LANGUAGE, THINKING AND MEMORY

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LANGUAGE, THINKING AND MEMORY

• DEDUCTIVE REASONING

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LOGIC

• Originates in the attempt to specify valid forms
  of argument.
• A deductively valid form of argument is one in
  which the conclusion must be true if the premises
  are true.
• E.g.
• The pig is (directly) to the left of the cow
• The cow is (directly) to the left of the horse
• SO, the pig is to the left of the horse.

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NATURAL DEDUCTION SYSTEMS

• One way of doing logic is to set up systems of
  rules (natural deduction systems) that specify
  possible steps in logically valid arguments e.g.
  modus ponens, from
• if p then q and p, infer q
• (p and q can be any sentences, as long as p
  is the same each time and q is the same each time
  - hence forms of argument)
• The doctrine of mental logic claims that we have
  such rules in our minds and that we use them in
  reasoning.

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A PROBLEM FOR MENTAL LOGIC

• Of the many conclusions that people might draw
  (and which are logically valid), only some are
  drawn.
• Furthermore, the ones that are chosen are chosen
  in a way that is (partly) systematic.

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AND A SOLUTION

• (from Deduction by Johnson-Laird Byrne)
• People use three extra-logical principles when
  making deductions.
• A conclusion should not contain less (semantic)
  information than the premises it is drawn from.
• The conclusion should result in a simplification
  of the information in the premises.
• A conclusion should not repeat something that was
  explicitly stated in one of the premises.

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CONDITIONAL REASONING(A TYPE OF DEDUCTIVE
REASONING)

• Based around two rules of logic
• Modus ponens if p then q p therefore q
• Modus tollens if p then q not q therefore not
  p
• People find modus tollens harder than modus ponens

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TYPES OF CONDITIONAL

• Conditional reasoning can be about three types of
  states of affairs (introduced in the if clause
  of the conditional)
• really possible
• really impossible
• counterfactual
• Counterfactual situations ... were once real
  possibilities, but are so no longer because they
  did not occur (e.g.Gordon Brown led the Labour
  Party at the 1999 General Election)

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TYPES OF CONDITIONAL (cont.)

• Ordinary conditionals implicitly contrast the
  actual state of affairs with real possibilities
  (If the stock market continues to fall in
  2004)
• Counterfactuals contrast the actual and the
  counterfactual (If Gordon Brown had been
  leader)
• Uniform interpretation For any conditional, the
  antecedent (in the if clause) describes a state
  of affairs which is to be presupposed in
  interpreting the consequent (in the main clause).
  The consequent then has the same interpretation
  as it would if it were said unconditionally in
  the situation described by the antecedent. So,
  the conditional as a whole is true if the
  consequent must be true whenever the antecedent
  is.

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MENTAL MODELS THEORY

• Representation of If p then q
• p q
• .
• Each line represents a situation that is
  consistent with the statement if p then q
• First line is a state of affairs in which p is
  true and q is true (which is consistent with if
  p then q)
• Square brackets exhaustive representation of p
  (i.e. no other types of model in which p is true
  - q must be true in all of them).
• The second initial model (the dots) has no
  explicit content, but indicates that there may be
  other situations consistent with if p then q.

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MODUS PONENS IN MENTAL MODELS THEORY

• Modus ponens is easy, because the additional
  premise p means that there are no models in
  which p is not true.
• So, the explicit model (first line)
• p q
• is the only possible model, and q is true.

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MODUS TOLLENS IN MENTAL MODELS THEORY

• Modus tollens is harder, because it requires the
  fleshing out of the implicit model, which can
  represent situations of two kinds (both
  compatible with if p then q).
• not-p q
• not-p not-q
• not q rules out the (original) explicit model
  and the first implicit model, leaving only
• not-p not-q
• So, not p is true.

