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Deduction and Induction

Deduction and Induction. Types of Inferences. “Deduction” and “induction” are properties of inferences, not statements. Statement = true or false Inference = leads to certainty or leads to probability . Examples. P1: People at their desks are students. P2: Students study a lot.

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Deduction and Induction

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  1. Deduction and Induction

  2. Types of Inferences “Deduction” and “induction” are properties of inferences, not statements. Statement = true or false Inference = leads to certainty or leads to probability

  3. Examples P1: People at their desks are students. P2: Students study a lot. Deductive conclusion: People at their desks study a lot. Inductive conclusion: People at their desks will be studying tonight.

  4. Deduction: No new information in conclusion Thus, establishes the conclusion with certainty Induction: New information in the conclusion (the problem of induction) Thus, establishes the conclusion with probability Essential Distinctions

  5. Deductive Inference Examples Mathematical inference Inference from definition Dysjunctive syllogism

  6. Inductive Inference Examples Argument from sign Prediction

  7. Certainty and Probability • Psychological: • Your individual state of mind • Your relation to the statement • Logical • Content of the statements • The statement’s relations to each other

  8. Certainty and Probability • In other words: • Psychological certainty is a state of mind; it expresses something about your attitude toward a statement. • Logical certainty is a characteristic of arguments; it arises from a relationship between statements.

  9. Two Final Suggestions 1. Your only concern, in determining what kind of inference is presented, is how the conclusion follows from the premise(s). Ignore questions of truth. 2. If you are still unsure about the nature of the inference after applying the “reasonable person” test, interpret the inference as inductive.

  10. A Note About Inferences It is not essential that a deductive inference be drawn from the general to the particular; nor is it essential that an inductive inference be drawn from particular to general.

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