Lecture Three: Problems of Induction

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Lecture ThreeProblems of Induction
Confirmation

• Dr
• Emma Tobin
• Philosophy
• Bristol

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Science vs Pseudo-ScienceDemarcation Criteria

• (1) Truth
• (2) Induction
• (3) Assign Probabilities
• (4) Explanatory Power
• (5) Testability
• (6) Falsifiability
• (7) Puzzle-Solving
• Traditionally, (1) was the chief demarcation
  criteria.

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The Aristotelian Method

• The tool Deductive logic
• Account of knowledge deduction from first
  principles.
• The truth of the conclusion is guaranteed by the
  truth of the premises in a valid argument
• All things seek their natural place
• The natural place of the element fire is at the
  top of the
• terrestrial sphere.
• ?Therefore, flames near the surface of the earth
  rise.
• No expansion of knowledge from the premises to
  the conclusion because knowledge of the
  conclusion is contained in the premises.

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Problems with the Deductive Arguments

• Science aims to generate novel predictions/theorie
  s.
• But, in deductive arguments, we never move beyond
  the premises from the conclusion.
• The role of sensory experience and
  experimentation is marginal.
• Difficult to test the major premise in a
  deductive argument. How do we test P1?
• (P1) All things seek their natural place
• (P2) The natural place of the element fire is at
  the top of the
• terrestrial sphere.
• ?Therefore, flames near the surface of the earth
  rise.

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Bacons Naïve Inductivism

• (1) Observation (2) Induction
• Observation must be undertaken free of prejudice
  (free from the 4 idols and background theory.)
• The data of observations must be collated in
  observation statements.
• A host of observation sentences collated together
  will result in the formulation (by induction) of
  scientific laws and theories.

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Examples of Induction

• Commonsense example
• I have observed that (in the past) the sun rose
  in the east and set in the west everyday .
• ?The sun will always rise in the east and set in
  the west.
• Scientific Example
• Galileos law of free fall (All bodies fall with
  a uniform acceleration).
• Legend has it that Galileo climbed to the top of
  the leaning tower of Pisa and dropped
  simultaneously heavy and light balls. He observed
  that they hit the ground at the same time.
• He induced that All bodies fall with a uniform
  acceleration from these observations.

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The Problem of Induction

• When can we legitimately infer a law/theory from
  a set of observation sentences?
• How many observation sentences is enough?
• How can we perform unprejudiced observations?
  Is observation theory-independent?
• Can we assume that the world is uniform?
• Is there a Principle of Induction that
  sanctions our inference from observation
  sentences to universal generalisations? (Humes
  problem)
• Does the inductive method produce knowledge?

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David Hume (1711-1776)
Humes A Treatise of Human Nature was published
in 1739. Re-cast later as the First Second
Enquiries Concerning Human Understanding.
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Humes Skeptical Problem of Induction

• All induction is based on the assumption that
  there is uniformity in nature.
• We believe that the sun will rise tomorrow,
  because it has done in the past and we assume
  that nature remains uniform.
• The inference from the constant conjunction of
  regularities to the positing of a power of
  necessary connection that underpins those
  regularities is often made.
• Humes sceptical problem for induction is how can
  we justify our assumption that nature will remain
  uniform?

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• We have sought in vain for an idea of power or
  necessary connection in all the sources from
  which we could suppose it to be derived. It
  appears that, in single instances of the
  operation of bodies, we never can, by our utmost
  scrutiny, discover any thing but one event
  following another without being able to
  comprehend any force or power by which the cause
  operates, or any connection between it and its
  supposed effect. (E Sec VII, Pt II 58)

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Humes Argument

• P1) All knowledge is either known by experience
  (matters of fact) or intuition (relations of
  ideas).
• P2) We do not intuit the Uniformity of Nature.
• P3) We do not experience the Uniformity of
  Nature.
• ?We do not know that there is uniformity in
  nature.
• Hume concludes that induction is not a rational
  procedure at
• all, but a psychological habit.

