PHI 2100 Lecture 8 Inductive Arguments, Abductive Arguments Deductive and Inductive Arguments • A deductive argument is intended to provide a conclusive support for the conclusion

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PHI 2100 Lecture 8 Inductive Arguments, Abductive Arguments Deductive and Inductive Arguments • A deductive argument is intended to provide a conclusive support for the conclusion. As such, the truth of the premises provide absolute support for the conclusion. Such arguments are good arguments. • Bu there are some arguments that can make the conclusion highly likely but not absolutely true. Inductive Arguments Inductive Argument- Definition • An inductive argument is an argument in which the conclusion is probably true if the premises are true. • In other words, under the assumption that the premises are true, it is improbable for the conclusion to be false. Inductive Arguments- Strong, Weak • An inductive argument that provides high degree of support for its conclusion is called strong. So, if its premises are true, it is highly likely that the conclusion will be true. • An inductive argument that provides a low degree of support for its conclusion is called weak. • An inductively strong argument with true premises is called cogent. Examples of Inductive Arguments 1.Most cats have fleas. So, Kitty, your cat, probably has fleas. 2.A recent Gallup poll says that 16-24 year olds spend a median of 3 hours a day on social media. John is a 17 year old. He, most likely, spends about 3 hours a day on social media. Examples of Inductive Arguments 3.When I bought an LQX phone a few years ago, it lasted a long time. If I buy a phone similar to phone LQX, most likely it will last a long time too. 4. Research suggests that eating lots of fruits and vegetables may provide some protection against cancer and heart disease. So, eating healthier increases quality of life. Examples of Inductive Arguments 5. Few cars in the US are electric. So, you car is probably electric. 6.I have bought a lottery ticket for the last 10 weeks, and I have not won anything. So, the next time I buy a lottery ticket, I will win. Characteristics of inductive arguments • They are extremely important in scientific and everyday reasoning. • They are not truth-preserving since the truth of the conclusion cannot be guaranteed by the truth of the premises. • They are ampliative: their conclusion always goes beyond the premises. Characteristics of inductive arguments • The strength or weakness of an inductive argument admits of degrees, unlike the certitude or absoluteness of deductive arguments. • The strength of an inductively argument depends on the presence or absence of additional relevant information. • 90% of people in community Q believe that the earth is flat. James is a member of community Q. So, most likely James believes that the earth is flat. Misconception about Inductive Arguments • Inductive arguments go from particular to general. • Here is a counterexample to the above misconception: • So far, all presidential Republican candidates have been while males. So, the next Republican presidential candidate will be a white male. Common Types of Inductive Arguments • Arguments from analogy • Generalizations • Statistical arguments, such as surveys. Abductive Arguments Abductive Arguments Definition • It was invented by Peirce, (1839-1914), an American philosopher and logician. • Abduction is concerned with finding a hypothesis to explain a phenomenon. • A good abductive argument is also called an inference to the best explanation. Abductive Argument What does it do? • An abductively good argument tries to find the best answer to the question `What is the best explanation for this phenomenon or state of a?airs?’ • It is ampliative, and informative inference. It tries to o?er a plausible pattern that explains the phenomenon at hand. • It is commonly used in science and everyday life. Abductive Arguments • Not all explanations are equally good, some are better than others. It takes careful thinking, substantive theoretical understanding, scientific testing, etc to come up with an inference to the best explanation. Abductive Argumentation Takes the following form: 1.Begins with one or more facts in need of explanation. 2.Critically examines as many plausible potential explanations as possible. ( A potential explanation is one that, if true, would explain the facts in question. A plausible explanation is one that is consistent with existing, well-established theories and general background information.) 3.Ranks one explanation as the `best’ explanation on the basis of the standard measures such as explanatory scope, simplicity, consistency, etc. 4.Concludes that the explanation ranked as the best explanation is probably true. Abductive Arguments General Structure • The general form of an abductive argument : • Surprising fact F has been observed. • If H were true, F would be a matter of course. • So there is some reason to believe that H is true. Examples of Abductive Arguments • A crime has been committed. The defendant’s fingerprints were all over the scene. The only explanation for this is that defendant is guilty. So, most likely the defendant is guilty. • You go to work and notice that there are decorations everywhere, but there are balloons and flowers at a specific desk. You conclude that one of your co-workers most likely have their birthday. Examples of Abductive Arguments • As you are walking on campus, you see a greater than usual amount of people standing outside the main entrance of the library. The fire department and police are also there. You conclude that there might have been a fire or fire alarm had been