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Arguments

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					                 LOGIC I
General methodology and
   introduction to formal
                     logic
                    DRAFT
l   Lectures on informal logic are based on
    books by Fogelin & Sinnot-Armstrong, Fisher
    and Thomson and on lectures by Jesper
    Kallestrup.
Lecture I
Informal reasoning
l  Skills:
- recognizing reasoning (arguments)
- identifying conclusions
- identifying reasons (premises) and
   assumptions
- evaluating reasoning
l   Logical theory           l   Logical pragmatics
l   Semantic relationships   l   Use of propositions by
    (relationships between       an arguer to carry out
    true or false                the goal of dialogue
    propositions)                (e.g. convince or
l   Argument = set of            persuade the second
    propositions                 arguer)
l   Context irrelevant
A seaman drafted to our ship just before we sailed
  form Halifaxhad never seen his new captain, who at
  sea often went hatless and wore a nondescript
  jacket.
The new man had just begun a forenoon watch on the
  gun deck when the captain came along. The skipper
  suddennly stooped and picked up a butted cigarette.
  He trust the butt at the seaman and demanded: „I
  want to know who the hell owns this damned thing”
The new hand considered for a moment, then said
  slowly to the rankless, hatless officer: „I’d say you
  do, mate. You found it.”
lContext of dialoge
Seaman: the ownership of the cigarette butt
Captain: the issue of keeping the ship clean
Types of argumentative
dialogue
l   Dialogue – a sequence of exchanges of messages or speech acts
    (typically questions and replies) between two (or more) participants
l   Every dialogue has a goal and requires cooperation between the
    participants to fulfill the goal
l   Each participant has an obligation to work toward fulfilling his own
    goal in the dialogue and also an obligation to cooperate with the
    other participant’s fulfillment of his own goal
l   One context of dialogue is the personal quarrel. A
    quarrel is a dialogue in which one tries to trick, cheat or
    even attack one’s opponent directly, rather than one’s
    opponent’s views, using abusive language, appeal to
    emotions, intimidation, one-sided criticism, etc. Any
    means are available no matter whether they are fair or
    reasonable.
l   Aggressive personal attack
l   Appeal to emotions
l   Desire to win the argument at all costs
l   A second context of dialogue is the (forensic)
    debate. In debates there are judges or referees
    who decide, maybe by voting, which side has
    the better argument. There are rules of
    procedure that determine who may speak and
    when and for how long. There are also some
    rules that disallow the more severe forms of
    personal attack, but many fallacious arguments
    may still be tolerated.
l   Audience
l   Rules are often very permissive and may
    allow fallacious arguments
l   Goal: win a verbal victory to impress the
    audience
l   A third context of dialogue is the persuasion dialogue (critical
    discussion). There are two participants each of whom has a
    thesis to prove. Internal proof by a participant means proof by
    inferring a proposition from the other participant’s concession in
    the dialogue. External proof is the introduction of new facts into
    the argument by appealing to scientific evidence or expert
    opinion. The best one can hope for is plausible commitment to
    an opinion based on reasoned evidence.
l   My goal is to persuade you of my thesis; hence I should prove
    that thesis from premises that you accept or are committed to
l   Your goal is to prove your thesis from the premises that I accept
    or am committed to
l   Goal – persuade the other party of your thesis
l   Method – prove your thesis
l   A forth context of dialogue is the inquiry in
    which premises can only be propositions that
    are known to be true, that have been
    established to the satisfaction of all parties to
    the inquiry. The inquiry seeks out as much
    certainty as can be obtained by the given
    evidence. The goal is to accumulate
    knowledge. The participants are neutral
    investigators of an objective truth. The inquiry
    is cooperative rather than adversarial.
l   In negotiation dialogue, the primary goal is
    self-interest and the method is to bargain.
    Bargaining makes no pretensions to be an
    objective inquiry into the truth of the matter.
l   Logical proof is not important
l   Frankly based on personal gain
l   Not neutral, not objective
l   Interest-based conflict
l   Information-seeking dialogue – one party
    has the goal of finding infromation that the
    other party is believed to possess
l   Action-seeking dialogue – one party has
    the goal to bring about a specific course of
    action by the other party
l   Educational dialogue – one party (the
    teacher) has the goal of imparting knowledge
    to the other party (the student)
dialogue         initial situation   method
                                                         goal

