Induction and Deduction

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Induction and Deduction

• Prof. Anthony Chen
• Department of Physics
• University of the West Indies
• Mona

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Course material
At UWI website go to Academic Faculties Facul
ty of Pure and Applied Sciences
Courses
FD12A Materials Induction and Deduction
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Induction and Deduction Objectives After complet
ing this section you should be able to
a) explain the term induction, citing examples,
and describe the inductive perspective of
scientific progress b) outline some of the probl
ems that have been identified with the use of
inductive methods in science c) explain the term
deduction and, with the use of examples,
describe the use of deductive inference in
science
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Topics

• Induction
• Deduction
• Properties and limitations of Induction
• Properties and limitations of deduction
• Comparative summary
• History
• Application

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Indu arrives at a generalization by process of
induction

• Observes fruits falling from trees, everything
  that goes up comes down.
  
• He is induced to believe that any object in the
  air that is not fixed will fall.

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Indu applies generalization to particular
object
Coconut or almond ?
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Dedu starts with a generalization

• Dedu knows Newtons law of gravity which applies
  to all bodies in the universe. When applied to
  the earth, it predicts that the earth will
  attract any body suspended above it. Thus the
  body will fall.
• .

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Professor Stephen Hawking with Bob Bishop and Sir
Alec Broers, next to the original COSMOS
supercomputer.
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Dedu deduces from Newtons law of gravity that a
coconut not suspended by it stem will fall to the
ground, although he has never seen a fruit fall
from a tree.
Both Indu and Dedu used deduction applying a
generalization to a particular object
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Induction
In
Latin inductioleading or bringing into
Truth
Each door (gap - -) is an observation. To arrive
at the generalization( truth) one has to enter
many doors (take many observations)
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Deduction
deductio leading away, drawing out
Truth
deduction
Once you know the truth, you need to make one
observation (exit one door) to make a deduction.
The basis for arriving at the truth may be ind
uction or it may be self evident. In science it
is arrived at by a hypothetico-deductive approach
(next lecture). NB. Indu arrived at a truth by in
duction and then made a deduction about coconuts
falling.
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Everyday usage of induction Person A, B, C, F,
I, W and Z like Bob Marleys music.
Inference Everybody likes Bob Marleys music.
In fact person D, E, X and Y may not like Bob Ma
rleys music.
Everyday usage of deduction Person A believes tha
t every word written in the Bible is true or
correct. In the Bible it is written that the wo
rld was created in 7 days. Therefore the
statement that the world was created in 7 days is
true. This type of reasoning is properly ref
erred to as axiomatic-deductive since it is based
on an axiom, namely that every word written in
the Bible is literally true.
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Science (Latin scientia, from scire, to know),
Pure science -Systematized knowledge, based on o
bjectively verifiable sense experience
Applied science - the search for practical uses
of scientific knowledge Technology application
of science Scientific Process careful and unb
iased observations, making inferences and
generalizations formulating laws and theories
(induction), , testing generalizations making
predictions (deduction) and further testing of
predictions. Called the scientific -
hypothetico-deductive method, involves induction
and deduction and more (next lecture).
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Oxford Dictionary Induction is the inference o
f a general law from particular instances
Deduction is the inferring of particular
instances from a general law In other words In
duction is the process of reasoning from the
particular to the general as opposed to the
inverse process of deduction. The basis of
induction is the assumption that if something is
true in a number of observed instances, it is
also true in similar, but unobserved, instances.
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Text book Induction The type of reasoning that t
akes us from a list of observations to a
universal statement or law is called inductive
reasoning and the process is called induction.
An inductive statement or inference is a stateme
nt about the properties or behaviour of a group
of objects or situations that is formulated on
the basis of direct evidence from a sample of the
objects or situations.
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• Use of inductive reasoning in Science
• We attempt to find generalizations that will
• apply universally ? scientific laws or theories.
  
  
• Make our inferences objective rather than
  subjective.
  
