1.3 Deduction And Induction

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Course lecture I developed over section 1.3 of Patrick Hurley\\\'s "A Concise Introduction to Logic".

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1.3 Deduction And Induction

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

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