Logic

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Logic

• The Science (or Art) of Evaluating Arguments

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The Basics of Argument

• Argument a series of statements, one or more of
  which (premises) are claimed to provide support
  for one of the others (the conclusion).
• In a good argument, the premise(s) provide(s)
  support for the conclusion
• In a bad argument the premises do not support
  the conclusion.

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A statement is

• A declarative sentence or clause that contains a
  falsifiable representation of fact.
• E.g.
• Wenzel has terrible taste in clothes.
• It is imperative that the U.S. build a missile
  defense system.
• Canada is in Eastern Europe.
• Water is a universal solvent.

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Non statements include

• Questions Where did you get that awful haircut?
• Proposals Lets find a stylist that can undo
  some of the damage.
• Suggestions I suggest you fix that before you
  let yourself be seen in public.
• Commands My husbands home, hide in the closet.

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Two categories of statements

• Premises statements of fact that provide
  evidence or reasons.
• Conclusions a statement that the evidence or
  reason is supposed to support or imply.

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A simple argument

• The possibility of nuclear weapons in the
  hands of rouge states poses great danger to the
  safety of the United States. An anti-ballistic
  missile system offers protection from the threat
  of ballistic missiles. Therefore, the nation must
  build a missile defense system.

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Conclusion Indicators

• Therefore
• Wherefore
• Thus
• Consequently
• Accordingly
• We may conclude that
• 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 form
• As

• Given that
• Seeing that
• For the reason that
• Inasmuch as
• Owing to

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Evaluating a Simple Argument

• The possibility of nuclear weapons in the hands
  of rouge states poses great danger to the safety
  of the United States. An anti-ballistic missile
  system offers protection from the threat of
  ballistic missiles. Therefore, the nation must
  build a missile defense system.
• P1 The possibility of nuclear weapons in the
  hands of rouge states poses great danger to the
  safety of the United States.
• P2 An anti-ballistic missile system offers
  protection from the threat of ballistic missiles.
  
• C Therefore, the nation must build a missile
  defense system.

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Analyzing Simple Arguments I

• Since the good, according to Plato, is that which
  furthers a persons real interests, it follows
  that in any given instance when the good is
  known, men will seek it.
• As the denial or perversion of justice by the
  sentences of courts, as well an in any other
  manner, is with reason classed among the just
  causes of war, it will follow that the federal
  judiciary ought to have cognizance of all causes
  in which the citizens of other countries are
  concerned. (Hamilton, The Federalist No. 80. )
• Punishment, when speedy and specific , may
  suppress undesirable behavior, but it cannot
  teach or encourage desirable alternatives.
  Therefore, it is crucial to use positive
  techniques to model and reinforce appropriate
  behavior that the person can use in place of the
  unacceptable response that has been suppressed.
  (Mischel and Mischel, Essentials of Psychology)
• To every existing thing God wills some good.
  Hence, to love any thing is nothing else than to
  will good to that thing, it is manifest that God
  loves everything that exists. (Aquinas, Summa
  Theologica)
• Poverty offers numerous benefits to the nonpoor.
  Antipoverty programs provide jobs for
  middle-class professionals in social work,
  penology and public health. Such workers future
  advancement is tied to the continual growth of
  bureaucracies dependent on the existence of
  poverty. (Palen, Social Problems)

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Analyzing Simple Arguments I (cont)

• If a piece of information is not job relevant,
  then the employer is not entitled qua employer to
  know it. Consequently, since sexual practices,
  political beliefs, associational activities,
  etc., are not part of the description of most
  jobs, that is, since they do not directly affect
  ones job performance, the are not legitimate
  information for an employer to know in the
  determination of the hiring of a job applicant.
  (Brentken, Privacy, Polygraphs and Work)
• Anyone familiar with our prison system knows that
  there are some inmates who behave little better
  than brute beasts. But the very fact that these
  prisoners exist is a telling argument against the
  death penalty. If the death penalty had been a
  truly effective deterrent, such prisoners would
  long ago have vanished. (The Injustice of the
  Death Penalty, America)
• Since the secondary light from the moon does
  not inherently belong to the moon, and is not
  received from any star or from the sun, and since
  in the whole universe there is no other body left
  but the earth, what must we conclude? What is to
  be proposed? Surely we must assert that the lunar
  body (or any other dark and sunless orb) is
  illuminated by the earth. (Galilei, The Starry
  Messenger)
• Neither a borrower not a lender be, For loan oft
  loses both itself and friend, And Borrowing dulls
  the edge of husbandry. (Shakespeare, Hamlet)
• The possibility of nuclear weapons in the hands
  of rouge states poses great danger to the safety
  of the United States. An anti-ballistic missile
  system offers protection from the threat of
  ballistic missiles. Therefore, the nation must
  build a missile defense system.

