Lecture 3: 15th September

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Lecture 3 15th September
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The Problem of Induction

• Do we know the sun will rise tomorrow?
• The sun rose on Monday
• The sun rose on Tuesday
• The sun will rise tomorrow
• But this argument relies on the uniformity of
  nature The future will resemble the past
• Why believe this?

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Why think nature is uniform?

• Nature was uniform till Sunday
• Nature was uniform till Monday
• Nature will be uniform till today
• But this argument assumes that the future will
  resemble the past it assumes that induction is
  justified.

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DNA A brief case study

• DNA consists of a backbone (sugar phosphate)
  and a sequence of bases.
• But how do these chemicals fit together
  physically?
• Watson and Crick constructed models out of plates
  and wire.

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• X-ray photographs of DNA showed that there must
  be between 2 and 4 polynucleotide chains.
• Watson and Cricks first attempt was a three
  chain model.
• Rosalind Franklin pointed out that there wasnt
  enough space for water molecules to hook onto the
  DNA in their model.

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• They next tried a two chain model.
• They found that bonds of adenine-thymine and of
  guanine-cytosine had the same diameter, meaning
  the spiral staircase would have a uniform
  diameter if only those pairs bonded.
• This explained Chargaffs discovery that every
  species had the same amounts of adenine and
  thymine, and the same amounts of guanine and
  cytosine.

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Models
Model
Real World
Representation
The model fits the real world / the model doesnt
fit the real world. Recall the correspondence
theory of truth.
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Types of model

• Physical models.
• Watson and Crick built scale models of DNA to
  see how the molecules fitted together.
• Diagrammatic models.
• Diagrams are often useful for modelling some
  part of the world. Maps.
• Theoretical models.
• Descriptions. Words and sentences provide models
  of the world.

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Does the model fit?

• Data All the information that my be directly
  relevant to whether the model in question does
  fit.
• Data must be obtained through a process of
  physical interaction with the world.
• The data can be reliably detected.

Real World
Observation
Data
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Predictions from models

• If the model is true, what will happen?
• The prediction need not be made first.

Model
Calculation
Prediction
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Components of a scientific episode
Real world
Model
Representation
Reasoning
Observation
Prediction
Data
Agree/ Disagree
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Three-chain model
DNA
Three-chain model
Representation Fails!
Reasoning
Observation
Negative evidence
Small water content
Large water content
Disagree
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Two-chain model
DNA
Two-chain model
Representation
Reasoning
Observation
Positive evidence
Predicted pattern of x-ray picture
X-ray picture
Agree
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Real world
Model
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Representation
Reasoning
Observation
Prediction
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Data
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Agree/ Disagree
Do the data and prediction agree?
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The data provide evidence that the model does
not fit the real world
No
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Was the prediction likely to agree with the data
even if the model does not fit the real world?
The data provide evidence that the model does fit
the real world
No
Yes
Inconclusive
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• If the prediction was likely to be true anyway,
  there is little support for the hypothesis.
• Why are you throwing cup cakes from your
  window?
• To keep the elephants away
• But there arent any elephants
• Works well, doesnt it!

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Crucial Experiments

• When there are two or more theories, each of
  which gives a different prediction regarding a
  particular observation.
• When the observation is made, all but one of the
  theories is eliminated.
• Denying the consequent
• If H then O
• Not O
• Thus Not H

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Mutations

• Causal hypothesis Exposure to a virus causes
  mutation
• Chance hypothesis Mutations arise by chance
• Experiment Allow 20 bacteria cultures to grow
  for while. Then inject them with the virus.
  Compare the number of bacteria.
• If all the cultures have the same number of
  mutations, the causal hypothesis is confirmed
• If the cultures have different number of
  mutations, the chance hypothesis is confirmed.
• The cultures had different numbers of mutations.

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Falsificationism

• Karl Popper (1902-1994)
• Falsificationism Science proceeds
• not by confirming theories, but by
• falsifying them.
• Popper argued that this solved the
• problem of induction.
• Demarcation criteria A theory
• is scientific if and only if it is
• falsifiable.
• Philosophical problems There is a green swan
• What if two theories remain, but one is far more
  plausible than the other?
• Now well look at practical problems for
  falsifying theories.

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When prediction and data disagree

• Falsification
• If H then O
• Not O
• Thus Not H
• But do we ever have a simple case of denying the
  consequent? No.
• The data may be mistaken
• The prediction may be mistaken
• An auxiliary assumption may be false.

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The data may be mistaken

• The standard model of particle physics was shown
  to be experimentally incorrect at least three
  times between 1973 and 1978. In each case,
  however, the experiments were later shown to be
  in error.
• - Alan Guth in The Inflationary Universe
  (1997) p.129.

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• Some auxilliary assumption may be false.
• We never have
• If H then O
• Not O
• Thus Not H
• But instead
• If (H A1 A2) then O
• Not O
• Thus Not (H A1 A2)
• Not H or Not A1 or Not A2
• The Duhem-Quine thesis No hypothesis can be
  tested in isolation..

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• A scientific theory is declared invalid only if
  an alternate candidate is available to take its
  place. No process yet disclosed by the historical
  study of scientific development at all resembles
  the methodological stereotype of falsification by
  direct comparison with nature. This remark does
  not mean that scientists do not reject scientific
  theories, or that experience and experiment are
  not essential to the process in which they do so.
  But it does meanthat the act of judgment that
  leads scientists to reject a previously accepted
  theory is always based upon more than a
  comparison of that theory with the world.
• - T. S. Kuhn in The Structure of Scientific
  Revolutions p. 77

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Model Development

• A) An old model is presented
• B) An experimental test of the old model yields
  negative evidence
• C) A new model is formulated that accounts for
  the negative evidence obtained in the old model
• This new model will then have further predictions
  that can be tested.

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Ad hoc theories

• Theories that are modified to fit the date after
  the fact.
• Dark energy is a hypothetical posit designed to
  explain the acceleration of the universe.
• Ad hoc modifications can make scientific theories
  unfalsifiable.

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Prediction vs Accomodation

• Hypothesis P was formulated earlier and predicts
  E
• Hypothesis was formulated after E was found and
  predicts E
• Which is better supported by E?
• Logically they appear to be equally well
  supported
• E
• H

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Why might P be better supported?

• A) P is simpler
• But are simpler theories more likely to be true?
• B) P is probably supported by other evidence
  why else would it have been formulated?
• But both these responses admit that E gives no
  better support to P than to A. It is other
  evidence that is doing the work.