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PHIL 1F91 Lecture Notes - Swami Vivekananda, Stoicism, Modus Ponens

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Brian Lightbody

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PHIL 1F91 September 28th, 2012
Lecture Four: Inductive Arguments
- We now know that in order for a deductive argument to be valid, it must conform to a valid logical
- We also examined a number of fallacious forms of reasoning. Such inference patterns are
fallacious because they are invalid
- We will now examine how to assess inductive arguments
Inductive Arguments: Probability
- Inductive arguments are arguments that are not necessarily or absolutely true. They only have a
high degree of probability
1. Every swan that I have seen has been white
Therefore: all swans are white
- Even if we accept premise one to be true, the conclusion may still be false
Three Types of Inductive Arguments
TYPE ONE: Enumerative
- As the name implies, enumerative inductive arguments make a universal claim about something
(like a swan) based on an observation of that thing
What makes for a good enumerative inductive argument?
Three components:
1) A large sample size
2) An unbiased sample
3) A causal connection
Take the following (outdated) example: The next Prime Minister of Canada will be Michael
Ignatief. Our justification? The majority of people we polled the day before election day
said they would vote Liberal
Enumerative inductive arguments
Large sample size: Out of a poll of 3,000,000 people 75% claimed they would vote Liberal
Unbiased sample: These 3,000,000 people were selected at random
Causal connection: We only took into account those factors that had a direct causal
relation to our prediction
Fallacies and enumerative inductive arguments
1) Fallacy of the small sample size: predicting Ignatief will become the next Prime Minister
based on a poll of 20 people
2) Biased sample: polling only Liberal delegates
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PHIL 1F91 September 28th, 2012
3) Questionable cause: Claiming there is a causal connection between a person‟s favorite
color and the party the person will vote for
TYPE TWO: Analogical Inductive Arguments
- Analogical arguments compare something that is very well known to something that is less known
to draw a conclusion:
1) The human heart is like a motor pump
2) Every motor pump can be repaired when it fails
Therefore: the human heart can be repaired when it fails
Analogical Arguments continued
An analogical argument is considered strong when there are a number of similarities
between the two things being compared
What do you think? Is this analogy particularly strong?
We answer the question by examining the similarities and dissimilarities between the two
things being compared
Fallacy: Questionable Analogy
We criticize an analogical argument if we can show that there are more dissimilarities
between the two things being compared than similarities
1) A human being is like a dog
2) Every dog can be trained to be obedient
Therefore: a human being can be trained to be obedient
TYPE THREE: Inference to the best explanation or Abductive Arguments
- Inference to the best explanation usually combines two of the following rules:
1) Principle #1: Ockham‟s razor or the K.I.S.S : an explanation A is better than explanation B if
(all other things being equal) explanation A is simpler than explanation B
Ockham’s razor
Think about the Simpson‟s episode “Grandpa‟s Love Tonic”
The adults of Springfield have been mysteriously disappearing at dinner time for the past
week. Unknown to the children of Springfield, they have been “going to bed” early thanks
to Grandpa‟s Love Tonic
The more components you add on to an explanation, the more improbable the explanation
becomes. It is unlikely that the saucer people exist and unlikely that reverse vampires
exist. Let us give each of these possibilities 1/1000 probability. However, when we claim
that both of these things exist and are „working together‟ the probability jumps to 1/1000 x
1/1000 = 1/1,000,000 (Bayes‟ Restricted Conjunction Rule)
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