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Inductive Arguments. Copyright 2007 Makoto Suzuki. Review of Inductive Arguments. We will now begin our discussion of inductive arguments. Recall: the condition of a good inductive argument is cogency, i.e., the premises being all true and the argument being strong.
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Inductive Arguments Copyright 2007 Makoto Suzuki
Review of Inductive Arguments • We will now begin our discussion of inductive arguments. • Recall: the condition of a good inductive argument is cogency, i.e., the premises being all true and the argument being strong. • A strong inductive argument is one in which the premises provide partial (but non-negligible) support for the conclusion. • That is, if all of the premises were true, then they would give us good reason – though not conclusive reason – to accept the truth of the conclusion.
Three Inductive Arguments • Statistical Syllogism • Special Versions: • Arguments from authority • Arguments from consensus • Inductive Generalization • Arguments from Analogy • We will study them in order while also reviewing the fallacies associated with each type of arguments.
Sample Arguments- Statistical Syllogism • 92% of freshmen at OSU are state residents. Jessica is a freshman at OSU. Jessica is a state resident. • Very few employees at the OIE are state residents. James is an employee of the OIE. James is not a state resident.
General Statistical Syllogism • The general form of a statistical syllogism is: X percentage of all F’s are G’s. a is an F. a is a G. (Or “a is a non-G”, when X is very small.) • The class F is known as the reference class - it is referred to in the second premise. • The class G is known as the attribute class - something is attributed to it in the conclusion.
A Note on Statistical Syllogisms • The statistical generalization need not be stated numerically: • ‘Almost all’, ‘most’, ‘very often’, ‘hardly ever’, and other similar expressions are frequently used.
Two Standards of the Strength of Statistical Syllogisms • Percentage • When the form of the conclusion is “a is a G”, the closer the percentage in the generalization is to 100, the stronger the statistical syllogism is. • When the form of the conclusion is “a is a non-G”, the closer the percentage is to 0, the stronger the statistical syllogism is. • Relevance of the reference classto the attribute class
The Fallacy of Incomplete Evidence • The fallacy of incomplete evidence is committed when one fails to take into account all available relevant evidence when choosing the reference class for one’s statistical syllogism. • Remember, any evidence that might influence the probability of an individual belonging to the attribute class is relevant evidence.
The Fallacy of Incomplete Evidence – An Example • Approximately 91% of professional philosophers are men. Therefore, Sarah Sawyer, who is a professional philosopher, is a man. • This argument commits the fallacy of incomplete evidence because it fails to take into account the fact that almost all people whose first name is Sarah are women.
A Version of Statistical Syllogism: Arguments from Authority • Arguments from authority have the general form: • Most of what authority (a) say on subject matter S is correct. • p is what (a) says on S. • • p is correct.
Arguments from Authority – An Example • Most of what Stephen Hawking has to say about the universe at the time of the Big Bang is correct. • Stephen Hawking says that the universe was more highly ordered at the time of the Big Bang than it is today. • The universe was more highly ordered at the time of the Big Bang than it is today.
Arguments from Authority – More Examples • The director of the National Weather Service issued a report that hurricane Betty is heading for Miami. Therefore, it must be the case that hurricane Betty is heading for Miami. • Since the sign over the freeway says that the freeway will split approximately two miles ahead, the freeway will split approximately two miles ahead.
Appeal to Inappropriate Authority (Ad Verecundiam) • The fallacy of appeal to inappropriate authority is committed when an argument appeals to an authority that is not legitimate; that is to say, the argument does NOT satisfy one of the following conditions of proper appeal to authority: • 1.The authority invoked is an expert in the area of knowledge under consideration; • 2.There is general agreement among the experts in the area of knowledge under consideration; • 3.There is no good reason to suspect that the authority is biased on the subject matter.
Appeal to Inappropriate Authority – Examples • References to popular figures, usually celebrities or sports personalities, in ads for products about which they have no special knowledge. • Ex.: There must be something to psychical research. Three famous physicists, Oliver Lodge, James Jean, and Arthur Stanley Eddington, took it seriously.
Another Version of Statistical Syllogism: Arguments from Consensus • Arguments from consensus take the following general form: • When most people make a claim about a subject matter S, the claim is often true. • p is a claim most people make about S. • • p is true.
Arguments from Consensus • Arguments from consensus are generally fallacious. • The exceptions are the cases where the ‘most people’ are also a proper authority on the subject matter in question. • Remember that in general the mere fact that many people believe something does not make it the case.
Argument from Consensus –Examples • An advertisement argues that one brand of car must be best by stating: "50 million Americans can’t be wrong!” • The majority of people believe in some kind of soul, therefore one should believe that souls exist. • Working one’s way through college is a cherished American concept. (Dr. Newman, former president of the Univ. of Rhode Island)
Inductive Generalizations • Inductive generalizations are arguments from the particular to the general. • The premise of an inductive generalization states what happens in the (observed) sample – the collection of particular cases on which the generalization is based. • The conclusion of an inductive generalization states what happens in the population – the collection of cases that the sample is a sample of.