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Simple Arguments II

• University administrators know well the benefits
  that follow notable success in college sports
  increased applications for admissions sic,
  increased income from licensed logo merchandise,
  more lucrative television deals, post-season game
  revenue and more successful alumni fund drives.
  The idea that there is something ideal and pure
  about the amateur athlete is self-serving bunk.
  (anon letter to and editor)
• College is a time in which a young mind is
  supposed to mature and acquire wisdom, and one
  can only do this by experiencing as much diverse
  intellectual stimuli as possible. A business
  student may be a whiz at accounting, but has he
  or she ever experienced the beauty of a
  Shakespearean sonnet or the boundless events of
  Hebrew history? Most likely not. While many of
  these neoconservatives will probably go on to be
  financially successful, they are robbing
  themselves of the true purpose of collegiate
  academics, a sacrifice that outweighs future
  salary checks. (Griffith, Conservative College
  Press.)
• At a time when our religious impulses might help
  heal the pains and strains in our society,
  todays television pulpiteers preach intolerance,
  censure, and discrimination. They package a
  believer life-style, and rail against everyone
  who doesnt fit it homosexuals, communists,
  Jews, and other non-Christians, sex educators and
  so on. Such intolerance threatens to undermine
  the pluralism that marks our heritage, The
  packaging of that intolerance in slick Hollywood
  programming or under the guise of patriotic
  fervor is skillfully accomplished on many fronts.
  That, however, does not make it right. (Kreitler,
  TV Preachers Religious Intolerance)

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Simple Arguments II

• Most of the environmental Problems facing us
  stem, at least in part, from the sheer number of
  Americans. The average American produces three
  quarters of a ton of garbage every year, consumes
  hundreds of gallons of gasoline and uses large
  amounts of electricity (often from a nuclear
  power plant, coal burning, or a dam). The least
  painful way to protect the environment is to
  limit population growth. (anon, letter to an
  editor)

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Identifying Arguments

• Conditions for the presence of an argument
• One of the statements must claim to present
  evidence of something.
• There must be a claim that the alleged evidence
  provides support for or the implication of
  something.
• For our purposes, the truth value of the
  statements is immaterial. All that matters is
  that a claim be made or implied.

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Types of Claims

• Factual Condition 1 on the preceding slide.
  Relatively easy to identify.
• Inferential Condition 2 on the preceding slide.
  More difficult to isolate. The passage expresses
  a reasoning process, that one or more elements in
  the passage supports a conclusion.

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Types of Inferential Claims

• Explicit Usually asserted by a premise or
  conclusion indicator.
• E.g. The human eye can see a source of light as
  faint as an ordinary candle at a distance of 27
  kilometers, through a non-absorbing atmosphere.
  Thus, a power searchlight directed from a new
  moon should be visible on earth to the naked eye.
  (Papalia and Olds, Psychology)
• Implicit May not include indicator words.
• E.g. The price reductionseen with the electronic
  calculator is the result of of a technological
  revolution. The calculator of the 1960s used
  integrated electronic circuits that contained
  about a dozen transistors or similar components
  on a single chip. Today, mass produced chips,
  only a few millimeters square, contain several
  thousand such components. (Biokess and Edelson,
  Chemical Principles)

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Arguments that Arent

• The mere presence of indicator words in a
  sentence does not guarantee that an argument is
  present.
• Compare
• Since Edison invented the phonograph, there have
  been many technological advances.
• Since Edison invented the phonograph, he deserves
  credit for a major technological development.

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Types of Non-Arguments

• Simple Non-Inferential Passages (lack a claim of
  proof)
• Warnings unsupported expressions intended to
  put someone on notice of a possible danger
• Be careful on the train to Comiskey Park.
• Advice recommendations for future conduct
• If you take a course from Wenzel get several sets
  of earplugs and stock up on NoDoz.

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Simple Non-Inferential Passages (cont).

• Statements of opinion unsupported statements of
  the authors (or someone elses) belief(s).
• A nation with a high moral tradition has an
  obligation to ensure that education is available
  to all of its citizens.
• Loosely Associated Statements generally related
  but lack an assertion of proof.
• Not to value men of worth will keep people from
  contention not to value goods that are hard to
  come by will keep them from theft not to display
  what is desirable will keep them from being
  unsettled of mind. (Lao-Tzu, Thoughts from Tao Te
  Ching)

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Simple Non-Inferential Passages (cont).

• Reports simple provision of information
• E.g. A brush fire raging in mountains above
  Moreno Valley, California is threatening a number
  of homes including that of a former dean of the
  College of Arts, Humanities, and Social Sciences.
• Can serve as premises for an argument, but
  because no supportive linkage is claimed, no
  argument exists.

