SFES2213: LOGIC AND CRITICAL THINKING Lecture 6

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SFES2213 LOGIC AND CRITICAL THINKINGLecture
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• Department of Science and Technology Studies,
  Faculty of Science, University of Malaya

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Deductive argument

• Definition
• An argument in which the premises are claimed to
  support the conclusion in such a way that it is
  impossible for the premises to be true and the
  conclusion to be false.
• Note Kesimpulan yang dibuat mesti (tidak boleh
  tidak) berdasarkan premis/ alasan yang
  dikemukakan.

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Deductive argument

• 4 tests to distinguish between deductive and
  inductive argument
• The indicator word test
• The strict necessity test
• The common pattern test
• The principle of charity test

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Common patterns of deductive reasoning

• Detecting common patterns is the quickest way to
  determine whether an argument is deductive or
  inductive.
• 5 common patterns of deductive reasoning
• Hypothetical Syllogism
• Categorical Syllogism
• Argument by Elimination
• Argument Based on Mathematics
• Argument from Definition

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Hypothetical syllogism(common patterns of
deductive reasoning)
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Hypothetical syllogism(common patterns of
deductive reasoning)

• A hypothetical syllogism
• is an argument consists of exactly 2 premises and
  a conclusion, with at least one hypothetical or
  conditional premise.

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Hypothetical syllogism(common patterns of
deductive reasoning)

• 5 types of hypothetical syllogism
• Modus ponens (logically reliable)
• Chain Argument (logically reliable)
• Modus tollens (logically reliable)
• Denying the antecedent (not logically reliable)
• Affirming the consequent (not logically reliable)

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Hypothetical syllogism(common patterns of
deductive reasoning)

• Modus ponens
• Examples-
• (1) If the Tigers beat the Yankees, then the
  Tigers will make the playoffs.
• The Tigers will beat the Yankees.
• So, the Tigers will make the playoffs.

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Hypothetical syllogism(common patterns of
deductive reasoning)

• (2) If I want to keep my financial aid, Id
  better study hard.
• I do want to keep my financial aid.
• Therefore, Id better study hard.
• - Notice that these 2 arguments have the same
  logical pattern/ form-

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Hypothetical syllogism(common patterns of
deductive reasoning)

• Logical pattern-
• If A then B.
• A.
• Therefore, B.

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Hypothetical syllogism(common patterns of
deductive reasoning)

• (2) Chain argument
• Consists of 3 conditional statements that link
  together
• Example
• If we dont stop for gas soon, then well run
  out of gas.
• If we run out of gas, then well be late for
  the wedding.
• Therefore, if we dont stop for gas soon, well
  be late for the wedding

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Hypothetical syllogism(common patterns of
deductive reasoning)

• Logical pattern
• If A then B.
• If B then C.
• Therefore, if A then C.

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Hypothetical syllogism(common patterns of
deductive reasoning)

• (3) Modus tollens
• - also called as denying the consequent
  because the argument consists of-
• (i) one conditional premise,
• (ii) a second premise that denies the consequent
  of the conditional (i.e. asserts to be false),
• (iii) a conclusion that denies the antecedent of
  the conditional.

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Hypothetical syllogism(common patterns of
deductive reasoning)

• Example
• If we are in Sacramento, then were in
  California.
• We are not in California.
• Therefore, were not in Sacramento.
• Logical pattern
• If A then B.
• Not B.
• Therefore, not A.

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Hypothetical syllogism(common patterns of
deductive reasoning)

• Note Modus ponens, chain argument, and modus
  tollens are all logically reliable patterns of
  deductive reasoning.
• Logically reliable argument pattern is
  absolutely guaranteed to have a true conclusion
  if the premises are true.

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Hypothetical syllogism(common patterns of
deductive reasoning)

• Two patterns that are not logically reliable
• (4) Denying the antecedent
• - the premises are true and the conclusion is
  false.
• Example
• If Shakespeare wrote War and Peace, then hes a
  great writer.
• Shakespeare didnt write War and Peace.
• Therefore, Shakespeare is not a great writer.

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Hypothetical syllogism(common patterns of
deductive reasoning)

• Logical pattern
• If A then B.
• Not A.
• Therefore, not B.

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Hypothetical syllogism(common patterns of
deductive reasoning)

• (5) Affirming the consequent
• The premises are true, and the conclusion is
  false.
• Example
• If we are on Neptune, then were in the solar
  system.
• We are in the solar system.
• Therefore, were on Neptune.