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FALLACIES

• Affirming the consequent
• if p then q q therefore p
• Denying the antecedent
• if p then q not p therefore not q
• P Q looking at the states of
• Not-P Q affairs compatible with
• Not-P not-Q if p then q shows why they
• are fallacies
• Both are valid on a biconditional reading of
  if...then (if p then q and if q then p)

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SUPPRESSION OF FALLACIES

• Markovits (1985)
• If there is a snow storm in the night then the
  school will be closed the next day.
• Fallacies would be to infer that if there wasnt
  a snowstorm the school would not be closed or
  that if the school were closed there had been a
  snow storm
• Fallacies reduced if they are in paragraph
  describing alternative reasons why a school might
  be closed (e.g. a teachers strike, or a plumbing
  fault).

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SUPPRESSION OF FALLACIES (cont.)

• Byrne (1989) suppression of modus ponens
• If she meets her friend she will go to the play.
• She meets her friend.
• Almost all subjects conclude that she will go to
  the play.
• Additional premise
• If she has enough money she will go to the play.
• Subjects no longer conclude, just from the fact
  that she meets her friend, that she will go to
  the play.

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QUANTIFIERS (Moxey and Sanford, 1987)

• Sentences of the form
• Quantifier of the A are B
• E.g. some of the A are B, most of the A are B
• Focus attention on one of two sets of things.
• The reference set those A's that are B's
• The complement set those A's that are not B's
• Many of the fans went to the match.
• They thought it would be an exciting game.
• They the fans who went to the match

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QUANTIFIERS (Moxey and Sanford, 1987)

• Many of the fans went to the match.
• They thought it would be an exciting game.
• They the fans who went to the match (the
  REFERENCE set)
• BUT
• Few of the fans went to the match.
• They thought it would be an exciting game
• sounds odd with reference set focus.

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COMPLEMENT SET FOCUS

• A more appropriate continuation would be
• Few of the fans went to the match.
• They thought it would be an boring game.
• They the fans that didnt go (COMPLEMENT
  set).
• Focus on complement set is related to the need to
  explain why a significant proportion of the
  larger set (the fans, in the examples above) do
  not have a certain property (going to the match).

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SYLLOGISMS

• Two premises, one conclusion, for example
• All A are B
• All B are C
• So, All A are C

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SYLLOGISMS THE FOUR MOODS

• Premises and conclusion must have one of four
  forms
• All A are B (A)
• Some A are B (I)
• No A are B (E)
• Some A are not B (0)
• From AffIrmo and NEgO

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SYLLOGISMS THE FOUR FIGURES

• Johnson-Laird's version
• A - B B - A A - B B - A
• B - C C - B C - B B - C

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THE MENTAL MODELS THEORY OF SYLLOGISTIC REASONING

• Mental model representations of statements in the
  four moods of the syllogism according to
  Johnson-Laird and Byrne (1991)
• All A are B Some A are B
• a b a b
• a b a b
• .... ....
• No A are B Some A are not B
• a a
• a a
• b a b
• b b
• .... ....

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THE MENTAL MODELS THEORY OF SYLLOGISTIC REASONING

• Interpretation of the representation
• Each line represents an individual whose
  existence is compatible with the premise
• a b is an individual who is both a and b
• As before, square brackets means that there are
  no other types of individual who are a (except
  those that are b)
• As before, again, the dots represent an
  implicit individual, meaning that there may be
  other kinds of individual that are compatible
  with the statement all A are B (e.g. those that
  are neither a nor b)

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FLESHING OUT THE MODEL OF ALL A ARE B

• a b a b a b
• -a b -a b
• -a -b

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VALID CONCLUSIONS

• A conclusion is valid if it is true in all models
  that are compatible with the premises
• Models of the individual premises may be combined
  in various ways
• Every syllogism has either one, two, or three
  logically distinct models

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A ONE-MODEL SYLLOGISM

• All A are B All B are C
• a b b c
• a b b c
• .... ....
• These two models can be combined to produce
• a b c
• a b c
• ....