quarrel          Emotional disquiet Personal attack      „Hit” out at other

debate           Forensic contest    Verbal victory      Impress audience

Persuasion       Difference of       Internal and        Persuade other
(critical        opinion             external proof
discussion)
inquiry          Lack of proof       Knowledge-based Establish proof
                                     argumentation
negotiation      Difference of       bargaining          Personal gain
                 interests
Info-seeking     Lacking             questioning         Find information
                 information
Action-seeking   Need for action     Issue imperatives   Produce action

educational      ignorance           teaching            Imparting
                                                         knowledge
Arguments
Socrates is a man.
All men are mortal.
Socrates is mortal.
Since Socrates is a man and
all men are mortal,
Socrates is mortal.

Socrates is a man,
since all men are mortal and
Socrates is mortal.
Socrates is a man.
All men are mortal.
Therefore Socrates is mortal.

Since Socrates is a man,
all men are mortal and
Socrates is mortal.
l   An argument is a train of reasoning aimed at
    establishing a particular claim, the conclusion, from
    a number of other claims, the premises. The
    premises are offered as reasons to believe or accept
    the conclusion. Arguments attempt to persuade
    others to accept a claim by offering reasons or
    evidence in support of that claim. One must do two
    things in propounding an argument: justify the
    premises by providing reasons or evidence, and
    show how the conclusion follows from the premises.
l   The bus is late. It must have broke down.

l   That bird can’t be a robin. It doesn’t have a
    red breast.

l   You should try to appear confident in your job
    interview. The employers are looking for
    someone who can speak confidently in
    public.
l   He must be older than he says. He told us he
    was forty-two, but he has a daughter who is
    at least thirty years old.
l   She didn’t turn up for their date. She
    obviously doesn’t really want to be his
    girlfriend. If she’d wanted a serious
    relationship with him she wouldn’t have
    missed the date.

l   The engine won’t fire. The carburettor must
    be blocked.
Reason indicators

Because ….
For ….
Since ….
Follows from the fact that …..
The reason being …..
Firstly, ….secondly,
May be inferred from the fact that ….
Conclusion indicators
l   Therefore
l   So
l   Hence
l   Thus
l   Accordingly
l   Consequently
l   Which proves that
l   Justifies the belief that
l   I conclude that
l   Which implies that
l   Which allows us to infer that
l   It follows that
l   Establishes the fact that
l   Demonstrates that
l   (1) People who diet lose weight. Wojciech
    Mann cannot have dieted. He hasn’t lost
    weight.
l   (1*)    People who diet lose weight. But
    Wojciech Mann hasn’t lost weight.
    (Therefore), he cannot have dieted.
l   (1**)   People who diet lose weight. But
    Wojciech Mann cannot have dieted.
    Therefore, he hasn’t lost weight.
l   People who diet lose weight. Wojciech Mann
    is a good journalist despite his weight.
    Wojciech Mann would be a better journalist if
    he dieted.
l   (1***)  People who diet lose weight. Since
    Wojciech Mann hasn’t lost weight, he cannot
    have dieted.
l   John broke the window because he tripped.
l   John broke the window because he has
    forgotten his key.
l   John must have broken the window because
    he was the only person in the house.
Indicative conditional vs.
argument

l   If international terrorism continues to grow,
    there will be a worldwide crisis.

l   Since international terrorism continues to
    grow, there will be a worldwide crisis.
Standard form of arguments
Socrates is a man.
All men are mortal.
_____________________
Socrates is mortal.
l   Since Chicago is north of Boston, and
    Boston is north of Charleston, Chicago is
    north of Charleston.

l   Toward evening, clouds formed and the sky
    grew darker; then the storm broke.

l   Both houses of Congress may pass the bill,
    but the President may still veto it.
l   Texas has a greater area than Topeka, and Topeka
    has a greater area than the Bronx Zoo, so Texas
    has a greater area than the Bronx Zoo.

l   Other airlines will carry more passengers because
    United Airlines is on strike.

l   Since Jesse James left town, taking his gang with
    him, things have been a lot quieter.
l   Things are a lot quieter because Jesse James left
    town, taking his gang with him.

l   Witches float, because witches are made of wood,
    and wood floats.

l   The hour is up, so you must hand in your exams.

