Categorical Syllogisms

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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 in standard form or
  informally in natural language
• 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 keep in mind Two premises and a
conclusion diagram only the premises Three
terms, each used twice if more, use immediate
inference In diagramming, draw in alphabetical
order A, E, I, O
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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
9
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 -- 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.
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Obversion (the ONLY immediate inference that
changes the claim type and the only one valid for
all claim types) 1. Move horizontally across the
Square of Opposition. 2. Replace the predicate
term with its complement.