the argument.

Polls Say Obama wants to poll the voters of New Hampshire to determine if he will win the presidential election there. Your job is to produce a reasonably accurate assessment of public opinion. UNH: Say that you poll the faculty at the University of New Hampshire. Is this sample representative: of the target class, I.e. the voters of the state of NH? Any relevant differences?

Random samples Finding representative samples: How do you find a sample that will share all the relevant properties with the target class? We must use a random selection process. A random selection process: gives every member of the target class an equal chance of becoming ____________________. No guarantees of representative-ness though…

Error margins No precise answers: Even if our sample is random and even if it is representative of the target: our poll probably won’t get a precise answer to the question “How many NH voters will vote for Obama?” Our poll will provide us with an answer that is reasonably close to the precise one. Our answer will have an error margin.

Sample Size When polling, like in the Obama case, how many individuals does the sample need to contain? A table: Sample size Error margin Range (of % points) 10 +/-30 60 25 +/-22 44 50 +/-14 28 100 +/-10 20 250 +/-6 12 500 +/-4 8 1000 +/-3 6 1500 +/-2 4