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Hypothetical syllogism(common patterns of
deductive reasoning)

• Logical pattern
• If A then B.
• B.
• Therefore, A.

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Hypothetical syllogism(common patterns of
deductive reasoning)

• Note
• Even though Denying the antecedent and Affirming
  the consequent are not logically reliable
  patterns of reasoning they should be treated as
  deductive because they have a pattern of
  reasoning that is characteristically deductive.

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categorical syllogism(common patterns of
deductive reasoning)

• Defined as a three-line argument in which each
  statement begins with the word all, some, or no.

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categorical syllogism(common patterns of
deductive reasoning)

• Example
• (1) All oaks are trees.
• All trees are plants.
• So, all oaks are plants.
• (2) Some Democrats are elected officials.
• All elected officials are politicians.
• Therefore, some Democrats are politicians.
  
• Can you guest the logical pattern of these
  arguments?

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categorical syllogism(common patterns of
deductive reasoning)

• Logical pattern
• (1) All A are B.
• All B are C.
• So, all A are C.
• (2) Some A are B.
• All B are C.
• Therefore, some A are C.
• - Because such arguments have familiar form of
  rigorous logical reasoning, they should be
  treated as deductive.

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Argument by elimination(common patterns of
deductive reasoning)

• Definition
• An argument seeks to logically rule out various
  possibilities until only a single possibility
  remains.

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Argument by elimination(common patterns of
deductive reasoning)

• Example
• (1) Either Joe walked to the library or he drove.
• But Joe didnt drive to the library.
• Therefore, Joe walked to the library.
• Either A or B.
• Not B.
• Therefore, A.

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Argument by elimination(common patterns of
deductive reasoning)

• (2) Either Dutch committed the murder, or Jack
  committed the murder, or Celia committed the
  murder.
• If Dutch or Jack committed the murder, then the
  weapon was a rope.
• The weapon was not a rope.
• So, neither Dutch nor Jack committed the murder.
• Therefore, Celia committed the murder.

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Argument by elimination(common patterns of
deductive reasoning)

• Logical pattern
• Either A or B or C.
• If A or B, then D.
• Not D.
• So neither A nor B.
• Therefore, C.
• Note because the aim of such argument is to
  logically exclude every possible outcome except
  one, such arguments are always deductive.

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Argument based on mathematics(common patterns of
deductive reasoning)

• Definition
• The conclusion is claimed to depend largely or
  entirely on some mathematical calculation or
  measurement (perhaps in conjunction with one or
  more nonmathematical premises).

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Argument based on mathematics(common patterns of
deductive reasoning)

• Example
• Eight is greater than four.
• Four is greater than two.
• Therefore, eight is greater than two.
• Logical pattern
• A is greater than B.
• B is greater than C.
• Therefore, A is greater than C.

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Argument based on mathematics(common patterns of
deductive reasoning)

• (2) Light travels at a rate of 186,000 miles per
  second.
• The sun is more than 93 million miles distant
  from the earth.
• Therefore, it takes more than eight minutes for
  the suns light to reach the earth.
• Argument (1) the word greater refers to some
  sort of measurement.
• Argument (2) Argument based on certain
  calculation.

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Argument based on mathematics(common patterns of
deductive reasoning)

• Caution Argument based on mathematics can be
  deductive-
• Example My blind uncle told me that there were 8
  men, 6 women, and 12 kids at the party.
• By simple addition, therefore, it
  follows that there were 26 people at the
  party.
• Conclusion clearly does not follow from the
  premise, because perhaps my blind uncle
  miscounted
• - Best treated as inductive.

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Argument from definition(common patterns of
deductive reasoning)

• Characteristic The conclusion is presented as
  being true by definition.
• Example (1) Janelle is a cardiologist.
  Therefore, Janelle is a doctor.
• (2) Bertha is an aunt. It follows that she is a
  woman
• Because the statement that follows by definition
  is necessarily true if the relevant definition is
  true, this argument is treated as deductive.

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conclusion
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• Thank you.
• Any question(s)??

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References
Bassham, Irwin, et. al. Critical Thinking A
Students Introduction. 3rd edition. New York
McGraw-Hill, 2008.
Jones, Royce. Foundations of Critical Thinking.
New York Harcourt, Inc., 2001.
Macer, Darryl. Moral Games for Teaching
Bioethics.Haifa UNESCO Chair in Bioethics, 2008.