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P1 - All knowledge comes from matters of fact or
relations of ideas

• All the objects of human reason can naturally be
  divided into two kinds
• Relations of Ideas are analytic a priori truths
  (e.g. 224)Propositions of this kind are
  discoverable by the mere operation of thought,
  without dependence on anything existent in the
  universe. (E Sec IV20). It is impossible that
  these truths could have been otherwise.
• Matters of Fact are synthetic a posteriori
  truths (e.g. London is the capital of England.)
  These are contingent. (E Sec IV21)
• Any idea or fact that does not come about by
  either abstract reasoning concerning quantity or
  number or experimental reasoning concerning
  matters of fact is not knowledge. Humes Fork

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P2 - We do not intuit the uniformity of nature

• The uniformity of nature cannot come from
  intuition (e.g. like 2 2 4).
• It is not a matter of logical necessity that the
  future must resemble the past.
• We can conceive of a chaotic, radically
  contingent world.
• So the principle of induction is not logically
  necessary.

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P3 - We do not experience the uniformity of
nature

• An Inductive judgment is neither a direct report
  of our experience nor logically inferred from it.
  
• Objection we know many facts about experience
  that we do not directly see or infer from
  experience (e.g. that smoking causes cancer)
• How can we know such facts?

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Causation

• Hume claims that we all reasoning that goes
  beyond past and present experiences in based on
  cause and effect.
• We believe in cause and effect!
• We have an intuition that like causes always
  bring about like effects.
• We make causal inferences based upon past
  experience. (e.g. We believe that because
  descending objects have fallen towards the ground
  in the past that the ball that I am about to drop
  will fall to the ground now.)

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We do not get the idea of the necessity of cause
and effect from experience.

• Hume is sceptical
• When we look about us towards external objects,
  and consider the operation of causes, we are
  never able to, in a single instance, to discover
  any power or necessary connexion any quality,
  which binds the effect to the cause, and renders
  the one an infallible consequence of the other.
  We only find that the one does actually, in fact
  follow the other. (E Sec VII P1 50)

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We do no get the idea of necessity of cause and
effect by intuition.

• From the first appearance of an object, we never
  can conjecture what effect will result from it.
  But were the power or energy of any cause
  discoverable by the mind, we could foresee the
  effect, even without experience and might at
  first pronounce with certainty concerning it, by
  the mere dint of thought and reasoning.
• (E Sec VII, P 1 50)

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ConclusionCausation is not in the world.

• We have sought in vain for an idea of power or
  necessary connection in all the sources from
  which we could suppose it to be derived. It
  appears that, in single instances of the
  operation of bodies, we never can, by our utmost
  scrutiny, discover any thing but one event
  following another without being able to
  comprehend any force or power by which the cause
  operates, or any connection between it and its
  supposed effect. (E Sec VII, Pt II 58)

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Humean Analysis of Causation

• (1) Events of Type A precede events B in time.
• (2) Events of Type A are constantly conjoined in
  our experience with events of Type B.
• (3) Events of Type A are spatio-temporally
  contiguous with event of Type B.
• (4) Events of Type A lead to the expectation that
  events of Type B will occur.

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Instinct/Habit vs Reason

• It is always possible that a causal relation
  could be different in the future, independent of
  how many observtions of it that we have made in
  the past.
• But, in the past we have observed causal
  relations and believed that they will continue to
  hold and been right!
• Humes reply If we assume that the future will
  resemble the past, because the future has
  resembled the past, in the past, then we have no
  independent grounds for believing it.
• There is no rational foundation for our belief in
  causation it is merely a custom of habit.

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Some Influential Replies to the Problem of
Induction

• Induction is rational (Common-sense Response)
• Develop a method(s) for inductive proof.
  (Mill/Carnap/Reichenbach)
• Induction is justified by a principle of the
  uniformity of nature (Kant)
• There really are necessary causal relations that
  we can discover (laws/causal relations)
  (Armstrong).

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Induction is rational (Common-sense Response)

• Induction is rational in an everyday sense.
• All laypeople assume in common sense that
  induction is rational and use it accordingly.
• Hume puts too strict a requirement for
  rationality in his epistemology.
• The skeptical problem of induction should be
  ignored.
• It is the speculative problem of a philosopher.

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Method(s) for inductive proof.

