1.3 Deduction And Induction
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The document provides an overview of deductive and inductive arguments, outlining their definitions and differences. Deductive arguments guarantee the truth of the conclusion if the premises are true, while inductive arguments suggest probability rather than certainty. Various forms and examples of each argument type are discussed, emphasizing criteria for evaluating argument strength and the context of their use.
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1.3 Deduction And Induction
- 1. 1.3 Deduction and Induction
- 2. Overview Examining deductive and inductive arguments. Telling the difference between the two. Different kinds of each argument form.
- 3. Types of arguments Deductive arguments An argument in which it is impossible for a conclusion to be false if its premises are true. The conclusion claims to follow necessarily from the premises. Example: All math classes are time-consuming. All hard classes are math classes. Therefore, it necessarily follows that all hard classes are time-consuming. Inductive arguments An argument in which it is improbable for the conclusion to be false if its premises are true. Conclusion claims to follow probably from the premises. Example: Socrates was Greek. Most Greeks ate fish. Therefore, Socrates probably ate fish.
- 4. How do we tell inductive from deductive? The distinction between inductive and deductive arguments is based on the strength of an argument’s inferential claim. Reminder: An inferential claim is based on a certain reasoning process – it is the relationship between the premises and conclusion of an argument. But the strength of a claim is hardly ever stated outright, so we have to evaluate it. Three criteria for measuring an argument’s strength: 1) The occurrence of special indicator words. 2) The actual strength of the inferential link between the premises and conclusion. 3) The form of argumentation used by the person making the argument. Certain indicator words lean more towards inductive and some lean towards deductive. But they’re not always accurate. Pay attention to the context of the argument. Example: The word “probably” tends to be used in inductive arguments, and words like “therefore” and “necessarily” tend to lean towards deductive arguments.
- 5. Forms of deductive arguments Argument based on mathematics The conclusion depends on a mathematical or geometric measurement. Has to be deductive since it follows necessarily --- meaning there’s no room for it “probably” being right. Example: 1+1 = 2 There’s no room for a different answer by reevaluating the argument. 1 + 1 will always equal 2. If you have 1+1, then it’ll always equal 2. Argument from definition The conclusion is claimed to depend on the definition of a word or phrase used either in a premise or in the conclusion. They follow necessarily because the argument depends completely on the definition of the word being used. Example: John is a kleptomaniac, so it follows forth that he steals things. The argument is deductive since the definition of the word leads the argument to one conclusion alone.
- 6. More deductive forms Categorical syllogisms Made up of exactly two premises and one conclusion. Begin with the words “all”, “some”, and “no”. (We’ll discuss these in much more detail in Chapter 5). Example: “ All ancient forests are sources of wonder. Some ancient forests are targets of the lumber industry. Therefore, some sources of wonder are targets of the lumber industry. Hypothetical Syllogisms Syllogisms (two premises and one conclusion) that have a conditional statement for one (or both) of its premises. Example: “ If monopolies continue to grow, then suppliers will be squeezed even further. If supplies are squeezed even further, then jobs will be forced overseas. Therefore, if monopolies continues to grow, then jobs will be forced overseas. If you have A, then you have B. If you have B, then you have C. Therefore, if you have A, then you have C. Hypotheticals work like chains…one leads to the next and ties them all together.
- 7. Inductive argument forms Prediction An argument that works based off our knowledge of the past in order to make a claim about the future. Example: There tends to be a lot of rain in the Midwest, so it will probably rain there tomorrow. Claims about the future can’t be known with any certainty, so they can’t be absolutely true, even though they can be justified. That makes them inductive. Argument from analogy Depends on the existence of an analogy (or similarity) between two separate things. Example: My Honda gets good gas mileage. So it follows that John’s Honda also gets good gas mileage. The truth of an argument like this is based on chance, so and that chance makes it an inductive argument.
- 8. More inductive argument forms Generalization An argument that is applied to a whole group based on knowledge gained from a small sample of people. Example: Five out of ten people in Ellis Hall said they support abortion. So I can say that half of Athens supports abortion. Statistical data is not always accurate, so the truth of this form of argument can not be made certain. It remains only probable. Argument from authority An argument that concludes something is true because an expert said it is. Example: Centrum vitamins work because Dr. Jones did a study that proved it. This type of argument is only true with probability since studies can be wrong or mistaken.
- 9. Even more inductive argument forms Argument based on signs Conclusion based on knowledge gained from a sign about what the sign claims to mean. Example: A sign on the side of the road says “School Zone” so I can assume that a school is somewhere up ahead. The sign could have been moved from somewhere else, or it could simply be wrong, so it can’t be true with absolute certainty. Causal inference Argument that proceeds from knowledge of a cause to a claim about its effect, or vice versa, that knowledge of an effect can provide information about its cause. Example: I left a soda in the freezer last night, so I can assume that it is frozen.
- 10. Things to keep in mind Overlaps can happen between arguments. Example: If one triangle has its hypotenuse as length X, then a congruent triangle will also have a hypotenuse as length X. This can be mistaken for an argument for analogy because you’re comparing two triangles. But it’s dealing with math, so it has to be an argument based on mathematics. Arguments dealing with science are unique, though. Dealing with the discovery of a scientific fact are typically inductive, since their reliability hasn’t been proven yet. There are a few exceptions, but for our purposes scientific arguments are deductive when they deal with the application of a scientific fact.