Logic in School Program

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Logic in School Program

• Creighton University
• Director Dr. Jinmei Yuan (jinmei_at_creighton.edu)
  Student Teachers Mark Holmberg Andrew
  Trapp Jason Bodewitz Elizabeth Epsen
• http//www.youtube.com/watch?vxrShK-NVMIU

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Overview

• Meet every week
• There will be quizzes (about every 2 weeks at the
  beginning of class), some homework assignments,
  tests, and in-class handouts/exercises
• The quizzes could be unannounced
• We will tell you the test dates in advance

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Overview Part II

• Typical schedule each day
• Journal exercise
• Go over questions from homework/previous class
  lesson (if any)
• Lesson
• Example problems / questions
• Assign homework problems / readings

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Class Notes

• Please raise your hand if you have a question or
  wish to answer one of ours
• We want to encourage everyone to get involved in
  class, so even if youre not sure of an answer
  for instance, still feel free to try to answer
  we are all learning together ?

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Lesson 1 Basic ConceptsArguments, Premises, and
Conclusions

• Logic the organized body of knowledge, or
  science, that evaluates arguments
• Aim to develop system of methods to use as
  criteria for evaluating arguments of others and
  for constructing our own to determine good
  arguments from bad arguments
• Syllogistic logic developed by Aristotle
  (384-322 B.C.) a kind of logic in which the
  fundamental elements are terms, and arguments are
  evaluated as good or bad depending on how the
  terms are arranged in the argument
• Modal logic also by Aristotle, but includes
  concepts such as possibility, necessity, belief,
  and doubt

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Arguments

• Argument a group of statements, one or more of
  which (premises) are claimed to provide support
  for, or reasons to believe, one of the others
  (conclusions)
• Good argument premises support the conclusion
• Bad argument premises do not support conclusion
  (even if they claim to)

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Arguments

• Made up of statements
• Statement a sentence that is either true (T) or
  false (?)
• Melatonin helps relieve jet lag. (T)
• No wives ever cheat on their husbands. (?)
• Truth values (of a statement)
• Many sentences, unlike statements, cannot be said
  to be T or ?
• Questions (Where is Tom?)
• Proposals (Lets go to a movie.)
• Suggestions (I suggest you get contact lenses.)
• Commands (Turn off the TV.)
• Exclamations (Wow!)

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Statements

• Premises
• Statements that set forth the reasons or evidence
• Conclusions
• Statements that the evidence is claimed to
  support or imply (claimed to follow from the
  premises)

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Example of an Argument

• Good Argument
• All film stars are celebrities. (Premise 1)
• Halle Berry is a film star. (Premise 2)
• Therefore, Halle Berry is a celebrity.
  (Conclusion)
• Bad Argument
• Some film stars are men.
• Cameron Diaz is a film star.
• Therefore, Cameron Diaz is a man.

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Conclusion Indicators

• Therefore
• Wherefore
• Thus
• Consequently
• We may infer
• Accordingly
• We may conclude
• It must be that
• For this reason
• So
• Entails that
• Hence
• It follows that
• Implies that
• As a result

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Premise Indicators

• Since
• As indicated by
• Because
• For
• In that
• May be inferred from
• As
• Given that
• Seeing that
• For the reason that
• Inasmuch as
• Owing to
• Example Expectant mothers should never use
  recreational drugs, since the use of these drugs
  can jeopardize the development of the fetus.

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Indicators

• Sometimes there are no indicators
• (Also, some passages that contain arguments
  contain statements that are neither premises nor
  conclusions)
• The space program deserves increased expenditures
  in the years ahead. Not only does the national
  defense depend upon it, but the program will more
  than pay for itself in terms of technological
  spinoffs. Furthermore, at current funding levels
  the program cannot fulfill its anticipated
  potential.

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Argument Reconstruction

• Break up compound statements
• Always list premises first, then
  conclusionsP1 The national defense is
  dependent upon the space program.P2 The space
  program will more than pay for itself in terms of
  technological spinoffs.P3 At current funding
  levels the space program cannot fulfill its
  anticipated potential.C The space program
  deserves increased expenditures in the years
  ahead.

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Inference Proposition

• Inference the reasoning process expressed by an
  argument
• InferenceArgument
• Proposition the meaning or information content
  of a statement
• PropositionStatement

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Homework

• Problems Exercise 1.1
• Pages 7-9, Numbers 1-21
• Try these on your own we will review some next
  class
• Reading Chapter 8 (Symbolic Logic)
• Pages 299-309