• John-Stuart Mill (A System of Logic BK III)
  assumes that induction is justified.
• Mill argues that induction is the only tool that
  science has and it is the role of the philosopher
  to analyse inductions, to distinguish between
  inductive proof as opposed to
  pseudo-inductions.
• Induction is proof it is inferring something
  unobserved from something observed it
  requires therefore, an appropriate test of
  proof and to provide this test is the special
  purpose of inductive logic. (IIIII5198)

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Mills Methods

• Mill argues that all induction is not simple
  enumerative induction as Hume supposed.
• He proposes 4 methods for arriving at inductive
  proof.
• Agreement (Soap)
• Difference (Gunshot)
• Residues (weight)
• Concomitant Variation (Varying the Heat)

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Induction is justified by a theory of
probability.

• Scientific theories have a high probability (e.g.
  Carnap/Reichenbach)
• Inductive logicians define the probabilities of
  different theories according to the available
  total evidence. If the mathematical probability
  of a theory is high then it is scientific, if it
  is low or zero it is nonscientific.
• This replaces the strict science/pseudoscience
  demarcation with a relative scale for determining
  how scientific a theory is.

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Induction is justified by a principle of the
uniformity of nature

• Kant denies Humes fork i.e. that all knowledge
  comes from either relations of ideas or matters
  of fact.
• Kant argues that there are truths which are both
  synthetic and a priori. (e.g. Space/Time/Casuality
  ).
• The fact that they are a priori explains the
  uniformity in nature.
• Nature is uniform because it is structured by the
  way we see it in space/time etc.
• Space/Time are a priori preconditions of us
  having any experience at all.

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There really are necessary causal relations that
we can discover

• Modern necessitarians (e.g. Armstrong) argue
  that there are necessary causal relations in the
  world.
• These are the result of laws of nature which
  relate particulars.
• They deny the empiricist dogma of direct
  observation and provide a metaphysical account of
  causation and laws.

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Goodman Confirmation

• The problem of induction is not a problem of
  demonstration but a problem of defining the
  difference between valid and invalid predictions.
  
• The validity of deduction depends upon conformity
  to the valid rules of the deductive syllogism.
  (e.g the laws of logic).
• According to which inductive rules can we
  validate for inductive predictions?
• The problem of Induction is replaced by the
  problem of defining confirmation.

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The Ravan Paradox

• A is a raven and A is black confirms all
  ravens are black.
• Then
• A is non-black and is a non-raven, confirms
  All non-black things are non-ravens.
• Because they are logically equivalent to all
  ravens are black.
• Hence All ravens are black is confirmed by the
  observation of a white cloud! (a non-black,
  non-raven).

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The New Riddle of Induction

• Suppose the future is like the past! (i.e. Humes
  Problem of Induction has been solved.)
• Every emerald that I have come across in the past
  was green.
• All emeralds are green
• Suppose that there is a property of objects
  grue (green before 2006 and blue after 2006).
• Every emerald that I have come across in the past
  was green.
• ? All emeralds are grue
• My observations confirm All emeralds are grue
  just as
• much as they confirm All emeralds are green.

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The Naturalist Reply

• Only projectible predicates can support
  confirmations and yield predictions.
• Projectible predicates are those that have been
  entrenched by the history of their use in
  inductive practices.
• Entrenched predicates generally pick out real
  natural kinds of thing.
• Grue is an artificial predicate and does not
  refer to a natural kind. It has not been
  successfully used in past inductive practices, so
  it cannot be confirmed.

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The Case of Jade

• Every piece of Jade that I have come across in
  the past was green
• ? All Jade is green
• However, true jade can be either of two
  different minerals, jadeite or nephrite.
• It is a theoretical possibility that all the
  past positive instance of Jade were really
  instances of Jadeite.
• So Jadeite is green would be confirmed rather
  than Jade is Green.

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Observation

• Even if we solve Humes problem then Goodmans
  problem remains.
• The possibility of predicates like Jade and
  Grue means that some predicates are projectible
  and others are not.
• Which predicates are projectible?
• How do we know whether we can trust the words
  that we use to record our observations?
• Perhaps we cannot free ourselves from Bacons
  idols to allow unprejudiced observation after
  all.

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Popper

• Popper takes the problems of induction seriously
  and claims that induction should play no role in
  the logic of science whatsoever.
• He will propose an alternative method for
  science. (Falsificationism)