Moon s Day, March 23: Elementary Reasoning

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1 Moon s Day, March 23: Elementary Reasoning EQ: What are INDUCTIVE and DEDUCTIVE arguments? Welcome! Gather pen/cil, paper, wits! Lecture/Discussion: Inductive vs. Deductive Activity/Homework: Inductive vs. Deductive ELACC12RL-RI2: Analyze two/more theme/central ideas of text ELACC12RI3: Analyze and explain how individuals, ideas, or events interact and develop ELACC12RL6: Distinguish what is directly stated in a text from what is really meant ELACC12RI6: Determine an author s point of view or purpose in a text ELACC12RI8: Delineate and evaluate the reasoning in seminal British texts ELACC12RL-RI9: Analyze for theme, purpose rhetoric, and how texts treat similar themes or topics ELACC12RL10: Read and comprehend complex literature independently and proficiently. ELACC12W4: Produce clear and coherent writing appropriate to task, purpose, and audience ELACC12W9: Draw evidence from literary or informational texts to support analysis ELACC12W10: Write routinely over extended and shorter time frames ELACC12SL1: Initiate and participate effectively in a range of collaborative discussions ELACC12L6: Acquire and use general academic and domain-specific words and phrases

2 Compare these three arguments: Robert is a teacher. All teachers are nice. Therefore, Robert is nice. Robert is a teacher. Robert is nice. Therefore, all teachers are nice. All teachers are nice. Robert is nice. Therefore, Robert is a teacher.

3 An argument is valid if its conclusion follows inevitably from its premises; i.e., if it is not possible for the premises to be true and the conclusion false. Premise: All brilligs have slythy toves. Premise: All Jabberwokks are brilligs. Conclusion: All Jabberwokks have slythy toves. An argument is invalid if its conclusion does not follow inevitably from its premises; i.e., if conclusion can be false even if premises are true. Premise: Some brilligs have slythy toves. Premise: All Jabberwokks are brilligs. Conclusion: All Jabberwokks have slythy toves. A valid argument is unsound if any premise is untrue. Premise: All brilligs have slythy toves. Premise: Mr. Saunders, despite protestations, is a brillig. Conclusion: Mr. Saunders has slythy toves.

4 Deductive and Inductive Reasoning Excerpted and adapted from Moore, Brooke Noel, and Richard Parker, Critical Thinking (New York: McGraw-Hill, 2012) Deductive Arguments Tends to move from general categories to particular instances True premises prove conclusion validity [is] the fundamental concept of deductive logic A [deductive] argument is valid if it isn t possible for the premise to be true and the conclusion false. If the premise were true, the conclusion could not be false. o Bill Clinton is taller than George Bush o George Bush is taller than Jimmy Carter o Therefore, Bill Clinton is taller than Jimmy Carter Deductive arguments are true or false no grey area Inductive Arguments Tends to move from particular instances to general categories True premises support but don t by selves prove conclusion Inductive Arguments are weak or strong, depending on how much support their premises provide for the conclusion. o Weak argument premises give less support Husband was mad at wife, so he s the murderer We know husband was mad at wife but lots of husbands are and don t kill o Strong argument premises give lots of support We found his fingerprints on the knife stuck in her chest and nobody else s prints were on it o Reasonable Doubt speaks to this scale

5 Label the following Inductive or Deductive. A = B; B = C; therefore, A = C. Mr. Collins has mud on his right sleeve. We had rain yesternight. Therefore Mr. Collins sat at the right side of his cab on his way here this morning. All fruits grow on trees. Apples are fruits. Therefore, apples grow on trees. Apples grow on trees. All fruits grow on trees. Therefore, apples are fruits. Apples are fruits. Apples grow on trees. Therefore, all fruits grow on trees.

6 William is a bachelor. All bachelors are single. Therefore, William is single. William is a bachelor. William is single. Therefore, all bachelors are single. William is single. All bachelors are single. Therefore, William is a bachelor.

7 Label the following Inductive or Deductive. All cats that you have observed purr. Therefore, every cat must purr. The Earth is a planet, and all planets orbit a sun, therefore the Earth orbits a sun. Since all humans are mortal, and I am a human, then I am mortal. All dolphins are mammals, all mammals have kidneys; therefore all dolphins have kidneys. All squares are rectangles, and all rectangles have four sides, so all squares have four sides. If Dennis misses work and at work there is a party, then Dennis will miss the party. Bob is a sumo wrestler. Sumo wrestlers weigh a lot. Bob weighs a lot. All birds have feathers and robins are birds, so robins have feathers. All birds have feathers and robins have feathers, so robins are birds. Robins have feathers, and robins are birds, so all birds have feathers. It is dangerous to drive on icy streets. The streets are icy now so it is dangerous to drive now. All cats have a keen sense of smell. Fluffy is a cat, so Fluffy has a keen sense of smell. The elm is a tree and all trees have bark, so elms have bark. The elm is a tree and all elms have bark; therefore, all trees have bark. Snakes are reptiles and reptiles are cold-blooded; therefore, snakes are cold-blooded. Jenny is a dancer. Dancers are thin and tall. Jenny is thin and tall. All observed cats in the area are brown. Tiny is a cat. Tiny is brown. Red meat has iron in it and beef is red meat, so beef has iron in it. Acute angles are less than 90 degrees and this angle is 40 degrees so this angle is acute. All noble gases are stable and helium is a noble gas, so helium is stable. Elephants have cells in their bodies and all cells have DNA, so elephants have DNA. All horses have manes and the Arabian is a horse; therefore Arabians have manes.

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