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Expository Passages

• Consist of a topic statement, followed by one or
  more sentences that elaborate on or develop the
  topic. If no attempt is made to prove a
  contention, no argument exists.
• There is a stylized relation of the artist to
  mass audience in sports, especially in baseball.
  Each player develops a style of his own the
  swagger as he steps to the plate, the unique
  windup a pitcher has, the clean-swinging and
  hard-driving hits, the precision and grace of
  infield and outfield, the sense of surplus power
  behind whatever is done. (Lerner, America as a
  Civilization)

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Expository Passages (cont.)

• In some cases expository passages can be treated
  as arguments.
• Skin and mucus membrane lining the respiratory
  and digestive tracts serve as mechanical barriers
  to entry by microbes. Oil gland secretions
  contain chemicals that weaken or kill bacteria on
  the skin. The respiratory tract is lined by cells
  that sweep mucus and trapped particles up into
  the throat, where they can be swallowed. The
  stomach has an acid pH, which inhibits the growth
  of many types of bacteria. (Mader, Human Biology)

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Illustrations

• A statement on a topic accompanied by one or more
  references to examples of the subject phenomenon.
• At high speeds ordinary objects behave in
  unexpected ways. For example, tornados have been
  know to drive small twigs through homes wood
  siding.

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Explanations

• A group of statements that shed light on an event
  the existence of which is generally agreed upon
  as a matter of fact.
• The space shuttle Challenger exploded because an
  O-ring failed in one of the booster rockets.
• The United States won the battle of Midway
  because the Japanese Navy suffered from
  overconfidence.

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Conditional Statements

• A statement in the form of if antecedent, then
  consequent is not an argument. These may also
  be stated in the form, consequent if
  antecedent.
• If you add water to a bucket it will weigh more
  than it did before.
• If both Saturn and Uranus have rings, then Saturn
  has rings.
• Can the second statement be stated in terms of an
  argument? How?

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Conditional Statements (cont.)

• Conditional Statements can be related to
  arguments, either as premises, conclusions, or
  both.
• If fast food vendors warn of the dangers of hot
  coffee, consumers assume the risk of burning
  themselves if they drink coffee while driving.
• FF vendors put warning labels on coffee cups.
• Therefore, consumers assume the risk of burns.
• If power companies make bad investments, they
  will be threatened with bankruptcy.
• If power companies are threatened with
  bankruptcy, the taxpayers will be forced to bail
  them out.
• Therefore, if power companies make bad
  investments, the taxpayers will be forced to bail
  them out.

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Conditional Statements (cont.)

• Rules for conditional statements
• A single conditional statement is not an argument
• A conditional statement may serve as the premise
  of an argument, the conclusion, or both.
• The inferential content of a conditional
  statement may be reexpressed to form an argument.

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Induction and Deduction

• Deductive an argument that contains premises
  that are presented in such a way that, if the
  premises are true, the conclusion must be true.
• Inductive a probabilistic style of argument.
  The support provided by the premises (if true)
  makes it likely, but not necessary that the
  conclusion is true.

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Deductive Arguments

• The Matterhorn is higher than Mount Whitney and
  Mount Whitney is higher than Mount Rainier.
  Therefore, the Matterhorn is higher than Mount
  Rainier.

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Types of Deductive Arguments

• Arguments based on mathematics
• E.g. a piece of property is measured to be 100
  feet wide by 200 feet deep. The property contains
  20000 square feet.
• Arguments from definitions arguments based
  simply on the definition of one or more of the
  words in the premise or conclusion.
• E.g. George is obtuse because he is not terribly
  bright.
• Syllogisms a form of argument consisting of two
  premises and one conclusion.

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Syllogisms

• Three types
• Categorical based on a quantification using
  terms such as all, no, or some.
• All women are short.
• Elena is a woman
• Therefore, Elena is short.
• Hypothetical a syllogism having a conditional
  statement as one or both premises
• If quartz scratches glass, then quartz is harder
  than glass.
• Quartz scratches glass.
• Therefore, quartz is harder than glass.
• Disjunctive a syllogism that incorporates a
  disjunctive term (an either or statement)
  as a premise.

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Inductive Arguments

• Predictions a prediction of some future event
  based on knowledge of past events.
• E.g. forecasting the weather (see chaos theory)
• Arguments from analogy a condition affect a
  known thing or situation is applied to a lesser
  known thing or situation because of attributes
  the two share.
• Joes Pinto is extremely fast. Therefore, Thomas
  Pinto is also fast.
• Inductive generalization generalizing to a
  group based on knowledge of a sample.
• See opinion surveys

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Induction (cont.)

• Argument from authority argument based on a
  statement or statements made by a authority on
  the subject.
• Causal inference arguments that proceed from an
  understanding of cause and effect.
• If you know that a bottle of water was left in
  the freezer overnight you might conclude that it
  had frozen.
• The Case of the Phantom sprinkler.