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DEDUCTIVE REASONING We reason deductively when we draw a conclusion from a set of given facts using the laws of logic

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Inspector Garble

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DEDUCTIVE REASONING If the butler murdered Uncle Alfred then there are fingerprints on the gun. The butler murdered Uncle Alfred or the maid did it. There are not fingerprints on the gun. Therefore the maid did it.

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The collection of statements below is called an ARGUMENT- a vehicle for reasoning consisting of If the butler murdered Uncle Alfred then there are fingerprints on the gun. The butler murdered Uncle Alfred or the maid did it. There are not fingerprints on the gun. Therefore the maid did it. A set of statements called PREMISES - the given facts or clues Followed by a final statement called the CONCLUSION which is said to be drawn from the given facts.

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An argument is either VALID or INVALID. VALID does NOT mean TRUE The sky is blue. Zebras have stripes. We are sitting in class. Therefore George W. Bush is president of the United States. Everything I say is true but the process of reasoning is not valid. The premises and the conclusion are not related. To examine the relationship that determines validity, we must first consider the STRUCTURE of the argument.

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WHODUNNIT? If the butler murdered Uncle Alfred then there are fingerprints on the gun. The butler murdered Uncle Alfred or the maid did it. There are not fingerprints on the gun. Therefore the maid did it.

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The STRUCTURE of the Argument If then or Not Therefore

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If b then f b or m Not f Therefore m

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This argument has the same structure as the previous example If Herman lives in Cleveland then Herman lives in Ohio. Herman lives in Cleveland or Herman lives in Philadelphia. Herman does not live in Ohio. Therefore Herman lives in Philadelphia.

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The STRUCTURE of the Argument If then or It is not true that Therefore

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The STRUCTURE of the Argument If then or It is not true that Therefore The butler murdered Uncle Alfred The maid did it There are fingerprints on the gun

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The STRUCTURE of the Argument If then or It is not true that Therefore

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The STRUCTURE of the Argument If then or It is not true that Therefore Herman lives in Cleveland Herman lives in Phila Herman lives in Ohio

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When we reason inductively we can never be certain that the conclusion is true. When we reason deductively we can be certain that the conclusion is true as long as the premises are true. It is difficult to separate these two modes of reasoning, because we often use them together - for example, in deductive reasoning, the premises are likely to be the conclusions of inductive reasoning. Inductive reasoning is uncertain - but it is our only way to know anything about the real world. Deductive reasoning is certain - but very artificial. However these artificial patterns govern the way we think, reason and communicate.

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Albert Einstein compares the two modes of reasoning - inductive and deductive - and outlines the great paradox in our ability to “know” things: “As far as mathematics is certain, it does not pertain to reality, and as far as it pertains to reality, it is not certain.” Logical reasoning

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Deductive Arguments and Inference Rules Terminology: Valid Argument: – truth of the premises guarantees the truth of the conclusion – It would be contradictory.

Deductive Arguments and Inference Rules Terminology: Valid Argument: – truth of the premises guarantees the truth of the conclusion – It would be contradictory.

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