pulled. “It is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence. If a man, holding a belief which he was taught in childhood or persuaded of afterwards, keeps down and pushes away any doubts which arise about in his mind… and regards as impious those questions which cannot easily be asked without disturbing itthe life of that man is one long sin against mankind.” W. K. Cli?ord, (1845-1879), from “The Ethics of Belief,” originally published in Contemporary Review, 1877; reprinted in The Rationality of Belief in God, ed. George I. Mavrodes , Prentice Hall, 1970, pp: 159-160. Questions for further thought • What is a di?erence between deductive and inductive arguments? • What does a good abductive argument attempt to do? • How do you understand the quote by Cli?ord? PHI 2100 Lecture 8 Inductive Arguments, Abductive Arguments Deductive and Inductive Arguments • A deductive argument is intended to provide a conclusive support for the conclusion. As such, the truth of the premises provide absolute support for the conclusion. Such arguments are good arguments. • Bu there are some arguments that can make the conclusion highly likely but not absolutely true. Inductive Arguments Inductive Argument- Definition • An inductive argument is an argument in which the conclusion is probably true if the premises are true. • In other words, under the assumption that the premises are true, it is improbable for the conclusion to be false. Inductive Arguments- Strong, Weak • An inductive argument that provides high degree of support for its conclusion is called strong. So, if its premises are true, it is highly likely that the conclusion will be true. • An inductive argument that provides a low degree of support for its conclusion is called weak. • An inductively strong argument with true premises is called cogent. Examples of Inductive Arguments 1.Most cats have fleas. So, Kitty, your cat, probably has fleas. 2.A recent Gallup poll says that 16-24 year olds spend a median of 3 hours a day on social media. John is a 17 year old. He, most likely, spends about 3 hours a day on social media. Examples of Inductive Arguments 3.When I bought an LQX phone a few years ago, it lasted a long time. If I buy a phone similar to phone LQX, most likely it will last a long time too. 4. Research suggests that eating lots of fruits and vegetables may provide some protection against cancer and heart disease. So, eating healthier increases quality of life. Examples of Inductive Arguments 5. Few cars in the US are electric. So, you car is probably electric. 6.I have bought a lottery ticket for the last 10 weeks, and I have not won anything. So, the next time I buy a lottery ticket, I will win. Characteristics of inductive arguments • They are extremely important in scientific and everyday reasoning. • They are not truth-preserving since the truth of the conclusion cannot be guaranteed by the truth of the premises. • They are ampliative: their conclusion always goes beyond the premises. Characteristics of inductive arguments • The strength or weakness of an inductive argument admits of degrees, unlike the certitude or absoluteness of deductive arguments. • The strength of an inductively argument depends on the presence or absence of additional relevant information. • 90% of people in community Q believe that the earth is flat. James is a member of community Q. So, most likely James believes that the earth is flat. Misconception about Inductive Arguments • Inductive arguments go from particular to general. • Here is a counterexample to the above misconception: • So far, all presidential Republican candidates have been while males. So, the next Republican presidential candidate will be a white male. Common Types of Inductive Arguments • Arguments from analogy • Generalizations • Statistical arguments, such as surveys. Abductive Arguments Abductive Arguments Definition • It was invented by Peirce, (1839-1914), an American philosopher and logician. • Abduction is concerned with finding a hypothesis to explain a phenomenon. • A good abductive argument is also called an inference to the best explanation. Abductive Argument What does it do? • An abductively good argument tries to find the best answer to the question `What is the best explanation for this phenomenon or state of a?airs?’ • It is ampliative, and informative inference. It tries to o?er a plausible pattern that explains the phenomenon at hand. • It is commonly used in science and everyday life. Abductive Arguments • Not all explanations are equally good, some are better than others. It takes careful thinking, substantive theoretical understanding, scientific testing, etc to come up with an inference to the best explanation. Abductive Argumentation Takes the following form: 1.Begins with one or more facts in need of explanation. 2.Critically examines as many plausible potential explanations as possible. ( A potential explanation is one that, if true, would explain the facts in question. A plausible explanation is one that is consistent with existing, well-established theories and general background information.) 