• Rational rather than ideological.
• As the number of facts established by observation
  increases, as facts become more precise due to
  improvements in our observational skill and our
  equipment ? more and more laws and theories of
  greater scope .

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For generalization to be considered valid the
following conditions must be fulfilled
1. The number of observations leading to the
generalization must be large. 2. The observatio
ns must be repeated under a wide variety of
conditions 3. No observation should conflict wi
th the derived universal law.
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Example of inductive reasoning
Galileos experiment using an incline plane.
The speed of any ball rolling down the incline
increases
Galileo showed by experiments that the rate of
increase of speed in the same for all balls.
One consequence all objects fall at the same
rate (if air resistance is neglected)
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Limitations of Induction Induction does not neces
sarily lead to true conclusions
In
Truth
The further in you go, the harder it is to open
or to find a door, you never know when you reach
the truth Thus induction is not a logically val
id process.
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Limitation of induction (cont)
Consider condition 1 There is not way of finding
out how many observations will be a large enough
number. Consider condition 2 it is difficult to
determine what is a sufficiently wide variety of
circumstances and what is a significant variation
in the circumstances Consider condition 3 We ma
y always find one condition under which the law
does not hold The laws inferred by induction can
not be firmly established, confirmed or proven.
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Deduction Oxford Dictionary Deduction is the
inferring of particular instances from a general
law In practice Deduction is the form of rea
soning by which a specific conclusion is inferred
from one or more premises (Premises are previous
statements from which another is inferred) . In
valid deductive reasoning, the conclusion must be
true if all the premises are true. Thus,
Premises All human beings have one head (genera
lization) Bertha is a human being, (applied
to particular) Conclusion Bertha has one head.

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Text book A deduction (that is, a deductive con
clusion or inference) is a statement about the
properties or behaviour of a particular object or
situation that is derived, by simple rules of
logic from a statement covering the whole class
of objects or situation to which the one under
consideration belongs.
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Examples Premises 1. Everyone who falls from the
top of this building suffers a severe injury
2. Jim has fallen from the top of the buil
ding Conclusion 3. Jim suffered a severe injury
Conditions for logical argument If statements 1
and 2 are true, then statement 3 is bound to be
true. This is the key feature of a logical
ly valid deduction if the premises of a
logically valid deduction are true, then the
conclusion must be true. The law also makes it
possible to make predictions like If Jim fall
from the building he will suffer severe injury.
Similarly in science we can make predictions from
the laws. E.G., Dedu used Newtons law of gravity
to predict that if a coconut breaks from its
stem, it will fall to the ground.
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Example based on law discovered by Galileo
Premises All objects are attracted to the
ground at the same speeds A folder and a bit
of paper are objects Conclusion A folder and
a bit of paper will fall to the ground at the
same speeds and will therefore arrive at the same
time.
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Example from the text Premises 1) All water fro
m the tap boils at 100 ºC at sea level
2) The water in my pot contains tap water at sea
level Conclusion If the temperature reaches 10
0 ºC, the water in my pot will boil.
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Example of invalid argument 1. Some persons with
spots have measles 2. Eileen has spots 3. Eile
en has measles
All persons with spots
Those with measles
Eileen ?
The form of the argument must be valid for the
conclusion to be acceptable
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Example true but unacceptable conclusion based
on invalid premises Premises All pigs have wi
ngs Animals with wings cant fly Conclusion P
igs cant fly The conclusion is true but the pr
emise is false. Thus the premises have to be tr
ue and the form of the argument valid for the
conclusion to be acceptable
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Limitations of Deduction
Truth?
Partial truth?
deduction
Untruth?
The truth many not be true. Even if you
reasoning or deduction process is valid, your
conclusion may not be true.
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• Induction and Deduction
• Deductive techniques of formal logic are always
  leading from the general to the particular and
  never vice versa.
  
• Inductive approaches, are aimed in an opposite
  direction, from the particular to the general,
  and allow for generalization and augmentation of
  existing knowledge.

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Induction and Deduction (cont.)

• Induction plays a useful role in furthering
  scientific knowledge
  
• From particular observations we can proceed to
  general laws.
  