Examples -Inductive Generalization 60% of the 2004 people polled voted for Bush. 60% of all voters voted for Bush. 99.5% of the sample of 6hr video tapes were over 6hrs in length. 99.5% of all of the 6hr videos are over 6hrs in length.
Inductive Generalizations: the Primitive Form • The primitive form of an inductive generalization is: X percentage of observed F’s are G’s. X percentage of all F’s are G’s. • The ‘statistics’ concerning the sample quoted in the premise are generalized to the whole population in the conclusion.
Fallacies Associated with Arguments based on Samples • Hasty Generalization • Biased Statistics • Misleading Vividness • All of the three fallacies are associated only with arguments based on samples (aka inductive generalizations).
The Fallacy of Hasty Generalization • The fallacy of hasty generalization is committed when one makes or accepts an inductive generalization based on the sample whose size is not large enough. • Ultimately the decision as to what size of sample we need depends on the subject matter of the generalization. • A small sample can be sufficient if there is not a lot of variety in the population about which the generalization is made. (See Q1 of p.70.)
Examples - The Fallacy of Hasty Generalization • I saw a flashy dresser driving a Lexus used food stamps at the grocery store. You see, welfare fraud is very common. • Six Arab fundamentalists were convicted of bombing the World Trade Center in New York City. The message is clear: Arabs are nothing but a pack of religious fanatics prone to violence.
The Fallacy of Biased Statistics • The fallacy of biased statistics is committed when one makes or accepts an inductive generalization based on the sample that lacks the required variety to be representative of the population.
Examples - The Fallacy of Biased Statistics • It has been concluded from a recent study involving more than 100,000 people in the state of Florida that 43 % of the American people now spend at least two hours a day in some form of recreational activity. • In Columbus 99% of the people standing just outside bars say that they disapprove of the current law against smoking in a bar. We may conclude that 99% of the people in Columbus disapprove of that anti-smoking law. • We have sent a questionnaire about the amount of salary to randomly selected Yale university graduates, and 70% of the replies say that they earn more than $80,000 a year. So 70% of Yale university graduates earn more than $80,000 a year.
Continued • In Japan we have visited randomly selected 10,000 households during daytime and asked whether married women with children may work full-time. 2/3 of them responded “No”. So we may conclude that 2/3 of Japanese population think that married women with children may not work full-time. • The prison system of the USA fails to deter people from crimes because the observed second offense rate is very high.
The Fallacy of Misleading Vividness • The fallacy of misleading vividness is committed when an inductive generalization that is strongly supported by premises citing sufficient and unbiased statistics is rejected on the basis of a small number of cases. • Frequently the cause of the fallacy is that a (few) vivid counterexample to the conclusion psychologically outweighs the statistics.
The Fallacy of Misleading Vividness • It is a fallacy to allow a (few) vivid case(s) to outweigh strong statistical data. • Good statistics have already taken the existence of such counterexamples into account.
Example - The Fallacy of Misleading Vividness • David: John, after looking at the data, I’ve decided to buy a Nissan because they are the most reliable cars on the road. • John: That can’t be true, my Nissan is always breaking down! • David: Really? I won’t be buying one then. • Note: I am not a fan of Nissan.
Arguments from Analogy • In an argument from analogy(also known as an analogical argument), it is argued that two things that are similar in some recognized ways are also similar in some further, as yet unrealized, respect.
Example - Argument from Analogy • Here is a strong analogical argument: The Encyclopedia Britannica has an article on symbiosis. The Encyclopedia Americana, like the Britannica, is an excellent comprehensive reference work. The Americana probably also has an article on symbiosis.
Example - Argument from Analogy • Here is another strong analogical argument: The genetic and other biological mechanisms behind skin cancer in mice and lung cancer in humans are very similar. Tar extracted from cigarette smoke when smeared on the skin of mice in laboratories causes skin cancer. Cigarette smoking causes lung cancer in humans.
A General Form of Arguments from Analogy • A general form of arguments from analogyis: Objects of type X have properties F, G, H, etc. Objects of type Y have properties F, G, H, etc. and Z. Objects of type X have property Z as well
The Fallacy of False Analogy • The fallacy of false analogyis committed when an argument from analogy is put forward, but that fails to meet the conditions for it to be strong. • Three Possible Reasons: • It uses irrelevant similarities; • There are not enough similarities; and, • The similarities are not sufficiently varied/diverse.
Examples - Fallacy of False Analogy • A cocker spaniel is a friendly little dog, and no one should be afraid to pet one. A pit bull terrier is no less of a dog than a cocker spaniel. Therefore, no one should be afraid to pet a pit bull terrier. • Roses are brightly colored flowers, and they make beautiful corsages. But dandelions are also brightly colored. Therefore, dandelions should make beautiful corsages.
