Philosophy 1100

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Philosophy 1100 Class 8
Title Critical Reasoning Instructor Paul
Dickey E-mail Address pdickey2_at_mccneb.edu Website
http//mockingbird.creighton.edu/NCW/dickey.htm
Today Submit Portfolio Turn in Exercise
8-2 Final Essay -- Questions? Wrap-up Chapter
7 Read Chapter 8, pp. 253- 261,
264-266. pp.271-279 pp. 281-284 Next
Week Final Editorial Essay Exercises 8-12 (Odd
problems) Read Chapter 9, pages 295-302,
317-321.
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Chapter Seven Logical Fallacies
Presenters Zechariah Ad Hominem
Fallacy Jaime The Genetic Fallacy Tracy The
Straw Man Jacquie The False Dilemma
Perfectionism Jonathan The Slippery
Slope Anthony Misplacing the Burden of
Evidence/Proof Amber Begging the
Question Emmanuel Formal Fallacies (Affirming
the Consequent Denying the Antecedent,
The Undistributed Middle) In your presentation,
you must define your fallacy type, give examples,
and distinguish it from other logical fallacies
that are similar. I encourage you to use
powerpoint slides in your presentation if
possible, but it is not necessary.
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The Top Ten Fallacies of All Time (according to
your author)
GROPES JAWS
Group Think Red Herring Argument From
Outrage Argument from Popularity Post Hoc, Ergo
Propter Hoc Straw Man Jump to Conclusion Ad
Hominem Argument Wishful Thinking Scare Tactic
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Chapter EightDeductive ArgumentsCategorical
Logic
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Categorical Logic

• Consider the following claims
• 1. Everybody who is ineligible for Physics 1A
  must take Physical Science 1.
• 2) No students who are required to take Physical
  Sciences 1 are eligible for Physics 1A.
• Are these different claims or the same claim?
• Categorical logic is important because it gives
  us a tool to work through the confusion with a
  technique to answer that question clearly.
• Such is done through the use of standard logic
  forms.

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Categorical Logic

• Categorical Logic is logic based on the relations
  of inclusion and exclusion among classes.
• That is, categorical logic is about things being
  in and out of groups and what it means to be in
  or out of one group by being in or out of another
  group.

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Four Basic Kinds of Claims in Categorical
Logic (Standard Forms)
A All _________ are _________. (Ex. All
Presbyterians are Christians. E No ________
are _________. (Ex. No Muslims are Christians.
___________________________________ I Some
________ are _________. (Ex. Some Arabs are
Christians. O Some ________ are not
_________. (Ex. Some Muslims are not Sunnis.
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Four Basic Kinds of Claims in Categorical Logic
What goes in the blanks are terms. In the first
blank, the term is the subject. In the second
blank goes the predicate term. A All
____S_____ are ____P_____. (Ex. All
Presbyterians are Christians.
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Venn Diagrams
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Categorical Logic
The Four Basic Kinds of Claims in Categorical
Logic can be represented using Venn Diagrams.
(See page 256 in textbook.)
The two claims that include one class or part of
a class within another are the affirmative claims
(I.e. the A-claims the I-Claims. The two
claims that exclude one class or part of a class
from another are the negative claims (I.e. the
E-claims and the O-claims.
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The Bottom Line? Translating Claims into Standard
Form for Analysis

• Two claims are equivalent claims if, and only if,
  they would be true in all and exactly the same
  circumstances.
• Equivalent claims, in this sense, say the same
  thing.
• Equivalent claims will have the same Venn
  Diagram.

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Some Tips

• The word only used by itself, introduces the
  predicate term of an A-claim, e.g.
• Only Matinees are half-price shows is to be
  translated as All half-price shows are matinees
• The phrase the only introduces the subject term
  of an A-claim, e.g
• Matinees are the only half-price shows also
  translates to All half-price shows are
  matinees.
• Claims about single individuals should be treated
  as A-claims or E-claims, e.g.
• Aristotle is left-handed translates to either
  Everybody who is Aristotle is left handed or
  No person who is Aristotle is not left-handed.

