7—Deductive Reasoning

  • View
    215

  • Download
    0

Embed Size (px)

Text of 7—Deductive Reasoning

  • 8/9/2019 7—Deductive Reasoning

    1/32

    9—Deductive Reasoning SJSU Spring 2014 Comm 41 Sect 04, 06 Minna Holopainen

    SJSU Spring 2014 Comm 41 Holopainen

    Photo Sonja Holopainen

    1

  • 8/9/2019 7—Deductive Reasoning

    2/32

    Agenda

    Syllogisms Aristotelian Logic Diagramming Arguments

    SJSU Spring 2014 Comm 41 HolopainenPhoto Sonja Holopainen

    2

  • 8/9/2019 7—Deductive Reasoning

    3/32

    Deductive Reasoning

    SJSU Spring 2014 Comm 41 Holopainen

    Syllogisms Aristotelian logic Diagramming arguments

    3

  • 8/9/2019 7—Deductive Reasoning

    4/32

    Two Logic Systems

    + Inductive Reasoning

    Finding patterns Forming conclusions

    - Deductive Reasoning

    Eliminating options Testing hypotheses

    X

    SJSU Spring 2014 Comm 41 Holopainen

    4

  • 8/9/2019 7—Deductive Reasoning

    5/32

    Logic

    Informal logic

    ! The study of natural language arguments

    ! Fallacies

    Formal logic

    ! The study of inference with purely formal content, where that content is made explicit.

    ! Concerned with the form of an argument

    ! Deductive

    ! Aristotle’s syllogistic logic

    SJSU Spring 2014 Comm 41 HolopainenPhoto Sonja Holopainen, 2009

    5

  • 8/9/2019 7—Deductive Reasoning

    6/32

    Types of Deductive Arguments

    Argument by elimination Argument based on mathematics Argument from denition

    SJSU Spring 2014 Comm 41 Holopainen

    6

  • 8/9/2019 7—Deductive Reasoning

    7/32

    Syllogisms

    SJSU Spring 2014 Comm 41 Holopainen

    7

  • 8/9/2019 7—Deductive Reasoning

    8/32

    Syllogisms

    ! Greek: "#$$%&'"()* ( syllogismos )—"conclusion," "inference"

    ! "A discourse in which, certainthings having been supposed, something di +erent from the things' supposed results of necessity because these things are so." (Aristotle’s Prior

    Analytics 24b18–20)

    Aristotle by Rembrandt Picture from http://www.uah.edu/colleges/liberal/philosophy/heikes/302/time/rembrant/aristotle- homer.jpg without permission. SJSU Spring 2014 Comm 41 Holopainen

    8

  • 8/9/2019 7—Deductive Reasoning

    9/32

    SYLLOGISMS

    Categorical Disjunctive Hypothetical

    ENTHYMEME

    Deductive forms of reasoning

    Picture from http://dm-lifeservers.com/wordpress/wp-content/sokrates.gif without permission. SJSU Spring 2014 Comm 41 Holopainen

    Major premise: All men are mortal. Minor premise:

    Socrates is a man. Conclusion: Therefore, Socrates is

    mortal.

    P or Q. Not P.

    Therefore, Q.

    I’ll have co ! ee or tea. Not co ! ee.

    Therefore, tea.

    If P, then Q. P. Therefore, Q.

    If P, then Q. Not Q. Therefore, not P.

    If P Q.

    If Q R.

    Therefore, P R.

    If I go to bed early, I will get enough sleep. If I get enough sleep, I will do well in my speech tomorrow. Therefore, if I go to bed early, I will do well in my speech tomorrow.

    An incomplete argument in which either a premise or conclusion is assumed

    Socrates is mortal because he is a man.

    Socrates is mortal because all men are mortal.

    9

  • 8/9/2019 7—Deductive Reasoning

    10/32

  • 8/9/2019 7—Deductive Reasoning

    11/32

    Aristotelian Logic

    SJSU Spring 2014 Comm 41 Holopainen

    11

  • 8/9/2019 7—Deductive Reasoning

    12/32

    Aristotle 384-322 BCE

    Student of Plato Teacher of Alexander the Great

    Picture from http://en.wikipedia.org/wiki/File:Aristotle_Altemps_Inv8575.jpg without permission. SJSU Spring 2014 Comm 41 Holopainen

    12

  • 8/9/2019 7—Deductive Reasoning

    13/32

    Four Categorical Claims

    SJSU Spring 2014 Comm 41 Holopainen

    13

  • 8/9/2019 7—Deductive Reasoning

    14/32

    SJSU Spring 2014 Comm 41 Holopainen

    14

  • 8/9/2019 7—Deductive Reasoning

    15/32

    All Some No

    Only children are noisy. At least one child is noisy.

    Not a single sweet thing turns sour in my mouth.

    Everything sweet turns sour in my mouth.

