Suppressing valid inferences with conditionals

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Suppressing valid inferences with conditionals

• Ruth M.J. Byrne, MRC Applied Psychology Unit,
  Cambridge
• (1987, 1988, 1989)

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Four Conditional Inferences

• Modus Ponens (MP)
• Modus Tollens (MT)
• Denial of the Antecedent (DA)
• Affirmation of the Consequent (AC)

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Modus Ponens

• Premise 1 (conditional)
• If P then Q
• Premise 2 (categorical sentence)
• P
• Valid conclusion
• Q

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Modus Tollens

• Premise 1 (conditional)
• If P then Q
• Premise 2 (categorical sentence)
• Q
• Valid conclusion
• P

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Correct inferences

• MP is generally self-evident for validity and the
  conclusion is deduced easily.
• Some tricky cases (20 in pocket, warnings)
• MT is more difficult to infer, but generally
  judged to be valid.

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Denial of the Antecedent

• Premise 1 (conditional)
• If P then Q
• Premise 2 (categorical sentence)
• P
• Invalid conclusion
• Q

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Affirmation of the Consequent

• Premise 1 (conditional)
• If P then Q
• Premise 2 (categorical sentence)
• Q
• Invalid conclusion
• P

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Incorrect inferences (fallacies)

• DA and AC are the most common errors among test
  groups.
• If she has an essay to write then she will study
  late in the library.
• She does not have an essay to write, so
• She will not study in the library. Nothing
  follows.
• She will study late in the library, so
• She has an essay to write. Nothing follows.

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Formal theories

• Fallacies are difficult for formal (rule-based)
  theories to explain.
• They are usually attributed to comprehension
  processes by which the premises are decoded into
  incorrect representations used by the rules (e.g.
  obverse of conditional).

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Suppressing invalid inferences

• When accompanied by alternative antecedents,
  people systematically reject invalid DA and AC
  conclusions.
• (Markovits, 1985 Rumain et al., 1983)

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Example (suppressing invalid inferences)

• If she has an essay to write then she will study
  late in the library.
• If she has some textbooks to read then she will
  study late in the library.
• She does not have an essay to write, so
• Nothing follows what if she has some textbooks
  to read?
• She will study late in the library, so
• Nothing follows maybe she has an essay to
  write, maybe she has some textbooks to read, or
  maybe something else.

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What if

• The opposite is true, and we can suppress valid
  inferences.

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Example (suppressing valid inferences)

• If she has an essay to write then she will study
  late in the library.
• If the library stays open then she will study
  late in the library.
• She has an essay to write, so
• Nothing follows what if the library doesnt
  stay open? She will study late in the library.
• She will not study late in the library, so
• Nothing follows what if the library doesnt
  stay open? She doesnt have an essay to write.

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Suppressing valid inferences

• Hypothesis 1 when accompanied by additional
  antecedents, people will systematically reject
  valid MP and MT inferences.

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Experiment 1 setup

• 24 subjects, 3 groups (no logic tuition)
• 3 argument types
• Simple conditional, conditional alternative,
  conditional additional
• 4 inference types
• MP, MT, DA, AC
• Given 3 conclusions which one follows?

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Experiment 1 results
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Experiment 1 summary

• Additional antecedents suppressed MP and MT
  inferences, while, as proven before, alternative
  antecedents suppressed DA and AC inferences.
• Alternative or additional antecedents in the
  second conditional must alter the interpretation
  of the first conditional.

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But why?

• Perhaps the relevant formal rule no longer
  applies to the interpretation.
• More plausible suppression depends on the
  categorical information supplied in the premises.

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What if

• We supply more categorical information.

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Example (not suppressing valid inferences)

• If she meets her friend then she will go to a
  play.
• If she has enough money then she will go to a
  play.
• She meets her friend and she has enough money,
  so
• She will go to a play.
• She will not go to a play, so
• She doesnt meet her friend.

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Example (not suppressing invalid inferences)

• If she meets her friend then she will go to a
  play.
• If she meets her family then she will go to a
  play.
• She does not meet her friend and she does not
  meet her family, so
• She will not go to a play. Nothing follows
  what if some other reason compelled her to go?
• She will go to a play, so
• She meets her friend. Nothing follows what if
  some other reason compelled her to go?

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Not suppressing valid inferences

• Hypothesis 2 when accompanied by additional
  antecedents together with the conjunction of both
  antecedents, people will systematically affirm
  valid MP and MT inferences (and invalid DA and AC
  inferences), as in the simple argument.

