Inductive Arguments

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Inductive Arguments
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1. A useless argument is one in which the truth
of the premisses has no effect at all on the
truth of the conclusion. 2. A weak argument is
one in which the likelihood of the conclusions
being true is not much affected by the truth or
falsity of the premisses. 3. A moderate argument
is one in which the likelihood of the conclusion
being false if the premisses are true is quite
low. 4. A strong argument is one in which the
likelihood of the conclusion being false if the
premisses are true is very low. 5. A valid
argument is one in which it is just impossible
for the conclusion to be false if the premisses
are true.
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Bob is an Australian             Most
Australians are happy            
----------------------------------            
Bob is happy     The sun has risen every
morning for (at least) the past 500
years             --------------------------------
---------------------------------------------     
        The sun will rise tomorrow
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D1. An inductive argument is an argument that
claims that the likelihood of the conclusion is
increased by the truth of the premisses, but is
not made certain by their truth.   D2. An
argument is Inductively Strong if and only
whenever the premises are true the conclusion is
highly likely.   D3. An inductive argument is
Justified if and only whenever the premises are
true the conclusion is highly likely.   D4. An
argument is Cogent if and only it is justified
and the premisses are true.
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Deductively valid Inductively justified
All ravens observed in the past have been black --------------------------------------------------------- The raven observed yesterday was black All ravens observed in the past have been black --------------------------------------------------------- Any raven observed will be black
  In this argument we have a premise providing conclusive support for the conclusion         The argument is logically good since the reason is conclusive   In this argument we have a premise providing (merely) strong support for the conclusion   The reason is not conclusive, however it is nonetheless a strong reason and so the argument is good           
  No further premises can undercut the argument's strength           Validity is said to be monotonic   The addition of further premises can undercut the argument's strength.  Add              'The observed group is atypical'         and the previously strong argument becomes weak!           Inductive strength is non-monotonic
  Valid arguments merely spell out the consequences already implicit in the premises (they are non-ampliative) Inductive arguments draw conclusions which go beyond the information contained in the premises (they are ampliative)
 

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Misconceptions   a. Valid arguments are better
than inductively strong ones.   No. getting
true premises to ensure the conclusion may be
impossible.   All ravens are black All observed
ravens have been black ------------------------   
          ----------------------------------------
----- Any raven on Pikes             Any raven
on Pikes Peak will be black                  
Peak will be black                    Certainty
is a virtue if obtainable, but where it is not
obtainable a high degree of probability is better
than none at all!
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Misconceptions   b. Valid arguments go from the
general to the particular, whereas inductively
strong ones go from the particular to the
general.   No. true for               Valid
Argument                               
Inductively Strong Argument             with
general premise and                   with
particular premises and             particular
conclusion                           general
conclusion                 All ravens are
black                            Raven1 is
black             ------------------------        
                     Raven2 is black            
That raven is black                          
                                               
                        Ravenn is
black                                             
                                                  
  ------------------------ All ravens
are black
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But not for               Valid Argument       
                          Inductively Strong
Argument             with particular premise
and                  with general premise
and             particular conclusion             
               particular conclusion    
           
                 All ravens we have seen
have been John and Phil are
extremists black            
----------------------------------                
-----------------------------------------------   
          John is an extremist                    
          The next raven we will see will be
black
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The Argument from Analogy   The Argument from
Design for the Existence of God (aka The
Teleological Argument)   Consider a watch. A
watch exhibits (a) complexity of parts (b)
suitability to fulfil a certain function (i.e.
telling the time) and (c) its complexity is what
enables it to fulfil this function. These three
features are extremely unlikely to have come
about by accident. No one on seeing a watch would
think it the product of chance. Even seeing it
for the first time, one would conclude that it is
the product of design by some intelligent
being. But many things in nature we observe (e.g.
the eye) are similarly complex, fulfil a function
(e.g. seeing) and their complexity enables them
to fulfil this function. So it is reasonable to
suppose that they too are made by an intelligent
being.   important parts can be summarized
thus   A watch has (a), (b), (c). The world
has (a), (b), (c). Watches require a
watch-maker    ----------------------------------
------- The world requires a world-maker
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Definition of an argument from analogy   1. It
is claimed that the Object (an argument, or a
natural phenomenon, or an idea, or what you
will) has properties P1, P2, , Pn. 2. The
Analogue also has properties P1, P2, , Pn.
3. The analogue has property P.
------------------------------------------------
--------- 4. Therefore the object has property
P.   enthymematic valid argument?   5. If
two objects share properties P1, P2, , Pn, they
will also share property P.
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Example               Bob is a blue-eyed, blonde
male             So is Henry             Bob is a
criminal             -----------------------------
----------             So is Henry              
Alan, Bob, Carl, David, , and Xavier are
blue-eyed, blonde males             So is
Zach.             Alan, Bob, Carl, David, , and
Xavier are criminals          
                                   