3.Ranks one explanation as the `best’ explanation on the basis of the standard measures such as explanatory scope, simplicity, consistency, etc. 4.Concludes that the explanation ranked as the best explanation is probably true. Abductive Arguments General Structure • The general form of an abductive argument : • Surprising fact F has been observed. • If H were true, F would be a matter of course. • So there is some reason to believe that H is true. Examples of Abductive Arguments • A crime has been committed. The defendant’s fingerprints were all over the scene. The only explanation for this is that defendant is guilty. So, most likely the defendant is guilty. • You go to work and notice that there are decorations everywhere, but there are balloons and flowers at a specific desk. You conclude that one of your co-workers most likely have their birthday. Examples of Abductive Arguments • As you are walking on campus, you see a greater than usual amount of people standing outside the main entrance of the library. The fire department and police are also there. You conclude that there might have been a fire or fire alarm had been pulled. “It is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence. If a man, holding a belief which he was taught in childhood or persuaded of afterwards, keeps down and pushes away any doubts which arise about in his mind… and regards as impious those questions which cannot easily be asked without disturbing itthe life of that man is one long sin against mankind.” W. K. Cli?ord, (1845-1879), from “The Ethics of Belief,” originally published in Contemporary Review, 1877; reprinted in The Rationality of Belief in God, ed. George I. Mavrodes , Prentice Hall, 1970, pp: 159-160. Questions for further thought • What is a di?erence between deductive and inductive arguments? • What does a good abductive argument attempt to do? • How do you understand the quote by Cli?ord? PHI 2100 Lecture 7 The Counterexample Method Counterexample: What does it do? • A counterexample refutes the original argument by showing circumstances in which the premises are true and the conclusion false. 2 Counterexample: What is it? • A counterexample to an argument is substitution instance whose premises are true (or well-known truths) and the conclusion false (or well-known falsehoods). 3 Why do counterexamples show Invalidity? • A valid argument guarantees the truth of its conclusion for if its premises are true, then the conclusion must be true. • A counterexample shows a situation where the premises are true and the conclusion is false. • A counterexample is an invalid deductive argument. 4 What is the counterexample method? • The counterexample method is the method of producing a counterexample to a given argument in order to show the invalidity of the original argument. 5 How to find a counterexample? • First, identify the form of the argument, using variables. • Second, replace the variables in a way that make your premises well-known truths and the conclusion a well-known falsehood. • Third, write down the counterexample. • Hint: be on the lookout for the structure of di?erent types of arguments! 6 • Some arguments • Some arguments contain expressions such as all, no, some. contain expressions such as: if, given that, either or, and, etc. • For the above • In the above arguments you need to replace their subjects and predicates with upper case letters. arguments, you need to replace whole statements with upper case letters. 7 A counterexample • should have nothing to do with the content of the original argument. • must have the identical structure of the original argument. 8 • Finding counterexamples requires ingenuity and practice. 9 1.No all-powerful beings are all knowing beings. No all-good beings are all-knowing beings. So, no all-powerful beings are all-knowing beings. 2.If Anika stayed home from work, the her car is in the garage. Anika’s car is in the garage. So, Anika stayed home from work. 10 Examples Construct a counterexample for each of the following arguments: 1.All determinists are fatalists. Some fatalists are not optimists. So, some optimists are not determinists. 2.Since all inquirers are not wishful thinkers and all people are inquirers, we may conclude that some people are not wishful thinkers. 11 3. All methodological monists are people who believe that the social sciences must use the scientific method. All physicists are people who believe that the social sciences must use the scientific method. So, all physicists are methodological monists. 12 4.Given that there is erosion of the integrity of science, then progress of science will be impeded. But there is no erosion of the integrity of science. So, the progress of science will not be impeded. 5.Obesity is either genetic or environmental. Obesity is genetic. So, it is not environmental. 13 6.If it hurts our pride to admit that we do not know or that we were mistaken, then we are less likely to admit that we are wrong. If we are less likely to admit that we are wrong, then we are going to be dogmatic or rush to judgment. It follows that if we are going to be dogmatic or rush to judgment then it will hurt our pride to admit that we do not know or that we were mistaken. 14 7.On the condition that energy taxes are increased, then either the deficit will be reduced or conservation will be taken seriously. If the deficit is reduced then inflation wil be checked. So if energy taxes are increased then inflation will be checked. 15 8.Mercy killing is morally permissible only if it promotes a greater amount of happiness for everyone a?ected than the alternatives. And mercy killing does promote a greater amount of happiness for everyone a?ected than the alternatives. Thus, mercy killing is morally permissible. 16 9.All miracles are highly improbable events. Some highly improbable events are cases of winning he lottery. So, some cases of winning the lottery are miracles. 10. All galaxies are structures that contain black holes in the center. So all galaxies are quasars since all quasars are structures that contain holes in the center. 17 Questions for further thought • Describe in your own words a counterexample. • Why do we have to talk about the form of an argument? • Describe in your own words what is the form of an argument. 18