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Experiment 2 setup

• 24 subjects, 3 groups (no logic tuition)
• 3 argument types
• Simple conditional, conditional alternative
  conjunction/consequent, conditional additional
  conjunction/consequent
• 4 inference types
• MP, MT, DA, AC
• Given 3 conclusions which one follows?

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Experiment 2 results
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Experiment 2 summary

• Combined additional antecedents didnt suppress
  MP or MT inferences, and combined alternative
  antecedents didnt suppress DA or AC inferences.
• Presumably, the conditionals were interpreted
  correctly, but nonetheless both fallacies and
  correct inferences were made in the presence of
  categorical information.

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What if

• Specific alternatives or additionals are
  suggested simply by general subject knowledge?

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Example (no duration)

• During the student protest, the policeman said to
  the student If you enter the building then I
  will arrest you.
• The student entered the building, so
• The policeman arrested the student.
• (Note this inference is not strictly valid as it
  is embedded within a description.)

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Example (short duration)

• During the 15-minute student protest, the
  policeman said to the student If you enter the
  building then I will arrest you.
• The student entered the building, so
• Nothing follows what if the protest was no
  longer in progress when the student entered the
  building? The policeman arrested the student.

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Example (long duration)

• During the 2-week student protest, the policeman
  said to the student If you enter the building
  then I will arrest you.
• The student did not enter the building, so
• Nothing follows what if other actions caused
  the student to be arrested?

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Suppressing valid inferences

• Hypothesis 3 when accompanied by assertions of
  short-duration, the plausibility of additional
  antecedents will be suggested, and people will
  systematically reject valid MP and MT inferences
  when accompanied by assertions of long-duration,
  the plausibility of alternative antecedents will
  be suggested, and people will reject invalid DA
  and AC inferences.

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Experiment 3 setup

• 24 subjects, 3 groups (no logic tuition)
• 3 argument types
• Simple conditional (no duration), conditional
  alternatives (long-duration), conditional
  additionals (short-duration)
• 4 inference types
• MP, MT, DA, AC
• Is the conclusion true? (Yes/No/Maybe/Cant Say)

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Experiment 3 results
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Experiment 3 summary

• Additional (short-duration) arguments suppressed
  MP and MT inferences, while alternative
  (long-duration) antecedents suppressed DA, but
  not AC, inferences.
• Perhaps the inconsistency is due to the
  considerable amount of contextual information
  already given in the descriptions.

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Labs vs. conversations

• In labs, it is common for subjects to assume they
  are being given all the information they need.
• In conversations, this is not always the case, so
  alternative options are often supposed.

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What does this tell us?

• Context can suppress both valid and invalid
  inferences.
• For formal theories, if suppression of an invalid
  inference implies no corresponding rule, then
  suppression of a valid inference should imply the
  same. Yet this is not the case.
• Suppression alone tells us nothing about the
  existence of the mental rules of inference
  proposed by formal theorists.

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Interpretation in formal theories

• Let us consider that the problem lies in
  interpretation.
• For alternative antecedents
• If P then Q (P ? Q)
• If R then Q (R ? Q)
• If P or R then Q (P v R ? Q)
• For additional antecedents
• If P then Q (P ? Q)
• If R then Q (R ? Q)
• If P and R then Q (P R ? Q)

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Semantics in formal theories

• P v R ? Q
• Blocks both DA and AC inferences
• P R ? Q
• Blocks both MP and MT inferences
• Semantic content plays a key role in developing
  an interpretation of these representations.
• Formal rules need additional information on
  comprehension, how premises with the same logical
  form are represented in different ways.

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Other explanations

• People rely on content-specific/domain-dependent
  rules instead of uninterpreted abstract rules.
• How do people reason in unfamiliar areas?
• People use a general semantic procedure. (i.e.
  mental models)

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Mental models

• Construct a model of a state of affairs.
• Attempt to formulate a conclusion.
• Search for alternative models that refute the
  conclusion.
• (Johnson-Laird, 1983)

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Simple example

• If P then Q
• P Q
• P Q
• o Q
• Wherever P exists, Q also exists, so given P, Q
  follows (MP). MT requires additional information
  to be added to the model.

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Extended example

• Adding a second conditional (if R then Q) depends
  on the meaning and general knowledge of how to
  integrate it in.
• For additionals
• P R Q
• P R Q
• o Q
• An assertion of P will no longer suffice to
  conclude Q.

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Extended example

• For alternatives
• P Q
• P Q
• R Q
• R Q
• o Q
• An assertion of P will now suffice to conclude Q,
  but the fallacies will be suppressed.

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The point

• Interpretation (and therefore context) plays a
  critical role in the interaction among statements
  of the same logical form.
• Theories based on mental models seem to better
  account for this process.

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The end

• Questions?