--------------------------------------------------
----------------------             So is Zach
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Evaluating Arguments from Analogy   1. for the
argument to be cogent, premises must be true.  
2. The analogy itself must be strong.
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Are similarities P1, P2, , Pn cited relevant or
important in relation to P?   relevant
disanalogies?   The philosopher David Hume, in
his Dialogues Concerning Natural Religion (1779)
thought the analogy between the world and a
machine was rather weak. In support of this we
could point to relevant disanalogies like the
world's containing objects with features
apparently not well suited to fulfil their
functions (cf. Stephen Jay Gould's The Panda's
Thumb)   The strength of the conclusion?  
Hume pointed to the fact that, even supposing
the analogy were a strong one, it would only
strongly support the very limited, much weaker
conclusion that there are Gods (not necessarily
one as required by advocates of the argument),
that are very powerful (not necessarily
all-powerful, all-good, all-knowing).
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The Inference to Best Explanation   This is
sometimes called Abductive Inference   You
return home to find your door broken and some
valuable items missing. This cries out for
explanation. Possible explanations include 1. A
meteorite struck your door and vaporised your
valuables. 2. Friends are playing a joke on
you. 3. A police Tactical Response Group entered
your house mistakenly. 4. You were
robbed. Explanation 4 seems the best, so you
conclude -----------------------------------------
------------------------------------- You were
robbed.
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More generally, inferences to best explanation
take the following form              
Phenomenon C is observed             Explanation
A explains C and does so better than any rival
explanation             --------------------------
--------------------------------------------------
----------             A
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Evaluating Inferences to Best Explanation  
What do we mean by "best explanation"?  
Firstly, how do we evaluate them for strength?
(See Text, pp. 267-70.)
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i. They should actually explain the event in
question as opposed to merely shifting the
burden of explanation onto something else itself
needing explaining. ii. They should be powerful
(i.e. widely applicable). iii. The simpler the
better. iv. They should be conservative with
respect to prior beliefs.   (Compare creationism
and evolutionary theory as rival explanations of
the diversity of the biological world.)
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Secondly, we want to be as confident as possible
that we have to hand all the "rival explanations"
there might be ... or at least, all strong
rivals.
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Example 1.   A man, when alone, always rides
the lift to the 10th floor and then walks the
last two floors to his 12th floor flat. He never
does this when someone else is in the lift. WHY?
The best explanation can reasonably be said to be
probably true by inference to best explanation.
But what are the candidates?
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Example 2.   The buried ruins of a town
believed to be that of the builders of the
pyramids, was unearthed in Egypt in the late
twentieth century and archaeological research
including the newly available method of DNA
analysis established (i) the workers were
well-fed (bone fragments in floors suggested they
ate fish and high-quality beef) (ii) they lived
in family groups (with 50 male, 50 female and
 24 children) (iii) their bones showed clear
signs of having been subject to medical
treatment for breaks and fractures. Yet (iv) The
ancient Greek historian Herodotus had claimed
that the pyramid builders were slaves.   How
can we explain (i)-(iii) given (iv)?  
Archaeologists concluded that we cannot and so
rejected Herodotus's claim.   The best
explanation of (i)-(iii) is that the pyramid
builders were not slaves!
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Is the claimed phenomenon C real or illusory?
Example.   I think that Phil always acts
strangely in my presence. I take this to be a
puzzling phenomenon requiring explanation. In the
circumstances I reasonably suppose, say, that the
best explanation of this is the idea that Phil
dislikes me ... and so I go on to infer that Phil
doesn't like me.                        
            In fact, Phil does not always act
strangely in my presence. I have a partial and
defective recall of social situations we have
been in together.  
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Inductive Generalisation   An argument is an
inductive generalisation if and only if a
generalised conclusion about the character some
class as a whole is drawn from characteristics of
a sample of the class.   a. Strong Inductive
Generalisation   Consider the inductive
generalisation   A Canadian quarter did not
work in the American telephone on occasion 1.
A Canadian quarter did not work in the American
telephone on occasion 2.             A
Canadian quarter did not work in the American
telephone on occasion 20. Canadian quarters do
not (ever) work in American telephones.   This
generalization claims that all of the members of
the target class possess a certain property.
Arguments like this are called Strong Inductive
Generalisations.
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b.                  Weak Inductive Generalisation
  Other generalizations claim no more than that
some of the members of the target class possess a
certain property. Arguments like this are called
Weak Inductive Generalisations.   For
example             Many of the people I know
who didnt graduate from college have gone into
real estate. -------------------------------------
--------------------------------------------People
who dont graduate from college tend to go into
real estate  
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c.                   Statistical Generalisation
  Our final class of generalizations claims
that some specific proportion of the members of
the target class possess a certain property.
Arguments like this are called Statistical
Generalisations.   For example             10
of people in this sample of the general
population indicated they would eat Zowie
Bars. --------------------------------------------
-------------------------------------10 of the
general population would eat Zowie Bars.
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Evaluating Inductive Generalisation  
1.                  Are the premises true?    
2.                  Is the sample large enough?
  A small sample may be unrepresentative  
This leads to the Fallacy of Hasty
Generalisation   On the other hand, it is not
generally the case that the substantial results
of a survey will be affected by the size of the
sample. What will change is the margin of error.
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3.                  Is the sample biased in some
other way?   A sample may be unrepresentative
due to the method of sampling having been such as
to select for particular characteristics which go
unnoticed. This leads to the Fallacy of Biased
Sampling.          Insufficient variation in
the sample                     Ignoring or
emphasising characteristics of a sample due to
Prejudice and Stereotypes           Eliciting
a particular characteristic from the sample by
Slanted Questions
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4. Is the inference justified?   There are
three factors that need to be considered.  
            i.      The sample size  
            ii.      The level of confidence  
            iii.      The margin of error  
These three factors are interdependent changing
one affects both the others.