Philosophical Method

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Philosophical Method

• Logic A Calculus For Good Reason
• Clarification, Not Obfuscation
• Distinctions and Disambiguation
• Examples and Counterexamples
• Revealing Our Deepest Convictions
• Testing Our Principles and Definitions

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Logic Primary Philosophical Tool

• Logic Gives Us Rules For Reasoning
• Arguments And Their Parts
• Premises
• Sub and Main Conclusions
• Note Relation Between Premises and Conclusion Is
  What Matters
• Calculus For Generating New Beliefs On Basis Of
  Old Ones

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Types Of Argument Two Main Forms Of Inference

• Deductive Inference
• Validity If The Premises Are True, The
  Conclusion Must Be True
• Distinguishing Validity From Truth
• Arguments Valid Or Invalid Not True Or False
• Premises True Or False Not Valid Or Invalid
• Logicians Care More About Truth Preservation Than
  Truth
• Soundness Valid AND True Premises

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Non-Deductive Reasoning

• Inductive Inference
• Probability If The Premises Are True, The
  Conclusion is Probably True
• Inference To Next Case
• Universal Generalization
• Inference To Best Explanation
• Appealing To Best Hypothesis
• Fallacies

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Syllogisms

• Is a systematic arrangement of arguments
  containing
• Major premise All As are Bs
• Minor Premise C is an A
• Conclusion C is a B

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Categorical Syllogisms

• Contain words like all, every, each etc
• Major premise
• All students (As) are Intelligent (Bs)
• Minor Premise
• You (C ) are a student (A)
• Conclusion
• You (C ) are intelligent (B)
• Not all premises are true ! ?

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Disjunctive Syllogisms

• Contain mutually exclusive choices. Words such as
  either, or , neither, but etc
• Major Premise
• Either students will attend classes or work at
  home
• Minor Premise
• Students do not attend classes
• Conclusion
• Therefore they work at home!
• Now you KNOW not all premises are true ! ?

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Conditional Syllogisms

• This is based upon a notion of hypothetical or
  future events/actions. It uses words such as if,
  supposing etc
• The major premise has antecedent and subsequent
  statements.
• IF the antecedent occurs then the subsequent will
  follow and become the conclusion

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Conditional Syllogisms (cont..)

• Major Premise
• Students will pass the course if their work
  is good enough
• Minor Premise
• Your work is good enough
• Conclusion
• Therefore you will pass

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Categorical Syllogisms

• Always have two premises
• Consist entirely of categorical claims
• May be presented with unstated premise or
  conclusion
• May be stated formally or informally
• Are intended to be valid

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Categorical Syllogisms

• All P are T
• Some T are D
• Some P are D

Things to notice Two premises and a
conclusion Three terms, each used twice
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All T are ZNo Z are FNo F are T
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All T are ZNo Z are FNo F are T
F
T
Z
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All T are ZNo Z are FNo F are T
F
T
Z
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Some voters are alcoholics.No alcoholics are
happy people.So some voters are not happy people.
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Some voters are alcoholics.No alcoholics are
happy people.So some voters are not happy people.
V - voters
H - happy people
A - alcoholics
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Some voters are alcoholics.No alcoholics are
happy people.So some voters are not happy people.
V
H
A
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Some voters are alcoholics.No alcoholics are
happy people.So some voters are not happy people.
V
H
A
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Only members may shop here. But only some
of our members are professionals. So,
some of the people who shop here are
non-professionals
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Only members may shop here. But only some of
our members are professionals. So, some of the
people who shop here are non-professionals
First, put the claims into a standard form.
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Only members may shop here. But only some of
our members are professionals. So, some of the
people who shop here are non-professionals
First, put the claims into a standard
form. All people who may shop here are members.
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Only members may shop here. But only some of
our members are professionals. So, some of the
people who shop here are non-professionals
First, put the claims into a standard
form. All people who may shop here are
members. Some members are professionals.
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Only members may shop here. But only some of
our members are professionals. So, some of the
people who shop here are non-professionals
First, put the claims into a standard
form. All people who may shop here are
members. Some members are professionals. Some
people who may shop here are non- professionals.
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Only members may shop here. But only some of
our members are professionals. So, some of the
people who shop here are non-professionals
Second, determine the categories. All people
who may shop here are members. Some members are
professionals. Some people who may shop here
are non- professionals.
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Only members may shop here. But only some of
our members are professionals. So, some of the
people who shop here are non-professionals
Second, determine the categories. All people
who may shop here are members. Some members are
professionals. Some people who may shop here
are non- professionals.
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Only members may shop here. But only some of
our members are professionals. So, some of the
people who shop here are non-professionals
Second, determine the categories. All people
who may shop here are members. Some members are
professionals. Some people who may shop here
are non- professionals.
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Only members may shop here. But only some of
our members are professionals. So, some of the
people who shop here are non-professionals
Second, determine the categories. All people
who may shop here are members. Some members are
professionals. Some people who may shop here
are non- professionals.
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Only members may shop here. But only some of
our members are professionals. So, some of the
people who shop here are non-professionals
Second, determine the categories. All people
who may shop here are members. Some members are
professionals. Some people who may shop here
are non- professionals.
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Only members may shop here. But only some of
our members are professionals. So, some of the
people who shop here are non-professionals
It makes things easier to assign variables to
the categories. M - members S - people who may
shop here P - professionals non-P -
non-professionals
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Only members may shop here. But only some of
our members are professionals. So, some of the
people who shop here are non-professionals.
All S are M Some M are P Some S are non-P
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Only members may shop here. But only some of
our members are professionals. So, some of the
people who shop here are non-professionals.
All S are M Some M are P Some S are non-P But
there is still work to do before validity can be
determined. The problem is that there are four
categories. At least one claim must be rewritten
if this is to become a proper syllogism.
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Only members may shop here. But only some of
our members are professionals. So, some of the
people who shop here are non-professionals.
All S are M Some M are P Some S are
non-P Rewriting one of these claims requires use
of at least one of the forms of immediate
inference conversion, contraposition, or
obversion. In this case, either the second
premise or the conclusion must be rewritten.
Does it matter which one?
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Only members may shop here. But only some of
our members are professionals. So, some of the
people who shop here are non-professionals.
All S are M Some M are P Some S are
non-P Logically, it makes no difference which
claim is rewritten. But since the conclusion
states the issue of the argument in a way that
someone presumably wants to think about it, lets
leave the conclusion as close to the original
statement as possible.
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Only members may shop here. But only some of
our members are professionals. So, some of the
people who shop here are non-professionals.
All S are M Some M are P Some S are
non-P Only one of the immediate inference rules
will change the second premise in the way needed
to create a well-formed syllogism.
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Only members may shop here. But only some of
our members are professionals. So, some of the
people who shop here are non-professionals.
All S are M Some M are P --gt Some M are not
non-P Some S are non-P Obversion (valid for all
claim types) 1. Move horizontally across the
Square of Opposition. 2. Replace the predicate
term with its complement.