l   Joe quit because his boss was giving him so much
    grief.
l   Red squirrels can eat yellow berries, hawthorn
    berries and rosehips. Grey squirrels can eat none of
    these. However, grey squirrels eat acorns which red
    squirrels cannot eat.

l   In recent years, the demand for computer-literate
    personnel has increased. More students are
    graduating in computing science than before. Some
    companies find that these graduates require further
    training before embarking on a career in computing.
l   The North American Wildlife Federation, which
    sponsors an annual watch for endangered species,
    reports that sightings of the bald eagle between
    1978 and 1979 increased by 35 per cent. In 1979,
    13,127 sightings were reported, 3,400 over the 1978
    count. This indicates considerable growth in the bald
    eagle population.

l   To make an assessment of modern art is an
    impossible task. For one can assess a work of art
    only when there are accepted rules and
    conventions. Modern art has no rules and
    conventions.
l   If the money supply were to increase at less than
    5% the rate of inflation would come down. Since
    the money supply is increasing at about 10%
    inflation will not come down.

l   If Russia were unsure about American reactions to
    an attack on Western Europe, and if her intentions
    were to conquer Western Europe, she would
    create local casus belli (causes of war) but since
    she has not done this, she cannot intend to
    conquer Western Europe.
l   If the civil population cannot be defended in the event of
    nuclear war, we do not need a civil defence policy. But, we do
    need a civil defence policy if ‘deterrence’ is to be a convincing
    strategy. Therefore deterrence is not a convincing strategy.

l   The materials of nature (air, earth, water) that remain
    untouched by human effort belong to no-one and are not
    property. It follows that a thing can become someone’s
    property only if he works and labours on it to change its natural
    state. From this I conclude that whatever a man improves by
    the labour of his hand and brain belongs to him and to him
    alone.
l   The only freedom which deserves the name is that
    of pursuing our own good in our own way, so long
    as we do not attempt to deprive others of theirs, or
    impede their efforts to obtain it. Each is the proper
    guardian of his own health, whether bodily, or
    mental and spiritual. Mankind are greater gainers
    suffering each other to live as seems good to
    themselves, rather than by compelling each to live
    as seems good to the rest.
l   Radioactive elements disintegrate and
    eventually turn into lead. If matter has
    always existed there should be no
    radioactive elements left. The presence of
    uranium etc. is scientific proof that matter
    has not always existed.
l   If the ‘nuclear winter’ scientists are right the
    population of Britain would be virtually
    eliminated in a nuclear war between the
    superpowers even if Britain suffered no
    direct nuclear attack. Quite apart from the
    radioactive fall-out, we would suffer the
    darkness, the subfreezing temperatures
    and the mass starvation of a nuclear winter.
l   Some people have solved their own
    unemployment problem by great ingenuity
    in hunting for a job or by willingness to work
    for less, so all the unemployed could do
    this.
Evaluating arguments
Validity
l An argument is valid if and only if (iff) it is not
  possible for the premises to be true and the
  conclusion false.
All ministers are paid.
Radosław Sikorski is a minister.
_________________
Radosław Sikorski is paid.
All ministers are paid.
Radosław Sikorski is paid.
_________________
Radosław Sikorski is a ministrer.
All MPs are paid.
Bronisław Komorowski is paid.
___________________
Bronisław Komorowski is an MP.
Truth
All MPs are paid.
Bronisław Komorowski is an MP.
___________________
Bronisław Komorowski is paid.
lSoundness
An argument is sound iff it is valid and all of its
 premises are true.
          All premises   At least one
          true           false premise



VALID     SOUND          UNSOUND



INVALID   UNSOUND        UNSOUND
l   Truth and falsity are properties of claims,
    propositions or statements
l   Validity and soundness are properties of
    arguments

l   Valid arguments are truth-preserving.
l   If the argument is invalid, it cannot establish its conclusion.
l   But it may still be a reasonable or persuasive argument by some
    other standards. It may be that the premises lend inductive
    support to the conclusion.
l   Inductive arguments do not guarantee the truth of their
    conclusion, but yield more or less highly probable conclusions.
l   Or it may be that the truth of the conclusion is the best
    explanation of the truth of the premises.
l   When we talk about validity, we typically mean deductive validity.
Valid or invalid?
l   If John has drunken seven pints of lager,
    then he can’t ride his bike. John can’t ride his
    bike. So, John has drunken seven pints of
    lager.