    Some sweets turn sour in my mouth.

    No child is noisy.

    Every page has a stain in

    it.

    There is a page that has a

    stain in it. Everybody’s feet were cold.

    There were a few people whose feet were cold.

    All cups were in the cupboard.

    There was a cup that was in the cupboard.

    Each respondent replied promptly.

    A number of respondents replied promptly.

    Not even one page has a

    stain in it. Nobody’s feet were cold.

    There were no cups in the cupboard.

    Not a single respondent replied promptly.

    Every time I call him he answers.

    Only sometimes when I call him he answers.

    He never answers when I call him.

    SJSU Spring 2014 Comm 41 Holopainen

    15

  • 8/9/2019 7—Deductive Reasoning

    16/32

    Four Categorical Claims

    SJSU Spring 2014 Comm 41 Holopainen

    16

  • 8/9/2019 7—Deductive Reasoning

    17/32

    Square of Opposition

    Source Stanford Encyclopedia of Phiosophy at http://plato.stanford.edu/entries/contradiction/. SJSU Spring 2014 Comm 41 Holopainen

    17

  • 8/9/2019 7—Deductive Reasoning

    18/32

    Practice Square of Opposition

    All board members drink co +ee.

    Some board members do not drink co +ee. Contradictories

    Everyone who lives must die.

    Nobody who lives must die.

    Contraries

    Mary always sleeps in class.

    Mary sometimes sleeps in class.

    Subalternates

    Some people like to dance.

    Some people do not like to dance.

    Subcontraries

    Graph from Stanford Encyclopedia of Phiosophy at http://plato.stanford.edu/entries/contradiction/. SJSU Spring 2014 Comm 41 Holopainen

    18

  • 8/9/2019 7—Deductive Reasoning

    19/32

    Four types of claims:

    A—All humans are mortal.

    E—No human is ageless.

    I—Some humans are happy.

    O—Some humans are not greedy.

    There are 256 types of categorical syllogisms: AAA,

    AEA, AIA, AOA, AAE, AAI, etc.

    SJSU Spring 2014 Comm 41 Holopainen

    19

  • 8/9/2019 7—Deductive Reasoning

    20/32

    Diagramming Arguments

    SJSU Spring 2014 Comm 41 Holopainen

    20

  • 8/9/2019 7—Deductive Reasoning

    21/32

    Good arguments

    SJSU Spring 2014 Comm 41 Holopainen

    Valid Strong

    Weak

    Implausible Plausible

    A sound argument has to be

    valid.

    21

  • 8/9/2019 7—Deductive Reasoning

    22/32

    Arguments’ validity and strength

    Bad argumentsGood arguments

    VALID INVALID

    Strong Weak

    Every way the premises could be true leads to the conclusion.

    It is extremely likely that the premises lead to the conclusion.

    It is very unlikely or impossible that the premises lead to the conclusion.

    Whether an argument is valid or strong does not depend on whether the premises are sound/plausible.

    SJSU Spring 2014 Comm 41 Holopainen

    22

  • 8/9/2019 7—Deductive Reasoning

    23/32

    Mortal things

    Men

    Valid All men are mortal. Socrates is a man.

    Therefore, Socrates is mortal.

    Weak All men are mortal. Socrates is mortal.

    Therefore, Socrates is a man.

    Mortal things

    Men

    Mortal things

    Men

    Reasoning with all

    Valid All S are P. Q is S. So Q is P.

    Weak All S are P. Q is P. So Q is S.

    SJSU Spring 2014 Comm 41 Holopainen

    23

  • 8/9/2019 7—Deductive Reasoning

    24/32

    Cranky

    Busy

    Students

    Valid All students are busy people. All busy people are cranky. So all students are cranky.

    Invalid/weak Some students are busy people. Some busy people are cranky. So some students are cranky.

    Cranky

    Cranky

    Reasoning in a chain with all and some

    Valid All S are P. All P are Q. So all S are Q.

    WeakSome S are P. Some P are Q. So some S are Q.

    SJSU Spring 2014 Comm 41 Holopainen

    24

  • 8/9/2019 7—Deductive Reasoning

    25/32

    Mammal

    Cats

    Fish

    Valid Every cat is a mammal. No sh is a mammal. So no sh is a cat.

    Invalid/weak Every cat is a mammal. No sh is a cat. So no sh is a mammal.

    Mammal

    Cats

    Fish

    Mammal

    Cats

    Fish

    Reasoning with no

    Valid All S are P. No Q is P. So no Q is S.

    Weak All S are P. No Q is S. So no Q is P.

    SJSU Spring 2014 Comm 41 Holopainen

    25

  • 8/9/2019 7—Deductive Reasoning

    26/32

    Delicious things

    Usually strong Almost all cookies are delicious. Madeline is a cookie. So Madeline is delicious.

    Weak Almost all cookies are delicious. Madeline is delicious. So Madeline is