• Induction may suggest hypothesis to be tested and
  modifications of laws.
  
• Induction can be said to have the potential of
  increasing our level of scientific knowledge.
  
• However that induction also has the potential of
  decreasing our level of scientific knowledge in
  the case where incorrect inferences are made.
  

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• Deduction, on the other hand, by itself does
  increase or decrease our level of knowledge
  
• By itself, It does not give us anything new in
  the sense that it does not lead to new laws.
  (With the aid of experimentation it can lead to
  new laws)
• By itself, we do not learn any new truths, only
  the application of known truth to a particular
  case.

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Induction and Deduction (cont.)

• The laws we infer from induction are not
  absolute.
  
• subject to change based on new observations
• The laws or truth arrived at by induction are
  best viewed as idealization or models created by
  scientist to describe patterns in nature found by
  their observations. Models can be modified
• Induction is not a logically valid process,
  whereas deduction is.
  
• An inductive statement always involves an
  element of doubt, as it is possible to make a
  wrong inductive inference from correct
  information. (In valid deductive reasoning doubt
  arises only from questioning the premises.)

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Induction and Deduction (cont.)

• It has been said that deductive reasoning is
  safer than induction as, provided the initial
  general statement is true, the deduction from it
  is also true. However both types of reasoning
  are needed in science since laws from which
  deductions can be made can only come about by
  observation, induction and deduction.

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Induction and Deduction in the history of science

• Sergey Belozerov (www.matrixreasoning.com)

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1983 Italian postage stamp honoring Archimedes
(287-212 B.C.) Shows a hydraulic screw (pump) he
invented
Archimedes allied Mathematics with observations
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During Dark Ages, world system was based on
preconceived notions which had their foundation
in religion and philosophy. Not much
observation, but axiomatic-deductive and
scholastic-deductive reasoning employed.
Post mortem examination was regarded as sinful.
Shows a physician and a monk (left) rebuking a
surgeon who has removed some organs from a cadaver
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During Renaissance, inductive reasoning based on
observations stressed
Francis Bacon emphasized the importance of
experiments and laid great stress on their
systematic use to build up a body of empirical
knowledge from which general theories could be
established and tested (Alan g. R. Smith,
Science and Society, Thames and Hudson, London,
1972).
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Galileo, the man who put all these ideas into
practice at one time or another in the course of
his life, was the first modern scientist, the
first to apply recognizably modern scientific
methods to the study of nature. (Alan G. R.
Smith, ibidem.).
He invented the telescope and used it to refute
the preconceived notion that the heavenly
bodies (e.g. moon and Jupiter) were perfect
spheres.
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Combined mathematics with observations
Theory of Gravitation
Laws of motion
Sir Isaacs Newton
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Lavoisier, Antoine (1743-1794)
the father of modern Chemistry
Experimental work stressed
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Charles Darwin (1809 -1882) The Origin of Species
(1859)
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Natural Selection
Charles Darwin and Alfred Wallace first proposed
the concept of natural selection in 1858.
The young of any species intensely compete for
survival due e.g., to food shortage.
Those surviving to produce the next generation
embody favorable natural variations the process
of natural selectionand these variations are
passed on by heredity. Therefore, each generatio
n will improve adaptively over the preceding
generations, and this gradual and continuous
process is the source of the evolution of
species. The concept of natural selection has
led to the modern day theory of evolution.
The concept of natural selection was based on
many years of observations (inductive reasoning)
and deductive reasoning
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1. Darwins five year voyage as a naturalist on
the H.M.S. Beagle (1831-1836)
Observation of fossils, of finches on Galapagos
Islands
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Albert Einstein (1879-1955)
Theoretical Physicist - used deductive reasoning
Named by Times Magazine as Man of the 20th Centu
ry Modern marvels are based on his work in
relativity, photoelectric effect, light and
quantum theory
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Modern Physics

• In cases where induction cannot be directly
  applied because the object or concept is
  unobservable, such as some elementary particles,
  and only their effects or footprints can be
  observed, hypothesis have to be made and
  deductions from these hypothesis can be tested by
  observations.