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A THREE-MODEL SYLLOGISM

• Some B are A
• No B are C
• so, Some A are not C
• The models of the premises are
• Some B are A No B are C
• b a b
• b a b
• .... c
• c
• ....

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FIRST MODEL

• The simplest way of combining these premises, by
  identifying the b's in the two models, is
• a b
• a b
• c
• c
• ....
• This model suggests the conclusion that no A are
  C, or conversely no C are A.

This model suggests the conclusion that no A
are C, or conversely no C are A.
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SECOND MODEL

• a b
• a b
• a c
• c
• ....
• This model suggests the conclusions some A are
  C, some C are A, some A are not C, and some
  C are not A, though only the last two of these
  four are compatible with the first model.

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THIRD MODEL

• a b
• a b
• a c
• a c
• ....
• This model is compatible with some A are not C
  (the valid conclusion) but not with some C are
  not A

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REASONS FOR DIFFICULTY OF SYLLOGISMS ACCORDING TO
MENTAL MODELS THEORY

• Number of models - because models must be
  constructed and manipulated in limited capacity
  short-term working memory.
• Figure - the difficulty of syllogisms in
  Johnson-Laird's four figures increases as
  follows
• A - B B - A A - B B - A
• B - C C - B C - B B - C

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BELIEF BIAS IN SYLLOGISTIC REASONING

• All of the Frenchmen are wine drinkers.
• Some of the wine drinkers are gourmets.
• so, Some of the Frenchmen are gourmets.
• Empirically true (or plausible), but does not
  validly follow - compare
• All of the Frenchmen are wine drinkers.
• Some of the wine drinkers are Italians.
• so, Some of the Frenchmen are Italians.

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EVANS, BARSTON POLLARD, 1983

• Do we follow our beliefs?
• People assessed the validity of a single
  conclusion from syllogistic premises
• No addictive things are inexpensive.
• Some cigarettes are inexpensive.
• so, Some cigarettes are not addictive.
• Beliefs had a bigger effect when the given
  conclusion was invalid.

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NEWSTEAD, POLLARD, EVANS AND ALLEN, 1992

• People do not accept (invalid) believable
  conclusions more than neutral ones
• Rather, they fail to accept unbelievable invalid
  conclusions, where they might have accepted
  invalid neutral (or believable) conclusions

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EVANS, BARSTON POLLARD, 1983 - ACCOUNT OF
BELIEF BIAS

• Selective Scrutiny
• people examine a conclusion and, if it is
  believable, accept it without engaging in
  reasoning. Only if it is unbelievable will they
  attempt to scrutinize the logic.
• Misinterpreted Necessity
• subjects fail to understand what it meant by
  logical necessity. They attempt to reason but,
  when a conclusion is neither definitely true nor
  definitely false they base their response on the
  conclusions believability, rather that
  concluding that it does not follow from the
  premises.

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LOCUS OF BELIEF BIAS EFFECTS (OAKHILL ET AL, 1989)

• Three possible loci
• Interpretation of premises.
• Determining which models of the premises are
  considered (for multi-model problems).
• Acting as a final filter on conclusions.

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LOCUS OF BELIEF BIAS EFFECTS (OAKHILL ET AL, 1989)

• Three types of problem
• one-model problems (all of which have a valid
  conclusion)
• multiple-model problems with a valid conclusion
  (determinate)
• Multiple-model problems without a valid
  conclusion (indeterminate)
• One model problems suggested a locus in
  filtering.
• Indeterminate models suggested a locus in
  determining which models are considered
  (French/gourmets example).

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A DIFFERENT ACCOUNT OF BELIEF BIAS

• Cherubini et al. 1998
• First set up a model relating the end terms of
  the syllogism which is consistent with ones
  knowledge of the world.
• Then check to see if the premises are consistent
  with that model.
• If they are, accept the conclusion as valid