l   If it rains tomorrow, then the match will be
    cancelled. If the trains are not running
    tomorrow, then the match will be cancelled.
    Therefore, if it rains tomorrow, then the trains
    are not running tomorrow.
Most electors prefer A to B
Most electors prefer B to C
_________________________
Most electors prefer A to C
    1/3   1/3   1/3


1   A     C     B


2   B     A     C


3   C     B     A
Sound or unsound?
l   If George Bush will invade Russia, then Tony
    Blair is not a conservative MP. Tony Blair is a
    conservative MP. So, George Bush will not
    invade Russia.

l   Either Hugh Grant is German or PO won the
    last election. PO won the last election. So,
    Hugh Grant is not German.
l   Any argument must take something for
    granted. Basic reasons or basic premises are
    those that are presented without themselves
    being supported by other reasons or
    premises.
l   When a passage contains more than one premise
    we need find out whether joint reasons or
    independent reasons are being offered.
l   It is right to ban cigarette advertising because it
    encourages young people to start smoking. But
    even if it had no such influence on young people, it
    would be right to ban smoking because it could give
    existing smokers the mistaken impression that their
    habit is socially acceptable.
If the money supply were to increase at less
   than 5% the rate of inflation would come
   down. Since the money supply is increasing
   at about 10% inflation will not come down.
l   Some arguments are very complex in that
    they may contain an intermediate conclusion
    and a main conclusion. So, first premises are
    advanced in support of an intermediate
    conclusion, and then that conclusion itself
    features as a premise that is advanced
    together with other premises in support of the
    main conclusion.
l   A majority of prospective parents would
    prefer to have sons rather than daughters.
    So, if people can choose the sex of their
    child, it is likely that eventually there will be
    many more males than females in the
    population. A preponderance of males in the
    population is likely to produce serious social
    problems. Therefore, we should discourage
    the use of techniques which enable people to
    choose the sex of their child.
l   There is no way I can finish my paper before
    the 9 o’clock show, since I have to do the
    reading first, so I won’t even start writing until
    at least 9 o’clock.
I have to do the reading first.
I won’t even start writing until at least 9 o’clock.
________________________
There is no way I can finish my paper before
   the 9 o’clock show.
I have to do the reading first.
_______________________
I won’t even start writing until at least 9 o’clock.
__________________________
There is no way I can finish my paper before
   the 9 o’clock show
Assumptions = suppressed
(unstated) premises
l   We need to distinguish between premises,
    conclusions and assumptions. An
    assumption is something that is taken for
    granted in an argument without being
    explicitly stated.
l   Assumptions function in arguments either by
    giving support to the basic premises, or as a
    missing step within the argument—maybe as
    an additional premise that needs to be added
    in order for the conclusion to follow from the
    existent premises.
l   The burglar must have left by the fire escape.
    This person is not in the building now, but
    has not been seen leaving the building, and
    there are guards posted at each entrance.
Unstated premises:
l Shared facts
l Linguistic principles

Harriet is in New York with her son.
_____________________
Harriet’s son is in New York.
· Donald Tusk cannot become president of the
  United States because he was born in
  Poland.
Other kinds
You shouldn’t buy pornography, because it
 leads to violence toward women.
l   An argument based on suppressed premises
    is called an enthymeme and is said to be
    enthymematic.
argument
l   Some people say that the depiction of
    violence on television has no effect on
    viewer’s behaviour. However, if what was
    shown on television did not affect behaviour,
    television advertising would never influence
    viewers to buy certain products. But we know
    that it does. So it cannot be true that
    television violence does not affect behaviour.
Interpretation I
l   Basic reason: Television advertising affect
    viewers’ behaviour

l   Assumption: Television advertising and
    television violence are similar in that if one
    affects the behaviour of viewers, so does the
    other
l   Conclusion: Television violence affects
    behaviour
Interpretation 2
l   Basic reason 1:       Television advertising
    affect viewers’ behaviour
l   Intermediate conclusion: What is shown on
    television affects viewers’ behaviour
l   Main conclusion: Television violence
    affects viewers’ behaviour
Assert, assume, suppose
l   To assert is to claim that something is true, or to present
    something as true. Assertions are expressed by means of
    assertoric sentences, e.g. ‘the window is closed’. Premises and
    conclusions of arguments are asserted propositions. To assert
    that p is typically to express the belief that p.
l   To assume is to take something for granted without actually
    mentioning or asserting it. Assumptions (suppressed premises)
    are typically implicit, but can be made explicit by means of
    assertoric sentences.
l   To suppose is to take something for granted for the sake of
    argument. Suppositions are explicit, but are not asserted. To
    suppose that p needn’t express belief or acceptance that p. P
    isn’t presented as being true, but is put forward so that we may
    consider its implications. The supposition that p is often made in
    order to conclude that p is false.
Supposing for the sake of
argument that ....
l   suppositional arguments
l   In suppositional arguments, p is supposed to be true
    by the arguer. But the arguer doesn’t have to believe
    that p.

