Lecture 7 Grue

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Lecture 7Grue
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The new riddle of induction

• Nelson Goodman, Fact, Fiction and Forecast, 1955
• Goodman tried to show that there is no formal
  theory of confirmation.
• Deductive logic is formal in the sense that we
  can recognize good deductive (valid) arguments by
  their form.
• There was a similar idea about inductive logic,
  i.e., that good inductive arguments could also be
  recognized by their form.
• For example, it is claimed that if (1) all
  observed Fs are G, then this is a reason to
  believe (2) that all Fs are Gs.
• Or at least, it is claimed that we have more
  reason to believe (2) after we know that (1) is
  true than before we know (1).
• Or at least, this is the form of a supposedly
  good inductive argument

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Two inductive arguments with the same form

• Take first the following argument
• All observed emeralds are green.
• All emeralds are green.
• This argument has the required form for an
  inductive argument.
• Now consider the predicate grue that is defined
  as follows
• x is grue df x is first observed before
  2005 and is green, or is first observed after
  2005 and is blue.
• The word sounds a bit strange, but consider this
  argument
• All observed emeralds are grue.
• All emeralds are grue.
• This argument also has the required form for
  inductive argument!
• But it definitely looks like a bad argument.

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Somethings wrong with the predicate grue

• The first idea how to dismiss grue is to say
  that it is an artificial predicate, which is
  defined with the help of two color terms and an
  arbitrary date.
• Goodman responded that the artificiality of the
  predicate depends on the language. In our
  language, grue does looks like an artificial
  construction. But he says that in other languages
  it may be the other way around.
• For example, imagine some people using a language
  in which grue is a primitive (non-defined)
  color predicate. Imagine also that they use
  another predicate, bleen, which we would define
  as follows
• x is bleen df x is first observed before 2005
  and is blue, or is first observed after 2005 and
  is green.

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The grue-bleen color language

• People using terms grue and bleen would
  regard our color categories green and blue as
  artificial (being a combination of two colors and
  having an arbitrary date in their definitions)
• x is green df x is first observed before 2005
  and is grue, or is first observed after 2005 and
  is bleen.
• x is blue df x is first observed before 2005 and
  is bleen, or is first observed after 2005 and is
  grue.
• The color terms in the two languages are
  inter-translatable, and there is also some kind
  of symmetry that makes it difficult to condemn
  grue and bleen on formal grounds.
• Good inductive arguments are not recognizable by
  their form.
• The argument from All observed Es are Gs to
  All Es are Gs represents both the argument with
  green and grue.

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Green is grue if observed before t but bleen
after t
First observed before t
First observed after t
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Goodmans solution

• Inductive arguments project a past regularity
  into the future, or project an observed
  regularity into an unobserved region.
• Which predicates are projectible. That is, which
  predicates should be projected? Green or
  grue? Why?
• All observed emeralds are green. And all observed
  emeralds are grue. Which generalization should we
  believe on the basis of these data that all
  emeralds are green or that they are all grue?
• Goodmans answer projectible predicates (those
  that should be projected) are simply those that
  have often been projected in the past. He calls
  them entrenched predicates.
• Green is entrenched, but grue is not.
  Therefore, the green generalization is
  supported by the data.

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Criticisms of Goodmans solution

• Goodmans consists of two claims
• Green is an entrenched predicate (in contrast
  to alternatives like grue).
• Entrenched predicates should be projected.
• Both claims have been disputed
• Some philosophers produced predicates that were
  at least as well entrenched as green but which
  gave incompatible projections about emeralds. The
  advantage of green disappeared.
• More importantly, why should a mere fact that a
  given predicate was more frequently projected be
  taken as a sign that it will also better predict
  the future than another less often projected
  predicate?

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Is simplicity the answer?

• This argument is again based on two premises
• The predicate green is simpler than grue.
• We should project simpler predicates.
• Therefore, we should project green, not grue.
• Problems with each premise
• The predicate green is simpler than grue in
  our language, but not in the grue-bleen language.
• Why should we project simpler predicates?
  Simplicity is practical, economical but why
  should we think that it is a sign of truth.
• The problem of choosing the right answer among
  different extrapolations from a set of
  observational data connects with the curve
  fitting problem.

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Grue and curve fitting