Critical Thinking Lecture 13 Inductive arguments By David Kelsey

Inductive arguments An inductive argument is one which is intended to be strong. The premises of inductive arguments increase the likelihood that their conclusions are true. They never guarantee their conclusions are true though. And even if the premises of an inductive argument are true, it is still possible that the conclusion is false.

Prediction Inductive arguments make predictions. For example, we might predict it will be cool tomorrow since it has been cool this week. Thus, inductive argument assume something like that the future resembles the past.

A general formula We will use the following general formula to characterize inductive arguments: Some thing (or class of things) X and some other thing (or class of things) Y have some relevant similarities. But X has some further property or feature P. Thus, we infer that Y will also have that further property or feature P.

The Harley Example The Harley example: Some of my friends 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. Therefore, my Harley will leak oil.

Banging the Gate Shut Banging the gate: On Monday, Tuesday and Wednesday I left at 9am, and banged the gate shut loudly. On Thursday I will also leave at 9am and bang the gate shut loudly. On Monday, Tuesday & Wednesday the dog barked loudly at me as I left. Therefore, On Thursday the dog will bark loudly at me as I leave.

Peaches Peaches: The peaches I bought at the market were all sitting in a particular crate, were all about the same age and were all about the same ripeness. Every peach at the market is sitting in the same crate, is of the same age and is about the same ripeness. The peaches I bought were all mushy. Therefore, all of the peaches at the market are mushy.

The Sample The sample: the thing (or class of things) in our argument that is the basis of our inductive inference. The sample is the group of things we base our inference on. When I reason that my Harley will leak oil the basis of my inference are the other Harleys that leak oil And when I reason that the dog will bark on Thursday I base my inference on what happened Monday, Tuesday and Wednesday And when I reason that today the peaches will be mushy I base that inference on the peaches that I bought

The Target While the sample is what we base our inference on, the Target class is the target of our inference. The target is the class of items our prediction is about. While our prediction is drawn from the sample class, it is extended to the target class. For example, when I reason that my Harley will leak oil, the basis of my inference are the other Harley’s that leak, I then extend that claim to my Harley And when I reason that the dog will bark on Thursday, the basis of my inference is Monday, Tuesday and Wednesday, and I then extend this claim to Thursday And when I reason that the entire batch of peaches at the store are mushy, the basis of my inference are the three I bought, and I then extend the belief about those to all the peaches at the store

Variations on the Target class Single and Plural targets: The target can be a single thing, like the Harley or Thursday Or it can be an entire class of things, like the entire batch of peaches.

More variations on the Target Sometimes the members from the sample are drawn from the target class. And so every member of the sample is also a member of the target class. For example, when I reason that the peaches will be mushy. Sometimes the members of the sample aren’t members of the target at all. In this case the sample and target don’t share any members. For example, when I reason my Harley will leak oil.

The property or feature in question The property or feature in question: The sample has this feature so we predict that the target will as well just because the sample and target are similar. Examples: For example, When I reason that my Harley will leak oil because others do, the property in question is that of leaking oil. And when I reason that the dog next door will bark loudly on Thursday because it did on Monday, Tuesday and Wednesday, the property in question is… And when I reason that all the peaches at the store are mushy because the few I bought were, the property in question is…

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. Thus, the sample and target are always distinct classes. For example, when I reason that because other Harley’s leak oil so too will mine.

Inductive Generalizations An Inductive Generalization: Always has a class of things or events for a target. Always has it’s sample drawn from the target class. So the sample is always a part of the target class. For example, when I reason that because the peaches I bought at the market were mushy the whole batch of peaches at the market is mushy.

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. But our sample and target must be similar in respects that are relevant to the property or feature in question. For example, if I was inferring my Harley will leak oil because some others do I wouldn’t want to draw this inference just because the other Harley’s are merely the same color as my bike.

Representative and Biased Samples A Representative sample is a sample that is similar in relevant respects to the target. The more representative the sample is of the target class, the stronger an inductive argument is. A Biased sample is a sample that is significantly different from the target in one or more relevant respects. An inductive argument with a biased sample is weak.

Hasty Conclusions Hasty conclusion: Fallacy of anecdotal evidence: This is a fallacy that occurs when one makes an inductive argument and the sample is too small to warrant the conclusion about the target. For example, if I think the entire batch of peaches is mushy because the two I bought were. Fallacy of anecdotal evidence: This is a fallacy that occurs when one makes an inductive argument and her sample consists of only one item. Or if I think smoking doesn’t cause cancer because my one grandmother smoked forever and didn’t get it.

Polls Election polling is a kind of inductive generalization which is meant to estimate the winner of an election. The sample of the generalization is just the people who are polled and the target is just the entire voting population. For example, we might want to draw up a poll to determine who will win the next presidential election in the United States. In this case we would somehow have to pick a sample of voters that is representative of the entire voting population of the United States. We can find such a sample through a random selection process.

Random samples A random selection process gives every member of the target class an equal chance of becoming a member of the sample. There is no guarantees of representative-ness and so even using a random selection process gives us an error margin. An error margin will be a number by which our prediction could be off track. The error margin is usually depicted as a percentage +/- Think of error margins like when you buy a car and the sticker says you will get 30 mph…

Sample Size When polling how many individuals does the sample need to contain? 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