l   Suppose Darwin’s theory of evolution is true. Then
    there should be fossil evidence which shows
    species changing and evolving, but this evidence
    simply doesn’t exist so Darwin’s theory must be
    wrong.
l   In suppositional arguments the arguer often
    believes or knows that p is false. The arguer
    asks us to consider p with a view to drawing
    out its implications—implications which he
    takes to be implausible.
Supposition indicators:
l   Suppose that ...
l   Let us assume that...
l   Imagine that...
l   Consider the hypothesis/theory that...
l   Let us postulate that...
Conditionalisation

l   Suppose we have an argument which
    proceeds from some supposition R to the
    conclusion C by logically valid steps (i.e. the
    conclusion at each step follows from the
    reasons given for it) then the validity of the
    argument entitles us to infer the conditional
    (hence the name ‘conditionalisation’), if R
    then C.
Rule
l   If we have an argument which proceeds from
    a supposition R to a conclusion C and then
    conditionalises to the conclusion „if R then
    C”, whether this conditional conclusion is
    established does not depend on the truth of
    R. If other basic reasons are true and the
    argument is sound, „if R then C” is
    established whether R is true or false.
l   Suppose that Einstein’s theory of relativity is
    true. Then it follows that everything is
    relative. So, it follows that there are no
    absolute moral values. So, if Einstein’s theory
    of relativity is true, then there are no absolute
    moral values.
l   Suppose that u<Einstein’s theory of relativity
    is true>. Then it follows that u<everything is
    relative>. So, it follows that u<there are no
    absolute moral values>. So, if Einstein’s
    theory of relativity is true, then there are no
    absolute moral values.
Galileo’s argument
l   Suppose (as Aristotle believed) that the heavier a body is, the
    faster it falls to the ground and suppose that we have two bodies,
    a heavy one called H and a light one called L. Under our initial
    assumption, H will fall faster than L. Now suppose that H and L
    are joined together thus L/H. Now what happens? Well, L/H is
    heavier than H, so by our initial assumption it should fall faster
    than H alone. But in the joined body L/H L and H will each tend
    to fall just as fast as before they were joined, so L will act as a
    brake on H and L/H will fall slower than H alone. Hence it follows
    from our initial assumption that L/H will fall both faster and slower
    than M alone. Since this is absurd, our initial assumption must be
    false.
l   This style of reasoning is called reductio ad
    absurdum: a particular claim is supposed for
    the sake of argument. Then an absurdity - a
    contradiction for instance - is deduced via
    logically valid steps.
Induction versus deduction
All ravens are black.
______________
If there is a raven on top of Mount Blanc, then it
   is black.
All ravens we have observed are black.
_________________________
All ravens are black.
l   Deductive: P1, ..., Pn; therefore Q

l   Inductive: P1, ..., Pn; therefore Q is very
    likely to be true

Strong/weak
All ravens are black.
______________
If there is a raven on top of Mount Blanc, it is
   black.

All observed ravens have been black.
______________
If there is a raven on top of Mount Blanc, it is
   black.
l   Deductive – monotonic; conclusive support;
    hard to establish the truth of the premise
l   Inductive – nonmonotonic; partial support
l   The sun is coming out, so the rain should
    stop soon.

l   It’s going to rain tomorrow, so it is either
    going to rain or going to be clear tomorrow.
Inductive generalizations
In the past, when I tried to use 1 Euro coins in
  Polish supermarket trolleys, they have not
  worked.
_________________
1 Euro coins do not work in Polish supermarket
  trolleys.

