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Deductive Arguments
•
Intended to guarantee the truth of the conclusion
•
Ex. (1) All Decembers are cold
•
(2) it’s December
•
(C) it’s cold
Inductive Arguments
•
Intended to show that the conclusion is probable given the premises
•
Can insert ‘probably’ in the conclusion (do not regard it as part of the conclusion)
•
It is not deductively valid
•
Ex. (1) Most Decembers are cold
•
(2)
It’s December.
•
(C) (Probably) it’s cold.
Supply the Implicit Generalization
(1) Karen went out into the cold without a sweater
(C) Karen will get sick
(2) Everyone who goes out in the cold without a sweater gets sick – will give a valid
argument
(2) Most people who go out in the cold without a sweater get sick – will give an inductively
forceful argument
Probability
•
Express probability on a numerical scale between 0 and 1, expressed either as a decimal
or as a fraction
•
Proportions
o
Indicated by quantifiers
o
Ex. ‘most’ and ‘7/8 of’
•
Frequencies
o
How often something has occurred
•
Degree of Rational Expectation
o
How much one is entitled to believe given the evidence
Conditional Probability
•
The conditional probability of q given p is how probable q is assuming that p is true
•
Ex. The conditional probability that it’s sunny given that it’s June is how probable it is
that it’s sunny assuming that it actually is June
Inductive Forcefulness
(first pass)
•
An inductively forceful argument is one where the conclusion is probable given the
premises
•
An inductively forceful argument is one that is (1) not deductively valid but (2) where the
conditional probability of the conclusion given the premises is greater than .5 but less
than 1
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(1) Most bears are dangerous
(2) Smokey is a bear
(C) Probably, Smokey is dangerous
Points about Probability
•
Conditional probability is often stated implicitly (
we do not always express probabilities
as conditional probabilities
)
•
Probably comes in degrees (
different propositions may have various degrees of
probability
)
o
Inductive forcefulness comes in degrees
•
Propositions are still either true or false
o
Arguments are still either valid or invalid
•
“Probably” carries a
conversational implicature
of “very likely” –
it is also somewhat
vague
•
Degree of rational expectation is distinct from degree of actual expectation
•
Inductive forcefulness depends on the structure of the arguments
•
The degree of inductive force of an argument is independent of the truthvalues of the
premises
Generalizations again
•
“Some” is compatible with “all” for the purposes of this class
o
‘Some’, whereby ‘some A are B’ does not rule out that all A are B
o
‘Some A are B’ means ‘Some, perhaps all, A are B’
•
When using ‘some’ in our argumentreconstructions, we will take it to mean ‘at least one’
o
If only one A is B, then it will be true that some A are B
•
When supplying missing generalization, it is often more charitable to supply soft
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This note was uploaded on 04/05/2012 for the course PHI 2100 taught by Professor Mikepatterson during the Spring '12 term at FSU.
 Spring '12
 MikePatterson

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