Logic and Reason

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Logic and Reason
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Deductive ReasoningReasoning that moves from the
general to the particular

• Watchdogs bark at strangers.
• The watchdog did not bark at the thief
• The thief was not a stranger!
• A syllogism consists of
• Two premises and a conclusion
• Three terms, each which occurs twice
• Quantifiers, such as all or some or no

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Truth and Validity Truth is concerned with what
is the case, validity is concerned with whether
conclusions follow from premises truth is a
property of statements, validity is a property of
arguments.
All ostriches are teachers Mr. Valaitis is an
ostrich Therefore, Mr. Valaitis is a teacher
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Deductive Validity

• An argument is deductively valid if the truth of
  the reasons absolutely guarantee the truth of its
  conclusion if the reasons are true, the
  conclusion must be true, there are no other
  possibilities.

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The Liar Paradox

• Suppose Epimenides of crete says to you Cretans
  are always liars. Is that true or false?
• (Epimenides by plato, c. 500 B.C.)

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Inductive ReasoningReasoning that goes from the
particular to the general

• Inductive inferences are generalizations from
  observations. All arguments consist of reasons
  and inferences. Inferences are the moves we
  make from reasons to conclusions.
• When I drop a ball it will fall
• The sun will rise tomorrow morning

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Inductive Inference

• Womens brains are on average smaller than mens,
  therefore women are less intelligent than men.

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Judging Inferences

• Test 1 - Could the reasons be true and the
  conclusion false at the same time? If so, then
  the inference fails.
• Test 2 - Are any of the reasons untrue or
  otherwise unacceptable? If so, then the inference
  fails.

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Alternative Hypotheses

• Good thinkers learn to consider all logically
  possible hypotheses. Can the theory be shown to
  be open to counterexamples?

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Summary

• A theory or an argument is defective if it
  entails a logical contradiction (deductive
  reasoning that is not valid), if its reasons or
  conclusions are untrue (inductive reasoning), or
  if it can be shown to be open to counterexamples.