Opinion polls; samples
samples
l   Unfair/biased
l   Large enough (not affected by runs of luck)
l   Representative

l   Phrasing of questions may influence the
    outcome
Slanted questions
l Which do you favour:
(a) preserving a citizen’s constitutional right to
  bear arms or
(b) leaving honest citizens defenseless against
  armed criminals?
l Which do you favour:
(a) restricting the sale of assault weapons or
(b) knuckling under to the demands of the well-
  financed gun lobby?
Informal judgmental heuristics
l   General strategy for solving a problem; we
    rely too heavily on them
The representative heuristics
l   You are randomly dealt five-card hands from
    a standard deck.
l   Which of the following two hands is more
    likely to come up?
(1)                 (2)
Three of clubs      Ace of spades
Seven of diamonds   Ace of hearts
Nine of diamonds    Ace of clubs
Queen of hearts     Ace of diamonds
King of spades      King of spades
l   Unimpressive strikes us as representative
l   Linda is 31 years old, single, outspoken and
    very bright. She majored in philosophy. As a
    student, she was deeply concerned with
    issues of discrimination and social justice,
    and also participated in anti-nuclear
    demonstrations.
Rank the following statements with respect to the
probability that they are also true of Linda:

l   Linda is a teacher in elementary school.
l   Linda works in a bookstore and takes Yoga
    classes.
l   Linda is active in the feminist movement.
l   Linda is a bank teller.
l   Linda is an insurance sales person.
l   Linda is a bank teller and is active in the
    feminist movement.
The availability heuristic
l   In four pages of a novel (about 2000 words),
    how many words would you expect to find
    that have the form ----ing (seven-letter word
    that end with ing)?
l   In four pages of a novel (about 2000 words),
    how many words would you expect to find
    that have the form -----n-
l   The median estimates were 13.4 for ----ing
    word and 4.7 for -----n- word.
l   More available to our memory, naturally
    come to mind; easier to think of

l   Is the situation sufficiently standard to allow
    the use of informal judgmental heuristics?
l   Inductive/statistical generalisation: sample ®
    population
l   Statistical syllogism: population ®
    member/subset
Statistical Syllogisms
Ninety-seven percent of the Republicans in
  California voted for Bush.
Marvin is a Republican from California.
______________________
Marvin voted for Bush.

                     STRONG
Three percent of the socialists in California
  voted for Bush.
Maureen is a socialist from California.
_______________
Maureen didn’t vote for Bush.

                      STRONG
X percent of Fs have the feature G.
a is an F.
__________________
a has/ doesn’t have the feature G.

F – the reference class
Ninety-seven percent of the Republicans in California
  voted for Bush.
Marvin is a Republican from California.
______________________
Marvin voted for Bush.
Three percent of Clinton’s relatives voted for Bush.
Marvin is a relative of Clinton.
______________________
Marvin didn’t vote for Bush.               M
Forty-two percent of Republicans from
  California who were relatives of Clinton voted
  for Bush.
Marvin is a Republican from Cliafornia who is a
  relative of Clinton.
_________________
Marvin voted for Bush.     WEAK
Less than 1 percent of the people in the world
  voted for Bush.
Gale is a person in the world.
_______________________
Gale didn’t vote for Bush.
Reasoning about causes
l   General conditional:
l   For all x, if x has the feature F, then x has the
    feature G.

l   If something is a square, then it is a
    rectangle.
Causal generalizations
l   For all x, if x has the feature F, then x has the
    feature G.

l   X’s having the feature F is a sufficient
    condition for its having the feature G, and
    x’s having the feature G is a necessary
    condition for its having the feature F.
Causal correlation?
l   At one time there was a strong negative
    correlation between the number of mules in a
    state and the salaries paid to professors at
    the state university. In other words, the more
    mules, the lower professorial salaries.
l   There is a high positive correlation between
    the number of fire engines in a particular
    borough in New York City and the number of
    fires that occur there.
l   That F is a sufficient condition for G means
    that whenever F is present G is present .

l   That F is a necessary condition for G
    means that whenever F is absent G is
    absent.
The sufficient-condition test
(Mill’s Method of Difference)
A, B, C, D – candidates for sufficient conditions
G – target feature
l A        B          C           D           G
l ØA       B          C           ØD          ØG
l A        ØB         ØC          ØD          ØG
SCT: Any candidate that is present when G is
  absent is eliminated as a possible sufficient
  condition of G.
The necessary-condition test
(Mill’s Method of Agreement)
l   A     B          C         D          ØG
l   ØA    B          C         D          G
l   A     ØB         C         ØD         G