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Class Workshop Exercise 8-2
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Three Categorical Operations

• Conversion The converse of a claim is the claim
  with the subject and predicate switched, e.g.
• The converse of No Norwegians are Swedes is
  No Swedes are Norwegians.
• Obversion The obverse of a claim is to switch
  the claim between affirmative and negative (A -gt
  E, E -gt A, I -gt O, and O -gt I and replace the
  predicate term with the complementary (or
  contradictory) term, e.g.
• The obverse of All Presbyterians are
  Christians is No Presbyterians are
  non-Christians.
• Contrapositive The contrapositive of a claim is
  the cliam with the subject and predicate switched
  and replacing both terms with complementary terms
  (or contradictory terms), e.g.
• The contrapositive of Some citizens are not
  voters is Some non-voters are not
  noncitiizens.

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OK, So where is the beef?

• By understanding these concepts, you can apply
  the
• three rules of validity for deductive arguments
• Conversion The converses of all E- and I-
  claims, but not A- and O- claims are equivalent
  to the original claim.
• Obversion The obverses of all four types of
  claims are equivalent to their original claims.
• Contrapositive The contrapositives of all A-
  and O- claims, but not E- and I- claims are
  equivalent to the original claim.

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Class Workshop Exercise 8-4 8-5
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Categorical Logic

• Translate the following claims
• Everybody who is ineligible for Physics 1A must
  take Physical Science 1.
• I Ineligible for Physics 1A
• M Must take Physical Science 1.
• All I are M
• 2) No students who are required to take Physical
  Sciences 1 are eligible for Physics 1A.
• No M are non-I

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• Are these different claims or the same claim?
• 1) All I are M
• 2) No M are non-I
• -- Obverse is All M are I.
• -- Obverse is equivalent for all claims.
• Draw the Venn diagrams!
• Or alternately, consider
• The contrapositive of 2) is
• No I are Non-M.
• The obverse of 1) is
• No I are Non-M.

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Categorical Syllogisms

• A syllogism is a deductive argument that has two
  premises -- and, of course, one conclusion
  (claim).
• A categorical syllogism is a syllogism in which
• each of these three statements is a standard
  form, and
• there are three terms which occur twice, once
  each in two of the statements.

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Three Terms of a Categorical Syllogism

• For example, the following is a categorical
  syllogism
• (Premise 1) No Muppets are Patriots.
• (Premise 2) Some Muppets do not support
  themselves financially.
• (Conclusion) Some puppets that do not support
  themselves are not Patriots..
• The three terms of a categorical syllogism are
• 1) the major term (P) the predicate term of the
  conclusion (e.g. Patriots).
• 2) the minor term (S) the subject term of the
  conclusion (e.g. Puppets that are non
  self-supporters)
• 3) the middle term (M) the term that occurs in
  both premises but not in the conclusion (e.g.
  Muppets).

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USING VENN DIAGRAMS TO TEST ARGUMENT VALIDITY

• Identify the classes referenced in the argument
  (if there are more than three, something is
  wrong).
• When identifying subject and predicate classes
  in the different claims, be on the watch for
  statements of not and for classes that are in
  common.
• Make sure that you dont have separate classes
  for a term and its complement.
• 2. Assign letters to each classes as variables.
• 3. Given the passage containing the argument,
  rewrite the argument in standard form using the
  variables.

M xxxx S yyyy P zzzz
No M are P. Some M are S. ____________________ T
herefore, Some S are not P.
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• Draw a Venn Diagram of three intersecting
  circles.
• Look at the conclusion of the argument and
  identify the subject and predicate classes.
• Therefore, Some S are not P.
• Label the left circle of the Venn diagram with
  the name of the subject class found in the
  conclusion. (10 A.M.)
• Label the right circle of the Venn diagram with
  the name of the predicate class found in the
  conclusion.
• Label the bottom circle of the Venn diagram with
  the middle term.

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No M are P. Some M are S.

• Diagram each premise according the standard Venn
  diagrams for each standard type of categorical
  claim (A,E, I, and O).
• If the premises contain both universal (A
  E-claims) and particular statements (I
  O-claims), ALWAYS diagram the universal statement
  first (shading).
• When diagramming particular statements, be sure
  to put the X on the line between two areas when
  necessary.
• 10. Evaluate the Venn diagram to whether the
  drawing of the conclusion "Some S are not P" has
  already been drawn. If so, the argument is VALID.
  Otherwise it is INVALID.

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Class Workshop Exercise 8-11, 6 More from
8-11?
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Power of Logic Exercises
http//www.poweroflogic.com/cgi/Venn/venn.cgi?exer
cise6.3B
ANOTHER GOOD SOURCE http//www.philosophypages.c
om/lg/e08a.htm