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Abdus Salam was born in Jhang, a small town in
what is now Pakistan, in 1926. His father was an
official in the Department of Education in a poor
farming district. His family has a long tradition
of piety and learning.
Abdus Salam, Nobel Laureate in Theoretical
Physics, 1978
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Salam was a theoretical physicist, relied largely
on deductive reasoning. He worked on the
interactions between elementary particles,
smaller than electrons. We now know that the el
ementary building blocks of matter are quarks, as
they are called. But they have never been
isolated. We have to use deductive reasoning to
establish their existence. The accumulation of
many experimental results, which match
predictions based on quarks, convince us that
quarks are real.
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The scientific method is not static. The
scientific method has evolved over the years. It
involves an interplay between induction and
deduction. More on the scientific method the hy
pothetico-deductive approach in your next lecture.
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Application
Criticize the methodology (especially inductive
and deductive reasoning) used by Researches A, B
and C described below in investigating the
following A fossil of an apparently ancient bi
rd was discovered in the dense forest of the Blue
Mountains in April 2005. Researchers were
invited by the Institute of Jamaica to view the
fossil, and if necessary carryout further
investigations, and to comment on the finding.
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Methodology of Researcher A Because the fossil ap
peared to be so old, Researcher A came to the
conclusion that it was one of the first birds
created by God and is therefore 3566 years old,
which is how long ago the world was created by
God, according to scholars who have studied the
chronology of the Bible.
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Methodology of Researcher B According to Research
er B, the fossil looked like that of a
pre-historic bird which was discovered in Cuba in
1940. Researchers in Cuba estimated that the
pre-historic bird must have lived over 10,000
years ago. So researcher B came to the
conclusion that the fossil is over 10,000 years
old.
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Methodology of Researcher C Researcher C carries
out several investigations He tries to find othe
r fossils in the area. He send all fossils found
to 5 universities in North America for carbon
dating in order to determine the age of the
fossil. He consults his compendium on fossils, to
see which known fossil the ones found correspond
most closely to. Based on his investigations, Res
earcher C found several similar fossils in the
Blue Mountain area. All fossils were subjected
to carbon dating and found to be about 1000 years
old. The fossils found were similar in structure
to a fossil reported in his compendium which was
dated to be about 1000 years by several
researchers. Researcher C then comes to the
conclusion that the birds existed in Jamaica
about 1000 years ago.
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Researcher A made one observation, not
inductive. Research A used axiomatic-deductive me
thod twice. deductive reasoning 1 Any creature
that looks old was one of first created by God
This bird looks old Therefore this bird was one o
f first created by God
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• Deductive reasoning 2
• Anything written in the Bible is literally true
  
  
• From the chronologies written in the bible it can
  be deduced that God created the world 3566 years
  .
  
• Therefore the world was created 3566 years ago.
• There is no way of testing the premise, but the
  conclusion is contrary to current scientific
  evidence for the age of the universe.
  

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• Researcher B is in a sense not much different
  from Researcher A.
  
• He makes only one observation to come to his
  conclusion that the fossil is of the same type of
  as the birds found in Cuba not induction
  
• Deduction used
• Any fossil looking like the one found by he
  Cubans is 10,000 years old
  
• This fossil looks like that
• Therefore this fossil is 10,000 years old.

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Shortcoming

• He accepts the conclusion of the researchers in
  Cuba that birds of this type lived over 10,000
  years ago. Need to check the source
  
• Was the Cuban research sound
• Was it verified by others.

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Researcher C used the accepted inductive
procedure in coming to his conclusions
There should be as many observations as possible
(digging up other fossils, using several sources
of carbon dating) The research should be carried
out under as many different situations as
possible (again digging up other fossils, using
different sources of carbon dating, and using
other sources such as his compendium, which was
accepted by the scientific community)
No observation went contrary to his conclusion
the birds lived about 1000 years ago in Jamaica.