NCT: Any candidate that is absent when G is
 present is eliminated as a possible necessary
 condition of G.
l   A         B     ØC           D           ØG
l   ØA        B     C            D           G
l   A         ØB    C            D           G

l   Which of the candidates is not eliminated by SCT?
l   Which of the candidates is not eliminated by NCT?
l   Which of the candidates is not eliminated by either
    test?
l   A         B     ØC           D           ØG
l   ØA        B     C            D           G
l   A         ØB    C            D           G

l   Which of the candidates is not eliminated by SCT?
    C
l   Which of the candidates is not eliminated by NCT?
    C, D
l   Which of the candidates is not eliminated by either
    test? C
Inferences to the best
explanation
l   The idea is that a hypothesis gains inductive
    support if, when it is added to our stock of
    previously accepted beliefs, it increases our
    ability to make reliable predictions and
    illuminating explanations.
You come back home and discover that the lock
on your front door is broken and several valuable
objects are missing

Hypotheses:
l your house was burglarized;

l there was a drug bust and the authorities had
  the wrong address;
l your friends are playing a strange joke on
  you;
l a meteorite struck the door and then
  vaporized your valuables.
l   Your house begins to shake so violently that
    pictures fall off walls.

l   Your key will not open the door.
l   Which explanation is best?
l   Should contain only true claims
l   Shouldn’t be obscure
l   Should be simple
l   Should be powerfull
l   Should be conservative
Arguments from analogy
Object A has properties P, Q, R.
Objects B, C, D also have properties P, Q, R.
Objects B, C, D have property X.
_________________
Therefore, object A probably also has the
  property X.
l P, Q, R, X must be relevant and important
l   A – minivan Honda Odyssey
l   B – Honda Civic sedan
l   P – the same manufacturer
l   Q – similar engine
l   R – similar gearbox
l   X – is reliable
l   A – minivan Honda Odyssey
l   B – Ford
l   P – has a sun roof
l   Q – has four doors
l   R – is red
l   X – is reliable
Strong or weak?
l  The premises must be true
l The cited similarities must be relevant and important
l The presence of relevant dissimilarities?
l The weaker the conclusion, the stronger the argument:
- The Odyssey will run for ten years without any repairs.
- The Odyssey will probably run for ten years without any repairs.
- The Odyssey will probably run for at least five years without any
   repairs.
- The Odyssey will be very reliable.
- The Odyssey will be reliable.
l   This landscape by Cezanne is beautiful. He
    did another painting of a similar scene
    around the same time. So it is probably
    beautiful too.

l   My aunt had a Siamese cat that bit me, so
    this Siamese cat will probably bite me too.
The paradox of the raven
(confirmation)
(R) All ravens are black.
(R-) Nothing which is not black is a raven.

(R) and (R-) are logically equivalent, i.e. they
  are true or false together.

What would confirm (R)?
What would confirm (R-)?
l   Confirmation is not a simple matter of
    enumerative induction, that is the mere
    accumulation of confirming instances.
Hempel’s solution
l   It doesn’t have to be absurd.                 Carl Gustav Hempel
l   Let’s suppose that someone observed a             (1905-1997)
    white object. He thinks that it is a raven.
l   Further observation reveals that it is a
    shoe, not a raven.
l   So it supports (R) in a sense.
l   Conclusion: when you determine whether
    a given information confirms the given
    hypothesis you have to take context into
    account. The mere logical form does not
    settle the issue.
Enumerative induction
1st observed swan was white.
2nd observed swan was white.
3rd observed swan was white.
…..
__________________
All swans are white.
Russell’s chicken
l   1st day – The chicken is fed by the farmer.
l   2nd day – The chicken is fed by the farmer.
l   3rd day – The chicken is fed by the farmer.
l   …..
l   -------------------
l   The farmer comes and wrings its neck.
Grue (New riddle of induction)
l   All examined emeralds are green.

All examined emeralds are green.
_________________
All emeralds are green.

l   Grue: x is grue if it is green and examined (by now) or blue and
    unexamined (by now).

All examined emeralds are green.
_________________
All emeralds are grue.
l   Only well-entrenched predicates are
    projectible.
l   Green: x is green if it is grue if examined and
    bleen if not.

				
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